Roger wants to compare values across categories using vertical rectangles. which of the following charts must roger use?
Line chart
Clustered column chart
Pie chart Stacked
column chart

Answer:

\(x = 5\)

Step-by-step explanation:

\(-5x+37=6(x-3)\)

\(-5x+37=6x-18\)

\(-5x+37-37=6x-18-37\)

\(-5x=6x-55\)

\(-5x-6x=6x-55-6x\)

\(-11x=-55\)

\(\frac{-11x}{-11} = \frac{-55}{-11}\)

\(x=5\)

The sample space for this experiment consists of 12 possible outcomes.

The sample space is a collection of all possible outcomes of an experiment.

There are three types of soups, two types of salads, and two types of sandwiches. Therefore, the sample space consists of 3x2x2 = 12 possible outcomes.

There could be a tomato soup, a spinach salad, and a turkey sandwich, which would be one possible outcome in the sample space. There could also be a minestrone soup, a Caesar salad, and a grilled cheese sandwich, which would be another possible outcome in the sample space.

Therefore, the sample space for this experiment consists of 12 possible outcomes, each of which is unique and representative of the customer's randomly chosen lunch.

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Answers:

[-5, -2]

(-2, 3]

(3, 6]

=====================================================

Explanation:

This piecewise function is made of 3 separate functions of...

f(x) = 5 when  \(-5 \le \text{x} \le -2\)

f(x) = 4 when \(-2 < \text{x} \le 3\)

f(x) = -3 when \(3 < \text{x} \le 6\)

--------

The interval \(-5 \le \text{x} \le -2\) turns into the interval notation [-5, -2]

Use square brackets to include each endpoint. Each endpoint is included because of the closed filled in points.

In contrast, the interval \(-2 < \text{x} \le 3\) has an open hole at -2 and so it turns into (-2, 3]

A similar situation happens with the interval \(3 < \text{x} \le 6\) to become (3, 6]

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer: A

Step-by-step explanation:

Plug in each domain for x one by one to get y/range = {-15, -7, -1, 9, 17}

Answer:

a-x

b-/

Step-by-step explanation:

64/4x4=64

625x25/25=625

Answer:

I believe the answer is the third option.

Step-by-step explanation:

hope this helps and is right :)

Answer:

The first one seems like the only logical option

Step-by-step explanation:

How you tell, is if the sentence in side the dashes can be removed and the sentence still makes sense, then the dashes are being use correctly, for example the first sentence could be read the same and make sense as

"The parking lot was not a fun place to be"

The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).

One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)

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The dimensions (in m) maximize its volume  is  mathematically given as

\(x=\frac{4\sqrt{3}}{3}\) m   for Lenght and Width

\(h=\frac{2\sqrt{3}}{3}\) m  for height

Generally, the equation for is  mathematically given as

The equation for the area is given as

\(A=x^2+4xh\\\\A=16=4xh\\\\ A=16-x^2\)

\(h=\frac{16-x^2}{4x^2}\)

Volume of box

\(V=x^2 *h\\\\V=x^2*(\frac{16-x^2}{4x^2})\\\\V=4x-x^3\)

Therefore, by differentiating V and making x the subject of the formula we have

\(V'=4-\frac{3x^2}{4}\)

Therefore, with V' =0

\(x^2=16/3\)

\(x^2=\sqrt{16/3}\\\\x=\frac{4}{\sqrt{3}}\\\\\)

\(x=\frac{4\sqrt{3}}{3}\)

Now we will sub the value of x to the h equation

\(\begin{aligned}&h=\frac{16-(\frac{4}{\sqrt{3}})^2}{4 (\frac{4}{\sqrt{3}})} \\\\&h=\frac{16-\frac{16}{3}}{\frac{16}{\sqrt{2}}} \\\\&h=\frac{2 \sqrt{3}}{3} \mathrm{~m}\end{aligned}\)

Now we differntite the derivate of V (V')

\(V''=\frac{-3x}{2}\\V''=\frac{3(\frac{4\sqrt{3}}{3})}{2} \\V''=-2\sqrt{3} < 0 \\\\\) at maximium

In conclusion, the dimensions (in m) maximize its volume.

\(x=\frac{4\sqrt{3}}{3}\)    for Lenght and Width

\(h=\frac{2\sqrt{3}}{3}\)   for height

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Mercury is used to measure high temperatures and alcohol has a lower freezing point that mercury.

The freezing point of any substance, describe the transition of liquid into solid.

The freezing point of water is \(0\) °C or \(32\) °F.

At zero-degree water molecules are moving very slowly, and formation of solid begins i.e. Ice.

When salt or sugar is combined that is mixed with water or ice and it is evenly distributed, the freezing point is lowered.

Lowering of freezing point allows the street ice to melt at lower temperatures, it prevent the accumulation of dangerous, slippery ice.

Alcohol is used to measure the lower temperatures.

Mercury boils at \(357\) degree Celsius where as alcohol boils at \(78\) degree Celsius.

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The 14th term of the geometric sequence 10, 20, 40, ... is 81920.

"A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term."

The geometric sequence formulas include the formulas for finding its nth term and the sum of its n terms. We will see the geometric sequence formulas related to a geometric sequence with its first term 'a' and common ratio 'r' (i.e., the geometric sequence is of form \(a, ar, ar^{2},ar^{3} ,.............\)). Here are the geometric sequence formulas.

\(a_{n}=ar^{n-1}\)

Given geometric sequence

10, 20, 40, .........

From the given sequence

\(a_{1} = 10\), \(a_{2} = 20\), \(a_{3} = 40\)

Using the formula \(a_{n}=ar^{n-1}\)

⇒ \(a_{4} = 10(2)^{3} =80\)

⇒ \(a_{5} = 10(2)^{4} =160\)

⇒ \(a_{6} = 10(2)^{5} =320\)

⇒ \(a_{7} = 10(2)^{6} =640\)

⇒ \(a_{8} = 10(2)^{7} =1280\)

⇒ \(a_{9} = 10(2)^{8} =2560\)

.

.

.

⇒ \(a_{14} = 10(2)^{13} =81920\)

Hence, the 14th term of the geometric sequence 10, 20, 40, ... is 81920.

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Answer: 68

Step-by-step explanation:

The ratio of the perimeter of the smaller shape to the larger shape is:

25:100 or 1:4

Since the shapes are similar, the ratio of the area is going to be the same as the perimeter.

1:4 = 17: 68

Volume represents the capacity of the barrel. It tells us the quantity of a substance that it can hold.

When trying to determine the amount of paint needed to completely cover the outside of a wooden barrel, we need to find the surface area of the barrel. Thus, the answer is

False

The types of concurrent constructions that are needed to find the centroid of a triangle include the following: B. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex.

In Mathematics and Geometry, the centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.

Generally speaking, the centroid of a triangle simply refers to the point where the three (3) medians of the triangle meet or intersect. This ultimately implies that, a centroid is a point of intersection of the lines from each vertex of a triangle to the midpoint of the opposite sides.

In this context, the types of concurrent constructions would be modeled by answer option B.

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Complete Question:

What types of concurrent constructions are needed to find the centroid of a triangle.

A. intersection of the lines drawn from each vertex of a triangle and perpendicular to its opposite side.

B. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex.

C. intersection of the lines drawn to bisect each vertex of the triangle.

D. intersection of the lines drawn perpendicular to each side of the triangle through its midpoint

The theory of punctuated equilibrium is based on the observation that A) Long periods of intense speciation alternate with long brief periods of stasis.What is the punctuated equilibrium?

The punctuated equilibrium is a theory in evolutionary biology that posits that species tend to remain stable for long periods of time. This theory, in particular, challenges the traditional view that evolutionary change occurs continuously and gradually over time. Instead, it suggests that species change very little over long periods of time punctuated by brief bursts of rapid change.Based on the observation that long periods of intense speciation alternate with long brief periods of stasis, the theory of punctuated equilibrium is a paradigm-shifting theory in the study of evolutionary biology. It has also helped paleontologists, who rely on fossil records, better understand how species evolve over time.

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Answer: \(2^{21}\)

Step-by-step explanation:

The particular solution to the differential equation with the initial condition y(7) = 0 is:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:

Step 1: Write the given differential equation in the form dy/dx = f(x, y).

  In this case, dy/dx = y² - 4.

Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:

  dy / (y² - 4) = dx.

Step 3: Integrate both sides of the equation:

  ∫ dy / (y² - 4) = ∫ dx.

Let's solve each integral separately:

For the left-hand side integral:

Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).

Using partial fractions, we can decompose the left-hand side integral:

1 / (y² - 4) = A / (y - 2) + B / (y + 2).

Multiply both sides by (y - 2)(y + 2):

1 = A(y + 2) + B(y - 2).

Expanding the equation:

1 = (A + B)y + 2A - 2B.

By equating the coefficients of the like terms on both sides:

A + B = 0, and

2A - 2B = 1.

Solving these equations simultaneously:

From the first equation, A = -B.

Substituting A = -B in the second equation:

2(-B) - 2B = 1,

-4B = 1,

B = -1/4.

Substituting the value of B in the first equation:

A + (-1/4) = 0,

A = 1/4.

Therefore, the decomposition of the left-hand side integral becomes:

1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).

Integrating both sides:

∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.

Integrating the right-hand side:

∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy

= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,

where C₁ is the constant of integration.

For the right-hand side integral:

∫ dx = x + C₂,

where C₂ is the constant of integration.

Combining the results:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.

Simplifying the equation:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).

Combining the constants of integration:

C = C₂ - C₁, where C is a new constant.

Finally, we have the solution to the differential equation that satisfies the initial condition:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.

To find the value of the constant C, we use the initial condition y(7) = 0:

(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.

Simplifying the equation:

(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,

(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,

0 = 7 + C,

C = -7.

Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

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Answer:

Distance (d) =13.6

Step-by-step explanation:

\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\\(5,-4)=(x_1,y_1)\\(-3,7)=(x_2,y_2)\\\\d=\sqrt{\left(-3-5\right)^2+\left(7-\left(-4\right)\right)^2}\\\\d=\sqrt{(-3-5)^2+(7+4)^2}\\\\d=\sqrt{(-8)^2+(11)^2}\\\\d=\sqrt{64+121}\\\\d=\sqrt{185} \\\\d = 13.60147\dots \\\\\\d =13.6\)

2. 8.472 * 10^5 in standard form is

3. The scientific notation of 0.000067 is 6.7 * 10^-5

4. The division gives 4.455 * 10^3

Scientific notation is a way of expressing very large or very small numbers in a compact and convenient way.

In scientific notation, a number is written as a coefficient multiplied by a power of 10.

The coefficient is a number between 1 and 10 (or between -1 and -10 for negative numbers), and the power of 10 indicates the size of the number.

Calculator can be used to get numbers to scientific notation and in standard form

The required division can be performed using calculator to get 4.455 * 10^3

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First you have to figure out the side length of the triangle.

sin(60)= X/8

Let's call x the side length.

8 sin(60)=X

X=6.93

The multiply it by 4

The area is 27.72

The null hypothesis (H0) is that the mean lifetime of the batteries is 250 hours or greater, and the alternative hypothesis (Ha) is that the mean lifetime is less than 250 hours. To test the claim, we calculate the t-statistic using the provided data and compare it to the critical value at the 5 percent level of significance.

(a) The null and alternative hypotheses that should be tested are:

Null hypothesis (H0): The mean lifetime of the batteries produced by the manufacturer is 250 hours or greater.

Alternative hypothesis (Ha): The mean lifetime of the batteries produced by the manufacturer is less than 250 hours.

(b) To determine the t-stat for this hypothesis test, we need to calculate the sample mean, sample standard deviation, and the standard error. The sample mean is the average of the given data, the sample standard deviation measures the variability within the sample, and the standard error represents the standard deviation of the sample mean. Using the provided data, we calculate these values and then use them to calculate the t-statistic using the formula:

t = (sample mean - hypothesized mean) / (standard error / sqrt(sample size)).

(c) To determine if the claim is disproved at the 5 percent level of significance, we compare the obtained t-statistic to the critical value from the t-distribution table. The critical value is based on the desired level of significance (in this case, 5 percent) and the degrees of freedom (n - 1, where n is the sample size).

If the obtained t-statistic is less than the critical value, we reject the null hypothesis and conclude that there is evidence to suggest that the mean lifetime of the batteries produced by the manufacturer is less than 250 hours. If the obtained t-statistic is greater than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean lifetime is less than 250 hours.

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Answer: 28:9

Step-by-step explanation:

56:18

56÷2=28

18÷2=9

=28:9

The simplest term of the ratio 56:18 is 28:9.

Ratio is basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, there ratio will be a:b,

The given term is 56:18,

To convert this term in the simplest term,

Divide numerator by 2,

Term converts as 28:18,

Further divide denominator by 2,

Term converts as 28:9.

The simplest form of term is 28:9.

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Answer:

3(6 - 4) + 7²

3 x 2 + 7²

3 x 2 + 49

6 + 49

= 55

f(-3) = -1

We can find an unknown y-value by plugging an x-value into a given function.

Function Notation

Before we answer this question, we need to understand the notation of the equation. In function notation, the equation is given in terms of f(x).

For example, f(-3) represents the value of y when x = -3.

Finding f(3)

As stated above, to find f(-3) we need to plug -3 in for x. *Remember to use PEMDAS when solving.* This creates the new equation:

Then, distribute the exponent.

Next, multiply.

Distribute the negative.

Finally, add the remaining terms.

This means that when x = -3, y or f(-3) = -1.

please provide more informstion and the question that needs to be solved.

Marshall is wondering whether he can participate in the LLP again next year. The statement that is true is "He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

The Lifelong Learning Plan is a program that helps Canadian residents finance their post-secondary education through their registered retirement savings plans (RRSP). If an individual is attending school full-time, they can withdraw up to $10,000 a year from their RRSP under the program, or up to $20,000 in total. There are certain rules that must be followed by an individual participating in the LLP. For example, withdrawals must be made within four years of enrolling in an eligible educational program, and repayments must begin within the same period.

Here are the statements: Provided he repays his LLP balance in full by the end of this year, Marshall can participate in the LLP again next year.Marshall can only participate in the LLP once over his lifetime. However, his wife can make a LLP withdrawal from her RRSP on his behalf. He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000. He can only participate in the LLP a second time if he repays his LLP balance in full and waits 5 years before he returns to school.The correct statement is: He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

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Answer: 5 cm

Step-by-step explanation:

since the last step in finding area of a triangle is divide by 2, multiply the area by 2 to get the original number

30 x 2 = 60

area/base = height

60/12 = 5

The null hypothesis refers to the population, whereas the research hypothesis refers to the sample.

We have,

In statistics, the null hypothesis is a statement that assumes there is no significant difference between two groups or variables being compared.

It represents the default position that there is no relationship or effect between the variables of interest.

The null hypothesis is typically formulated as a statement about the population parameter.

On the other hand, the research hypothesis (also known as the alternative hypothesis) is a statement that proposes a significant difference or relationship between the variables being studied.

The research hypothesis is typically formulated as a statement about the sample, which is a subset of the population.

Thus,

The null hypothesis refers to the population, whereas the research hypothesis refers to the sample.

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