1. Students in Mrs. Henderson's third grade class are working on times tables, and they demonstrate mastery by
passing tests. Sofia has passed 4 tests so far. Her classmate, Jacob, has passed 8 of them. From now on, Sofia plans
to take and pass 3 tests per week. Meanwhile, Jacob plans to do 1 per week. At some point, Sofia will catch up to
Jacob. How long will it take?

Answer:

One pecan cheesecake = $9

One apple cheesecake = $20

Step-by-step explanation:

This is a system of equations problem, so we can set up these equations (Note: p = pecan cheesecake cost | a = apple cheesecake cost):

8p + 12a = 312

9p + 6a = 201

Now, we can solve the system of equations. Below is an example of using the elimination method to solve the system:

1.    8p + 12a = 312 --> -4p - 6a  = -156        

     9p + 6a = 201  -->  9p + 6a = 201

2.                                  5p         = 45

3.                                    p         = 9

4.  8(9) + 12a = 312

    72   + 12a = 312

              12a = 240

                 a = 20

1. We try to make one of the terms equal to the negative version of the other term to eliminate that term; here, I am eliminating "a". To do this, find a multiple of one of the equations where one of the terms is the negative version of the other term. In other words, divide/multiply the equation by a number so one of the terms in the equation is the negative version of the term in the other equation (I divided the first equation by -2 so 12a becomes -6a, the negative version of 6a in the second equation.

2. Next, add the two equations' corresponding terms

(-4p + 9p = 5p; -6a + 6a = 0; -156 + 201 = 45)

3. Simplify the equation (5p = 45; p = 45/5; p = 9)

4. Substitute the term you found back into one of the equations to find the other term.

The area of field hockey is larger by 3162.85 [tex]m^2[/tex].

The amount of unit squares that cover an enclosed figure's surface is its area. Square units like [tex]cm^2[/tex] and [tex]m^2[/tex] are used to measure area. A shape's area is a two-dimensional measurement. The space inside the perimeter or boundaries of a closed shape is known as the "area."

The hockey surface given here is in rectangular shape, so,

Area = length x breadth

Area of the hockey surface at a community centre is,

= 61 m x 30.5 m

=1860.5 [tex]m^2[/tex]

Area of field hockey played at outdoors,

= 91.5 m x 54.9 m

= 5023.35    [tex]m^2[/tex]

Clearly, we can see that area of field hockey is larger.

Difference between both the areas = 5023.35 -1860.5 = 3162.85 [tex]m^2[/tex].

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The value of the expressions are;

a. 2x² + 6

b. 3x² - 6x + 2x -6

c. y = 3

d. x = 2

From the information given, we have

a. 2x(x + 3)

expand the bracket

2x² + 6

b. (3x + 2)(x-3)

expand the bracket

3x² - 6x + 2x -6

c. 4y -2(6-y) = 6

expand the bracket

4y - 12 + 2y = 6

collect like terms

6y = 18

Then,

y = 3

d.  x(2x-4)= (2x + 1)(x-2)

expand bracket

2x² - 4x = 2x² - 4x + x - 2

collect like terms

x = 2

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It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).

The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.

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Answer:

The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)

Step-by-step explanation:

4x + 2y = 6 ....… (1)

x − y = 3 …..... (2)

Example, for equation 2 is:

x - y = 3

x = 3 + y

Put in equation 1:

4(y + 3) + 2y = 6

4y + 12 + 2y = 6

6y = -6

y = -6/6

y = -1

We have the value of y, then the value of x will be:

x = 3 + y

= 3 + (-1)

= 3 - 1

= 2

So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)

What does this problem ask for:

 --> which statement is sufficient to prove that:

     ∠ADB ≅ ∠ABD

Let's separate this image into two triangles: ΔADC and ΔABC

   --> prove that these triangles are congruent

       --> thus proving that: ∠ADB ≅ ∠ABD

Let's consider what evidence we have:

             --> thus: ∠ADC = ∠ABC

The minimum information that we have:

  --> prove that one pair of sides on both triangles are congruent

      --> based on the SSA Triangle Formula

             --> Two triangles that have two sides and one angle that are

                   equal, are therefore congruent

Based on the choices given:

 --> if DA = BA or DA is congruent to BA

  --> then ΔADC = ΔABC

Thus:

--> ∠ADC = ∠ABC

Answer: DA is congruent to BA

Answer: [tex]5x^{2} +6x[/tex][tex]-4[/tex]

Step-by-step explanation:

Synthetic division

Answer:

6°

Step-by-step explanation:

Two angles are called complementary if the sum of their measures equals to 90°:

The complementary angle of 84° = 90° - 84°

                                                       = 6°

Answer:   6

Step-by-step explanation:

The complementary angle means the sum of two angles equal to 90. Let x be the other angle.

x + 84 = 90

       x = 6

Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

[tex]A^2 = B ^2 + c^2[/tex]

AC = [tex]\sqrt{14^2- 9^2}[/tex]

AC = [tex]\sqrt{196- 81}[/tex]

Ac = [tex]\sqrt{115}[/tex]

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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The perimeter of one square which combined with other to form a rectangle of 288 cm² is 12 cm.

The area of rectangle is given by the formula -

Area = length × width

Now we know that all the sides of square are same. Also, the identical squares have been kept side by side. So, let us represent one dimension of square with b. Thus, length of rectangle will be (b + b)

Length of rectangle = 2b

Width of rectangle will be b. Now, finding the value of b first.

288 = 2b×b

Performing multiplication

2b² = 288

b² = 288/2

Performing division

b² = 144

b = ✓144

Taking square root

b = 12 cm

The perimeter of one square = 2(length + width)

Perimeter of one square = 2 ( 12 + 12)

Perimeter = 2 × 24

Performing multiplication

Perimeter = 48 cm

Thus, perimeter of one square is 48 cm.

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Given that AC bisects ∠BCD, the complete flowchart proof is given below:

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

A geometer is a mathematician who specializes in geometry.

GIven the shape in the image, the flowchart proof has been completed above.

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The coordinates of vertex D of the parallelogram is; (0, 1)

We are given the coordinates of the parallelogram as;

A(2,4), B(5,2) and C(3,-1)

Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.

The formula for the midpoint between two coordinates is;

(x1 + x2)/2, (y1 + y2)/2

Thus;

Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2

Midpoint of BD = (5 + x)/2, (2 + y)/2

Thus;

(5 + x)/2 = 5/2

x = 0

(2 + y)/2 = 3/2

2 + y = 3

y = 1

Coordinate of D = (0, 1)

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In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the error term come from a normal distribution.

In a simple linear regression model, the normal quantile plot of the residuals is a graphical tool used to assess the normality assumption of the error term (also known as the residual). The error term represents the difference between the actual value of the dependent variable and the predicted value by the model.

Assuming that the error term follows a normal distribution is important for various reasons. Firstly, the normal distribution is a very common assumption in statistics, and many statistical methods rely on it. Secondly, a normal distribution of the error term is essential for making reliable predictions and for computing valid confidence intervals.

The normal quantile plot of the residuals compares the distribution of the residuals against a theoretical normal distribution. The plot consists of a straight line if the residuals are normally distributed. However, if the plot shows deviations from the straight line, it indicates non-normality in the residuals.

If the normality assumption is not satisfied, we need to explore the reasons for the non-normality and consider alternative methods to analyze the data, such as non-parametric methods.

Therefore, the normal quantile plot of residuals is an essential diagnostic tool in simple linear regression, as it allows us to evaluate the assumption of normality and make appropriate adjustments to the model.

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The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

An equation can be stated  a  mathematical statement that is made up of two expressions connected by an equal sign.  In its normal form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

4 x = t + 2

or, x = (t + 2) /4

or, x = t/4 + 2/4

or, x = t/4 + 2

Hence, The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

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Answer: Perimeter: [tex]10mn^2+4m^2[/tex]; Area : [tex]6m^3n^2[/tex]

Step-by-step explanation: For Perimeter add like terms 7mn^2 and 3mn^2 add but 4 m^2 isolates. For area multiply 3 mn^2 and 4m^2 to get 12 m^3n^2 and then divide by 2 because it is right triangle.

The number of ways the letters can be permutated in the word SPEECHLESS is 100800.

What is meant by permutation?

An arrangement of items in a specific order is referred to as a permutation. A set can be permuted by arranging its components in a linear or sequential order, or by rearrangement of its components if the set is already ordered. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The  number of letters in SPEECHLESS = 10

The letter E repeats 3 times

The letter S repeats 3 times

The letters P,C,H,L repeats one time.

When there are repeating letters in a word, the total number of distinct ways the letters in the words can be permutated is:

[tex]N= \frac{n!}{r_1!r_2!.....r_m!}[/tex]

where N = number of arrangements

 n = number of letters

r = total number of times one letter is repeated in the word

For SPEECHLESS,

Therefore the number of ways the letters can be permutated  is:

[tex]N= \frac{10!}{3!3!}[/tex] = 100800

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Answer:

25/50

will equal to 1/2

Answer:

2

Step-by-step explanation: this is because the plus sign splits the terms so simply 2 terms

Answer:

Step-by-step explanation:

Since they are congruent, you know that 8=x-3. 11-3=8. and 14=x+6=8. x is 8

Answer:

y = 2x - 3

Step-by-step explanation:

Pick two random points for slope

slope = m = rise/run = [tex]\frac{(-3-(-5))}{0-(-1)} = \frac{2}{1} = 2[/tex]

y intercept form:

y = 2x - 3

Answer:

7 traders sell oranges and mangoes alone.

Step-by-step explanation:

(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)

(107 – x = 100)

(x = 107 – 100 = 7)

Therefore, 7 traders sell oranges and mangoes alone.

(b) (312_{four} + 52_{x} = 96_{ten})

(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})

= (48 + 4 + 2 = 54_{10})

(52_{x} = 5 times x^{1} + 2 times x^{0})

= ((5x + 2)_{10})

(therefore 54 + (5x + 2) = 96)

(56 + 5x = 96 implies 5x = 96 – 56 = 40)

(x = 8)

(therefore 312_{4} + 52_{8} = 96_{10})

Answer:

6g+3g=11+3-5

combine like terms

9g=11+3-5

calculate the sum of difference

9g=9

Step-by-step explanation:

reduce the greatest common factor on both sides

of the equation

g=1

If administrators at International University are curious how students' GAs after their first year compare to their high school GPs. The correct answer is: C. We cannot assume independence between the high school GPAs in the sample.

The GPAs of the students in the sample at the end of their first year at the university are likely to be correlated with their high school GPAs, as students with higher high school GPAs are likely to perform better in university as well.

Thus, the high school GPAs of the students in the sample are not independent of each other, and using the formula for the standard deviation of the sample would not be appropriate in this situation.

Therefore the correct option is C.

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The correct question is:

Administrators at International University are curious how students' GPAs after their fist year compare to their high school GPAs. They plan on taking an SRS of 80 of the 900 freshmen to look up their high school GPAs. They plan to look at the difference between the mean high school and the mean university GPA for students in the sample at the end of their first year. Why is it not appropriate to use the formula for the standard deviation of

The samples are not independent of each other.

We cannot assume independence between the university GPAs in the sample.

We cannot assume independence between the high school GPAs in the sample.

The samples are independent of each other.

Answer: A

Step-by-step explanation:

The sample is sampling the high school GPA and college GPA of the same students meaning the samples are not independent.

The correct classification of the statements is: False, True, False, True.

What is Function ?

Function can be defined in which it relates an input to output.

The point of symmetry on f-¹(x) is (4,6).

False. The point (4,6) is not on the graph of f-¹(x), so it cannot be the point of symmetry. We can verify that the function is not symmetric with respect to any vertical or horizontal line.

The domain of f-¹(x) is (-∞,4).

True. The cube root function is defined for all real numbers, so the expression inside the cube root must be nonnegative. Therefore, (z - 4) / 5 ≥ 0, which implies that z ≥ 4. This means that the domain of f-¹(x) is (-∞,4].

The graphs of f¹(x) and f(x) are reflections across the x-axis.

False. The graphs of f¹(x) and f(x) are not reflections across the x-axis. We can plot the functions to see that they have different shapes and are not symmetric with respect to the x-axis.

The range of f¹(x) is (-∞,∞).

True. The cube root function is defined for all real numbers, so f-¹(z) can take any real value. This means that the range of f¹(x) is (-∞,∞).

Therefore, the correct classification of the statements is: False, True, False, True.

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There are System A has 0 solutions and System B has 1 solution.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

System A:

Line 1: y = (1/2)x

Line 2: y = (1/2)x - 1

System B:

Line 1: y = -x - 1

Line 2: y = -2x - 1

Using these equations, we can determine the number of solutions for each system:

System A has two lines that do not intersect (they are parallel), so it has no solutions.

System B has two lines that intersect at a single point, so it has one solution.

Therefore, System A has 0 solutions and System B has 1 solution.

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The equation of the given information is y(x) = 5x+10

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

Given that cost of renting for different numbers of hours.

The initial cost, regardless of time, is; $10. then the cost will increase at a rate of $5 per hour that the boat is rented.

Therefore, the cost (y) of renting a paddle boat for 'x' hours is:

y(x) = 5x+10

here linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.

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The initial length of the scarf is 50 centimeters.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We can use the given information to find the rate at which Cassandra is knitting the scarf and the initial length of the scarf.

Let L be the initial length of the scarf in centimeters, and let r be the rate at which Cassandra is knitting the scarf in centimeters per hour. Then, we have:

L + 25h = length of scarf after h hours

Substituting h = 3 and the length of the scarf after 3 hours = 125, we get:

L + 25(3) = 125

L + 75 = 125

L = 50

Therefore, the initial length of the scarf is 50 centimeters.

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Cassandra is knitting a scarf. She increases the length of

the scarf by 25 centimeters each hour she knits. After 3

hours, the scarf is 125 centimeters long what is initial length of scarf.