1. Paula has x cups of food in a container to feed her dogs. She pours 1.5 cups of food into their bowls. There is now 5.25 cups left in the container. Which equation would be used to solve this problem?

a. 1.5 - x = 5.25
b. 5.25 - x = 1.25
c. x - 1.5= 5.25
d. x + 1.5= 5.25


2. A box of donuts cost $9. You want to send donuts to the local nursing home. Set up an equation to find how many boxes you can send if you have $72.

a. 72 = 9 + b
b. 72 = 9 - b
c. 72 = 9b
d. 72 = 9/b


3. Jordan is purchasing a board to build a bookcase. He wants to divide the board into 1.75 foot sections and he needs 6 sections. Which equation can be used to solve this problem?

a. b/1.75 = 6
b. 1.75b = 6
c. b - 1.75 = 6
d. b + 1.75 = 6

The velocity of the wind if the speed of the plane in still air is 550 miles per hour is of:

50 miles per hour.

To obtain the velocity of the wind, we need to consider the relation between velocity, distance and time, which states that velocity is distance divided by time, as follows:

v = d/t.

In which:

On the flight from Boston to London, the wind was helping the plane, hence the equation is given as follows:

v + vw = d/t

In which vw is the velocity of the wind.

We have that the parameters are given as follows:

v = 550, t = 5.

Hence:

550 + vw = d/5.

d = 5(550 + vw).

For the return flight, the wind was in the opposite direction of the plane, and the flight took 6 hours, hence:

550 - vw = d/6

Hence:

d = 6(550 - vw)

Hence the velocity of the wind can be calculated as follows:

5(550 + vw) = 6(550 - vw)

11vw = 550

vw = 550/11

vw = 50 miles per hour.

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No, 7 3x is not a factor of 3x² 7x.

Factor is an element that is used in mathematics and economics to describe the relationship between two or more variables. It is a numerical value that is multiplied by a given number to produce a product. Factors can also refer to the elements of a decision-making process, such as risk, cost, and potential reward. Factors are used to determine the potential outcome of a situation and to make decisions based on those outcomes.

A factor is a number that can be divided into another number without leaving a remainder. To test if 7 3x is a factor of 3x² 7x, it must be possible to divide 3x² 7x by 7 3x without leaving a remainder. However, this is not possible, as 3x² 7x is not divisible by 7 3x. Therefore, 7 3x is not a factor of 3x² 7x.

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In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

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By using the SSS triangle property we will find the angle of the triangle.

SSS means-Side Side Side

"SSS" is when we know three sides of the triangle, and want to find the missing angles.

To solve an SSS triangle we use the following steps:

First to calculate one of the angles we use the Law of Cosines

Apply the same process the Law of Cosines again to find another angle.

finally, use the angles of a triangle to add to 180° to find the last angle.

We use the "angle" of the Law of Cosines:

[tex]cos(C)=\frac{a^2+b^2-c^2}{2ab}[/tex]

[tex]cos(A)=\frac{b^2+c^2-a^2}{2ab}[/tex]

[tex]cos(B)=\frac{a^2+c^2-b^2}{2ab}[/tex]

By using these formulas the angles of a triangle are measured.

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The simplified form of the expression 10x⁻⁵/-5x¹⁰ is -2/x¹⁵. So Anja wrote the numerator as 15 instead of -2.

Exponentiation is the method of writing large numbers as the number in terms of power.

Exponent indicates how much time a number is multiplied to itself.

aᵇ read as a raise to b, implies that a is multiplies to itself b times.

We have to simplify the expression  10x⁻⁵/-5x¹⁰.

[tex]\frac{10x^-5}{-5x^1^0}[/tex] =  10 × [tex]\frac{1}{-5}[/tex] × x⁻⁵ × x⁻¹⁰

        = -2 x⁻¹⁵

        = [tex]\frac{-2}{x^1^5}[/tex]

Hence Anja simplified the expression as  [tex]\frac{15}{x^1^5}[/tex] which is not true. The correct simplified form is  [tex]\frac{-2}{x^1^5}[/tex].

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Answer:

its B

Step-by-step explanation:

i did the test

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

The total number of games is given as follows:

5 + 11 + 6 + 6 = 28.

He scored 2 touchdowns in 6 games, hence the probability is of:

p = 6/28 = 3/14.

He scored more than 1 touchdown in 6 + 6 = 12 games, hence the probability is of:

p = 12/28 = 6/14 = 3/7.

The estimated value is the mean, which is the sum of all observations divided by the number of values, hence:

Mean = (0 x 5 + 1 x 11 + 2 x 6 + 3 x 6)/28 = 1.46 touchdowns.

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The Slope of the line passing through the points (0,3) and (5,8) is 1 .

The Line is passing through the points (0,3) and (5,8) .

we know that the formula to calculate the slope of the line passing through the points(x1,y1) and (x2,y2) is denoted by  ;

Slope(m) =   ;

It is given that points through which line is passing is (0,3) and (5,8) .

substituting the values in the above formula ,

we get ;

Slope(m) = (8 - 3)/(5 - 0)

On simplifying further ,

we get ;

slope(m) = 5/5 = 1 .

Therefore , the slope of line is = "1" .

The given question is incomplete , the complete question is

What is the slope of the line passing through the points (0,3) and (5,8) ?

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The square root of 2 is "irrational" (cannot be represented as a fraction) because, if it could, we would have the nonsensical circumstance .

A square root is a factor of a number in mathematics that, when multiplied by itself, equals the original value. The square roots of 9, for instance, are 3 and -3. The Babylonians developed efficient approaches to approximate square roots as early as the second millennium BC.

here,

The square root of 2 is "irrational" (cannot be represented as a fraction) because, if it could, we would have the nonsensical circumstance that the fraction would have even integers at both the top and bottom and could thus always be simplified.

As a result, the square root cannot be expressed as a fraction.

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A removable discontinuity exists when a function is not defined at a certain point. An infinity discontinuity occurs when the function approaches infinity. A jump discontinuity occurs when the function has a finite jump in value at a certain point. An essential discontinuity exists when the limit of the function exists but the function is not defined at the point. A mixed discontinuity is a combination of the other discontinuities.

A removable discontinuity occurs when a function is not defined at a certain point. This means that the limit of the function as it approaches the point does not exist. However, if the function can be modified by adding or subtracting a constant to make the limit exist, then the discontinuity is removable. An example of this would be f(x) = 1/x, which is undefined at x = 0, but if we subtract 1 from both sides, the limit of f(x) as x approaches 0 is 0. An infinity discontinuity occurs when the function approaches infinity as it approaches a certain point. This means that the limit of the function as it approaches the point does not exist. An example of this would be f(x) = 1/x as x approaches 0, where the limit of f(x) is infinity. A jump discontinuity occurs when the function has a finite jump in value at a certain point. This means that the limit of the function from both sides of the point do exist, but they are not equal. An example of this would be f(x) = x + 1 for x >= 0 and f(x) = x for x < 0, where the function jumps from 0 to 1 at x = 0.An essential discontinuity exists when the limit of the function exists but the function is not defined at the point. An example of this would be f(x) = 1/x for x != 0, where the limit of f(x) as x approaches 0 is 0, but the function is not defined at x = 0. A mixed discontinuity is a combination of the other discontinuities. It occurs when the limit of the function as it approaches a certain point exists, but the value of the function at the point is undefined. An example of this would be f(x) = x^2 - 1 for x != 1, where the limit of f(x) as x approaches 1 is 0, but the function is undefined at x = 1.

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The symmetries of the graphs are mentioned below -

Given are the graphs as shown in the image.

For each graph we can discuss the symmetry below -

Graph {A} -

Graph {B} -

Graph {C} -

Therefore, the symmetries of the graphs are mentioned below -

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SSS (Side-Side-Side) , SAS (Side-Angle-Side) , ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) are the four postulates that defines the Congruency of a triangle.

What is Congruence of triangles ?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.

In Mathematics , Four postulates are defined in order to judge the congruency of a triangle , they are as followed :

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If the two shapes are congruent, then the two shapes has same scale factor.

Here we have to prove that the two shapes are congruent.

Here we know that the two shapes are given, if those two shapes are congruent then it must satisfies the following conditions,

Either all three pairs of corresponding sides are equal or if two pairs of corresponding sides and the corresponding angles between them are equal or at least if two pairs of corresponding angles and the corresponding sides between them are equal.

If any one of the given condition is satisfied, then those two shapes are said to be in the form of congruent to each other.

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-2.25 + 0.4 = -2.8

-1.85 = -2.8

-185/100 = -28/10

-37/20 = -14/5

The given expression is a complex expression and we can prove the given expression equal to 1 by using definition.

a+ib, often known as the generic form of complex numbers, is how complex numbers are expressed. In the complex numbers a+ib form, a represents the real component of the number, b represents the imaginary part, and i is defined as√(-1).  Complex numbers can take a variety of shapes.

z=a+bi is the general form of complex number

As by definition

i^2=-1

So

i^4=(i^2)^2

    =(-1)^2

    =1

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To create a 4 quadrant chart in Microsoft Word, follow the 13 steps given below.

1. Open a new Word document and click on the Insert tab.

2. Select Chart from the Illustrations group.

3. Choose the type of chart you want to create from the drop-down menu.

4. Click on the Design tab and select the Chart Layout option.

5. Select the Four Quadrant Chart option under the Layout section.

6. Enter the data for each quadrant into the chart.

7. Click on the Format tab and select the Chart Elements option.

8. Select the axes you want to use for the four quadrants from the drop-down menu.

9. Enter the labels for the four quadrants in the Axis Labels section.

10. Select the desired formatting options for the chart.

11. Click the Insert button to insert the chart into the document.

12. Adjust the position and size of the chart as desired.

13. Click the Save button to save the document.

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Answer: Monomial, binomial,trimonial,  polynomials

Step-by-step explanation:

The confidence interval of p±E is 0.555±0.444

Definition of confidence interval-A Confidence Interval is a region constructed using sampled data, of fixed size, from a population (sample space) following a certain probability distribution. The interval is constructed to contain a chosen population statistic with prescribed probability.

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals than contain either 95% or 99% of expected observations. Thus, if a point estimate is generated from a statistical model of 10.00 with a 95% confidence interval of 9.50 - 10.50, it can be inferred that there is a 95% probability that the true value falls within that range.

Given:-0.111<p<0.999=Confidence interval. we have to express it in the form p±E.

Explanation:-The midpoint of the interval is p.

p=[tex]\frac{0.111+0.999}{2}[/tex]=0.555

Next the error term E is the distance from p to the end of the interval.

E=0.999-0.555=0.444

So, finally we get the answer as p±E=0.555±0.444

The final answer is p±E=0.555±0.444

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Answer:

Arabella

Step-by-step explanation:

I am assuming the information in your table looks like this:

                    P(brushing in morning)      P(brushing in evening)

Braxton                       .72                                        .85

Arabella                      .82                                        .79

Now, to find the probability either of Braxton or Arabella brushes in both the morning and evening (knowing they are independent), we multiply them together.

P(Braxton brushes in morning AND evening) = .72 × .85 = .612 = 61.2%

P(Arabella brushes in morning AND evening) = .82 × .79 = .6478 = 64.78%

Since 664.77% > 61.2%, we know that Arabella is more likely to brush her teeth in both the morning and evening compared to Braxton

Arabella is more likely to brush both morning and evening than Braxton, as her probability of brushing both morning and evening is higher.

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

To find out who is more likely to brush both morning and evening, we need to calculate the probability of each person brushing both morning and evening and compare the results.

For Braxton, the probability of brushing both morning and evening is:

P(Braxton brushes both morning and evening) = P(Braxton brushes in the morning) × P(Braxton brushes in the evening)

= 0.72 × 0.85

P ( B ) = 0.612

For Arabella, the probability of brushing both morning and evening is:

P(Arabella brushes both morning and evening) = P(Arabella brushes in the morning) × P(Arabella brushes in the evening)

= 0.82 × 0.79

P ( A ) = 0.6478

And , P ( A ) > P ( B )

Therefore, Arabella is more likely to brush both morning and evening than Braxton, as her probability of brushing both morning and evening is higher.

Hence , the probability is solved

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The complete question is attached below :

Two friends argue over who brushes their teeth more often. To settle the argument, they keep track of the number of mornings and nights they brushand calculate a probability. These are shown in the table.Who is more likely to brush both morning and evening? Assume all events are independent.

The standard form of a quadratic equation is  ax² + bx + c = 0.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as it's degree is two.

The standard form of a quadratic equation is ax² + bx + c = 0.

Where, 'x' is the variable and a, b, c are constants.

Suppose you are given to find the roots of a quadratic equation

2x² + 6x + 4 = 0.

It says two numbers that multiply to 8 and add to 6.

So,

2x² + 2x + 4x + 4 = 0.

2x(x + 1) + 4(x + 1) = 0.

(x + 1)(2x + 4) = 0.

(x + 1) = 0 Or (2x + 4) = 0.

x = - 1 Or x = - 2.

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The mean varies in the distribution of sample data. Therefore, statement II is correct and option a is the correct option.

A statistic sampling distribution is a type of probability distribution created by choosing several random samples from the same population, each of a preset size. One can better understand the variations in a sample statistic by using these distributions.

The population's mean, from which the sample of items was taken, is the mean of the sampling distribution. Therefore, if the population mean is μ, then the sampling distribution mean is also μ.  In a population distribution, the mean does not vary from one sample to another. Also, the sample mean will always have the same mean in the sampling distribution. But the mean will vary if we take different samples in the distribution of sample data. Therefore, statements II is correct.

The complete question is -

Which of the following distributions has a mean that varies?

I. The population distribution

II. The distribution of sample data

III. The sampling distribution of the sample mean

a) ll only

b) III only

c) I only

d) all three distributions

e) II and III

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As the question is incomplete, an integer, a rational number that is not an integer, and an irrational number are explained with examples.

                                negative interger: -12, -6, -32 etc.

                                 zero integers: 0

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The length of side x is 3 in simplest radical form with a rational denominator.

To find the length of side x in simplest radical form with a rational denominator, you will need to follow these steps:

Write the equation that relates the length of side x to the other known quantities in the problem.

Remove the radical expression from the equation's other side.

Simplify the radical expression, if possible. This may involve finding the prime factorization of the number inside the radical and applying the rules for simplifying radicals.

If the radical cannot be simplified further, consider whether you can rationalize the denominator. To rationalize the denominator, you will need to multiply the radical expression by a fraction that has the radical in the numerator and the same expression under the radical in the denominator. This will eliminate the radical from the denominator.

Simplify the resulting expression by combining like terms and reducing the fraction, if necessary.

For example, suppose we want to find the length of side x in the following equation:

2x = √27 + 3

To solve for x, we need to isolate the radical expression on one side of the equation. By taking 3 away from both sides, we can accomplish this:

2x - 3 = √27

Then, multiplying both sides by 2 gives us:

x - 3/2 = √27 / 2

The radical expression √27 / 2 cannot be simplified further, but we can rationalize the denominator by multiplying the expression by the fraction (√27 / √27):

x - 3/2 = √27 / 2 * √27 / √27

This gives us:

x - 3/2 = 3√3 / 2

Finally, we can simplify the expression by combining like terms and reducing the fraction:

x = 3√3 / 2 + 3/2

x = 3/2 + 3/2

x = 3

Therefore, the length of side x is 3 in simplest radical form with a rational denominator.

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Answer:

you pay 370.30

you saved 158.70

I believe

Answer:

$370.3

Step-by-step explanation:

If you need to find 30% of $529 you need to put 30% into a decimal. 30/100 =0.3 so if we do 0.3 x 529 we get the answer $158.7.

Then we subtract 529 by 158.7 to get 370.3 as the sale price.

Similar triangles are those with the same form but different sizes. The expression's measure for the value of x is 32.5.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects.

In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

From the given diagram, since the triangle ABC is similar to DCE, hence the measure of the angle CDE is equal to ABC that is;

<CDE = <ABC

2x = 65

x = 65/2

x = 32.5

Hence the measure of the value of x from the expression is 32.5

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Answer:

306m

Step-by-step explanation:

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there are better explainations there :)

you're looking for the perimeter, so you need to add all the sides. that's 55+55+98+98, which is 306.

If the length of the cable is 10 cm. Then the weight of the cable will be 61.18 grams.

A proportion is a gathering of consecutively requested numbers an and b communicated as a/b, where b is never equivalent to nothing. At the point when two items are equivalent, a proclamation is supposed to corresponding.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The ratio of the weight to length will remain constant. Then the rate is calculated as,

Rate = 52 / 8.5

Rate = 6.1176 grams per cm

If the length of the cable is 10 cm. Then the weight of the cable is given as,

Weight = 6.1176 x 10

Weight = 61.18 grams

Assuming the length of the link is 10 cm. Then, at that point, the heaviness of the link will be 61.18 grams.

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Answer:

A. Triangle PNQ is translated along the vector <5,6> to map onto triangle P'N'Q'   OR
A. Triangle PNQ is translated right 5 units and up 6 units to map onto P'N'Q'
P (2,5) --> P' (7,11)
N (-3,-1) --> N' (2,5)
Q (4,0) --> Q' (9,6)

Step-by-step explanation:

Answer:

y=8x+2.

Step-by-step explanation:

Slope intercept equation: y=mx + or - b.

m or slope is 8. plug that into the slope intercept equation of y=mx+b

2 is positive. so its +2 after 8x.

The rate of change of the volume of the cube is 0.4s cm³/s

Rate of change is the rate at which a quantity increases or decreases with time.

Since the side of the cube is increasing at a constant rate of 0.2 centimeters per second. Its volume is given by V = L³ where L = length of side of cube.

Now, to find the rate of change of its volume, we differentiate the equation with respect to time, t.

So, V = L³

Differentiating, we have

dV/dt = dL³/dt

= dL³/dL × dL/dt

= 2L² × dL/dt

Since the rate of increase of the side of the cube is dL/dt = 0.2 cm/s, we have that

dV/dt = 2L² × dL/dt

= 2L² × 0.2 cm/s

= 0.4L² cm³/s

We know that the area of a cube s = L². So, substituting this into the equation, we have

dV/dt = 0.4L² cm³/s

= 0.4s cm³/s

So, the rate of change is 0.4s cm³/s

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