John sells cupcakes. He has been offered a salary position at two different companies to make and sell his cupcakes. The first company offered him a weekly salary of $ 800.00 $800.00​​ plus a commission of $ 0.30 $0.30​​ for each cupcake he sells. The second company offered him a weekly salary of $ 350.00 $350.00​​ plus a commission of $ 1.30 $1.30​​ for each cupcake he sells. How many cupcakes must John sell each week for the total pay from each company to be the same?


PLEASE ANSWER FAST WORTH 92 POINTS

If the rectangle is 9 cm longer than it's width , and the width is 1/7th of perimeter , then the length of rectangle is 15 cm and width of rectangle is  6 cm.

let the rectangle's length be  = l cm ;

and let the width of rectangle is  = w cm ;

the length is 9 cm longer than its width , that means ;

⇒ l = w + 9  ...equation(1)

and the width is 1/7 of perimeter , then

⇒ w = (1/7)(2l + 2w)

⇒ w = 2/7(l  + w)  .....equation(2) ;

substituting value of equation(1) in equation(2) ;

we get ;

⇒ w = (2/7) × ( w + 9 + w ) ;

on simplifying ,

we get ;

⇒ w = 6 .

from equation(1) ⇒ l = 6 + 9 = 15 .

Therefore , the length is 15 cm and width is 6 cm .

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On multiplying 55 × 35, the answer is  1925.

The simplest way to start teaching multiplication is to establish the relationship between the concept and addition, which your pupils should already be familiar with. Make sure your students understand the first principle of multiplication—that it is just repeated addition—before continuing on.

Your youngster can learn that multiplication is actually just a means to repeatedly add multiple groups of the same number by using objects like blocks and small toys. For instance, ask your youngster to arrange the blocks into six groups of three by writing the issue 6 x 3 on a sheet of paper.

        5 5

    ×  3 5

 ------------

     2 7 5

 + 1 6 5 ×

--------------

    1925

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There are 2 values of k, 12 and -12, for which the polynomial x^2 + kx - 36 has two distinct integer roots.

The polynomial x^2 + kx - 36 has two distinct integer roots if and only if its discriminant is a perfect square.

The value of the discriminant is given by:

b^2 - 4ac = k^2 + 4 * 36 = k^2 + 144

So, for the polynomial x^2 + kx - 36 to have two distinct integer roots, k^2 + 144 must be a perfect square.

We know that the difference of two consecutive perfect squares is equal to an odd number, so we can start testing values of k by incrementing k by 1 and checking if k^2 + 144 is a perfect square.

Starting with k = 0, we have k^2 + 144 = 144, which is not a perfect square. For k = 1, k^2 + 144 = 145, which is also not a perfect square.

For k = 2, k^2 + 144 = 148, which is still not a perfect square.

We keep incrementing k and checking until we find a value of k such that k^2 + 144 is a perfect square.

When k = 12, we have k^2 + 144 = 168, which is a perfect square (12^2).

Therefore, the polynomial x^2 + 12x - 36 has two distinct integer roots.

We can repeat this process for negative values of k to see if the polynomial has two distinct integer roots for those values.

We find that for k = -12, the polynomial x^2 - 12x - 36 also has two distinct integer roots.

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Answer: The value of 4.3x10^5 is 430000.

Step-by-step explanation:

To find the value of 4.3x10^5, you need to multiply 4.3 by 10 raised to the power of 5. This can be written as 4.310^5.

The value of 4.310^5 is 430000.

The expression that would render the both the sides equivalent is 3x+2-2

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here: The expression 2+8x-16

To find its equivalent we have an incomplete expression 5(x-3)+1

Now 5(x-3)+1=5x-15+1

                     =5x-14

Thus Adding 3x+2-2 to this expression we get

5x-14+3x+2-2=2+8x-16

Therefore, we can deduce that the missing term must be 3x+2-2

Hence, The missing expression is 3x+2-2

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Answer: Yes it's 15

Step-by-step explanation:

20/100 x 75 = 15

Above 95% confidence interval for population mean =(6.7149 to 9.2051)

Given that,

3.3.8 One of the writers asked her students how many hours a week they anticipated studying statistics outside of class in a pre-course, anonymous survey for her introductory statistics course. The average response time was 8.2 hours, with a standard deviation of 3.79 hours, from 49 students. Data were not significantly skewed.

To find : a) specify the study's observational unit. b) Determine if the variable is categorical or quantitative and the variable of interest. c) compute and present the 95% confidence interval for the parameter of interest using the theory-based inference applet. d) Was it appropriate to determine a confidence interval using the theory-based (t-distribution) technique in the setting of this study?

sample mean x= 7.960

sample size   n= 36.00

sample std deviation s= 3.68

std error sx=s/√n= 0.6133

for 95% CI; and 35 df, value of t= 2.030

margin of error E=t*std error    = 1.245

lower bound=sample mean-E = 6.7149

Upper bound=sample mean+E = 9.2051

from above 95% confidence interval for population mean =(6.7149 to 9.2051)

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The domain of g(x) - f(x) is all real numbers, or (-∞, ∞).

What is the domain?

The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value). In other words, it is the set of values for which the function is valid and can be used without producing any errors or undefined results.

To perform the function operation g(x) - f(x), we need to subtract the function f(x) from the function g(x).

g(x) = x² - x + 1

f(x) = 4x + 3

g(x) - f(x) = x² - x + 1 - (4x + 3)

g(x) - f(x) = x² - 5x - 2

The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).

For the function g(x) - f(x) = x² - 5x - 2, there are no restrictions on the input values, meaning that any value of x can be plugged into the function to produce a valid output.

Therefore, the domain of g(x) - f(x) is all real numbers, or (-∞, ∞).

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This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.

(a) What kind of research is this?

"Observational study" is the study's type.

Reason: This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.

Can this data be used to draw a causal conclusion about the link between elevated stress levels and muscle cramps?

No, an observational study was unable to draw any conclusions about the link between elevated stress levels and muscle cramps. The Chi-square test can be used to determine the relationship between increasing stress and cramps.

(c) Describe any potential confounding factors that could account for the correlation between greater stress and muscle cramps.

Muscle cramps may be impacted by the increased stress.

In this case, the factors under consideration are qualitative variables. Count the number of times that high school students have visited a doctor with a muscular ailment.

Confounding factors for stress may include anxiety over taking the exam, less sleep, spending more time studying, eating less, drinking more coffee, and other factors.

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The inequality says that the cost of each song is less than 4 dollars.

We want to see which situation can be represented by the inequality below.

8 + 4x < 12 + 3x

Where we know that each song costs x dollars.

The situation represented by that inequality can be:

"8 dollars plus 4 songs has less value than 12 dollars plus 3 songs"

We can also simplify the inequality to get:

8 + 4x < 12 + 3x

4x  -3x < 12  - 4

x < 4

We also can see that the cost of each song is less than $4.

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√131 lies between 11 and 12.

The numbers that include natural numbers and zero are called whole numbers.

Given is the square root of 131.

We can write the square root of 131 as -

√131 = 11.45

We can write the whole numbers as -

11 < 11.45 < 12

Therefore, √131 lies between 11 and 12.

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The equivalent of the expression -(-0.1p+4) is 0.1p-4

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.

For example: 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x² + 2y + 1) = 6x² + 12y + 6.

Similarly -( - 0.1p + 4) can be written in another for by multiplying the negative sign with every term in the parentheses.

therefore -1× -0.1p + -1×4 = 0.1p -4

This means -(-0.1p+4) and 0.1p -4 are equivalent

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Answer:

To find the diagonal length, you can use the Pythagorean theorem.

If one side is 28 inches, and the board is a square, the other side must also be 28 inches.

a = side 1

b = side 2

c = diagonal length

a^2 + b^2 = c^2

(28)^2 + (28)^2 = c^2

784 + 784 = c^2

1568 = c^2

Square root both sides.

c = about 39.6 inches diagonal length

The possible amounts of time for which they could rent the meeting room is 1.71 hours

The question states that

This implies that

35x + 5.80x ≤69.80

Solving the inequality to have

40.8x ≤69.80

Making x the subject of the relation we have

x≤1.71

In conclusion it takes the college 1.71 of time for them to rent the meeting room

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For the function y = f (x),  the average rate of change on the interval - 1 ≤ x ≤ 3 is -2.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The graph of the function f(x) is graphed and the graph is given.

The average rate of change is a measure of how much the function changed per unit, on average, over that interval.

For a function f(x) at interval [a,b], the average rate of change is given as -

[f(b) - f(a)]/(b - a)

The interval values is given as - [-1,3]

The value for f(a) as seen in the graph is - 4.

The value for f(b) as seen in the graph is - -4.

Substitute the values in the equation -

Average rate of change = [f(b) - f(a)]/(b - a)

A = (-4 - 4)/[3 - (-1)]

A = -8/(3 + 1)

A = -8/4

A = -2

Therefore, the value for average rate of change is -2.

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The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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Answer: y,x = -2,3 is your answer. I hope this helps!

Step-by-step explanation:

The area of the octagon is 0.875 units square.

Two unit squares share the same center. The overlapping region of the two squares is an octagon with perimeter 3.5.

Area of a triangle:

We need to know how to calculate the area of a triangle, in order to solve this question. The area of a triangle with base b and height h is [tex]\frac{hb}{2}[/tex]. An octagon is a 2D figure with 8 sides.

Let A, B, C, D, E, F, G, and H be eight consecutive vertices of the octagon. Let 0 be the common center of the square units.

Draw the segments OA, OB, OC, OD, OE, OF, OG and OH, connecting the vertices with the common center O of the squares.

The segments divide the octagon into 8 concurrent triangles.

In these triangles, AB, BC, CD, DE,EF, FG, GH, and HA are the bases; the height is 12 of a unit in all the triangles.

Thus, the area of the octagon=[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{2}[/tex]×(AB+BC+CD+DE+EF+FG+GH+HA)

        =[tex]\frac{1}{4}[/tex]×(Perimeter of the hexagon)=14×3.5=3.54=0.875

Therefore, the area of the octagon is 0.875 units square.

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The sample size of the data which has a sample mean of 0.7 is 20.

What is mean?

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

Cathy has obtained a sample mean of 0. 7 and, but she cannot remember if the sample size was 20 or 25,

Calculate the sample size as shown below,

As we know that the variance would be positive,

s² ≥ 1 / (n - 1) [Σ xi²-nx²]

0 ≥ 1 / (n - 1) [Σ xi²-nx²]

[10 - n × x × 0.7²] ≥ 0

n × x × 0.7² ≤ 10

n ≤ 10 / (0.7)²

n ≤ 20.408

Thus, the sample size is 20.

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The probability that a randomly selected battery of this kind lasts longer than 70 months is approximately 0.104(rounded off to the second decimal place).

The cumulative distribution function of an exponential distribution with a mean of 60 months is given by:

F(x) = 1 - e^(-x/60)

The probability that a randomly selected battery lasts longer than 70 months is given by:

P(X > 70) = 1 - F(70) = 1 - (1 - e^(-70/60)) = e^(-70/60) = 0.104

So, the probability that a randomly selected battery of this kind lasts longer than 70 months is approximately 0.104 (rounded off to the second decimal place).

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The median of the given set of numbers is 82.

Median is the middle element when the data set is arranged in an increasing or decreasing order.

Given is a stem and leaf plot.

We have to write each of the corresponding number in stem attached with each of the corresponding number in leaf plot.

So the numbers in the first row will be 71, 75, 77 and 78.

Numbers in the second row will be 80, 80, 81, 82, 84, 85, 86, 86, 87, 89.

Number in the third row will be 95.

Writing the numbers from the plot, we will get the values as,

71, 75, 77, 78, 80, 80, 81, 82, 84, 85, 86, 86, 87, 89, 95.

The numbers are already in the increasing order.

There are 15 number of data in the set.

Median is the middle element, that is 8th element, which is 82.

Hence the median of the data is 82.

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Answer:

The correct answer is C f(2)

By  using the unit circle , we found that the value of Sec(0°) is (b) Sec(0°) = 1  .

The Unit Circle is defined as a circle that have a radius of 1 which is centered at the origin of a coordinate plane.

The angle in the unit circle are measured in radians.

The Secant function, denoted by Sec(x), is defined as 1/Cos(x)  ;

we have to find the value of Sec(0°) ;

So , at 0 degrees, the point (1,0) lies on the unit circle and

the x-coordinate of this point is 1 which is the cos(0) and

the value of Sec(0) = 1/cos(0) = 1/1 = 1

Therefore , the value of Sec(0°) is = 1  .

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Answer: (x+1)^2 + (y-0)^2 = 8pi^2

Step-by-step explanation:

The least amount of time spent per week on meetings for the sample of 25 CEOs is 12 hours.

The least amount of time spent per week on meetings for the sample of 25 CEOs can be found by looking at the lowest value in the data set. The data set provided above lists the time spent per week on meetings for a sample of 25 CEOs, and the least amount of time spent is 12 hours per week.

This is the smallest value in the data set, and it represents the minimum amount of time spent on meetings among the CEOs in the sample.

Note that this data is a sample of 25 CEOs and not the entire population of CEOs, so it is not representative of all CEOs. Additionally, the time spent per week on meetings is a quantitative variable, and it is continuous. Therefore, it is recommended to use measures of central tendency (mean or median) and measures of dispersion (standard deviation, range) to make inferences about the population.

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following are true about ALL parallelograms are:

a. Opposite sides are congruent.

c. Opposite angles are congruent.

d. The diagonals bisect each other.

h. Consecutive angles are supplementary.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

There are six crucial parallelogram characteristics to be aware of:

A rhombus is what we have when all of the sides of a parallelogram are congruent. Rhombi can use the characteristics of parallelograms.

We have a quadrilateral that is referred to as a trapezoid if just one pair of its sides are parallel. While the nonparallel sides are referred to as legs, the parallel sides are known as bases. We have what is referred to as an isosceles trapezoid if the legs are congruent.

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The statement would e: A representative sample is one that accurately reflects a larger population.

The correct answer is an option (b)

We know that the sampling is used to find insights and observations about a population group.

A representative sample is nothing but a sample / a subset of a population that accurately reflect the characteristics of the larger group.

For example, consider a class of 50 students with 25 girls and 25 boys.

We can generate a representative sample that might include ten students: five girls and five boys.

As we know  the samples contain smaller, manageable versions of the larger group, they are useful in statistical analysis when population size is large.

Thus, a representative sample is used for obtaining insights and observations of the targeted population group.

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The complete question is:

A representative sample is one that accurately reflects a larger

a. dependent variable.

b. population.

c. control group.

d. correlation coefficient.