5
Eric runs a coffee shop and bought 5,480 cups at the beginning of the week. At the end of the
week, he had 20% of the cups left. How many cups does Eric have left?

Answer:

-4 and -16

Step-by-step explanation:

Let x = first number

Let y = second number

Given:

⇒ xy = 64

Given:

⇒ x + y = -20

Rewrite  x + y = -20  to make x the subject:

⇒ x = -20 - y

Substitute into xy = 64 and solve for y:

⇒ (-20 - y)y = 64

⇒ -20y - y² = 64

⇒ y² + 20y + 64 = 0

⇒ (y + 4)(y + 16) = 0

⇒ y = -4, y = -16

As x + y = -20

If y = -4 then x = -16

If y = -16 then x = -4

Therefore, the two numbers are -4 and -16

Let they be a and b

So

\(\\ \rm\rightarrowtail (a-b)^2=(a+b)^2-4ab\)

\(\\ \rm\rightarrowtail (a-b)^2=(-20)^2-4(64)=400-256=144\)

\(\\ \rm\rightarrowtail a-b=12\dots(2)\)

From both equations

Answer:

y=1

x=1/5

Step-by-step explanation:

Answer:

15a - 10

Step-by-step explanation:

-5(-3a + 2)

-5 · -3a = 15a

-5 · 2 = -10

15a - 10

Answer:

175

Step-by-step explanation:

its easy just multiply 7 and 25

A graphical tool used to help determine whether a process is in control or out of control is known as a Control Chart.

Control charts are essential in quality control and statistical process control (SPC). They allow you to monitor process performance and variability over time, enabling you to identify trends, shifts, or deviations from the established process baseline.

Control charts typically consist of a centerline, representing the process mean, and upper and lower control limits, which indicate the acceptable range of variation. Data points are plotted on the chart, and if they fall within the control limits, the process is considered to be in control. If data points fall outside the control limits or display non-random patterns, the process is considered out of control, signaling potential issues that need to be investigated and addressed.

In summary, control charts are a valuable graphical tool that assists in determining the stability of a process, facilitating continuous improvement efforts and ensuring product quality. They provide a visual representation of process variation and help identify when corrective actions are needed to bring a process back into control.

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The shape of the graph changes qualitatively at k = ± 2 and

\(k=\sqrt{(2)\).

The given function is f(x,y) = y-x²+y²+kxy.

The critical points of the function are found by taking the partial derivatives and equating them to zero:

∂f/∂x = -2x + ky = 0

y = 2x/k

∂f/∂y = 2y + kx = 0

y = -kx/2

Substituting y from the first equation into the second equation gives

x = k²x/4, so k² = 4 and k = ± 2.

Therefore, the critical points are (0,0), (2,4), and (-2,4)

We will now examine the critical points to see when the shape of the graph changes qualitatively.

There are two cases to consider:

Case 1: (0,0)At (0,0), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2 0;0 2].

The determinant of the Hessian matrix is -4, which is negative.

Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.

Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2k 2k;2k 2].

The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).

Therefore, the critical points (2,4) and (-2,4) are local minima when

k > √(2).

Thus, the shape of the graph changes qualitatively at k = ± 2 and

k = √(2).

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Answer:

you didn't send a pic of the table

The attached image shows the triangle with coordinates A(1,4), B(1,7) and C(3,5) and reflected over the line y = 2x + 1.

Reflection refers to the transformation of a geometric shape by flipping it across a line called the line of reflection.

When a shape undergoes reflection, every point on the shape is mapped to a corresponding point on the opposite side of the line of reflection, maintaining the same distance from the line.

For example, if you have a triangle and reflect it across a line of reflection, the resulting image will be a triangle with the same size and angles, but it will be facing in the opposite direction.

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Test the equation below for exactness. If exact, solve. If not, use an integrating factor (find it by inspection). The given equation is not exact. An integrating factor is required to solve it.

To determine if the equation is exact, we check the partial derivatives with respect to x and y. Differentiating (cos(wx) + wsin(wx)) with respect to y gives 0, while differentiating e with respect to x gives 0. Since the partial derivatives are not equal, the equation is not exact.

To find an integrating factor, we inspect the coefficients of dx and dy. Here, e is only dependent on y, so we can choose the integrating factor μ = e. Multiplying the entire equation by μ, we have (e*cos(wx) + ew*sin(wx))*dx + e²*dy = 0.

Next, we check if the equation is exact after multiplying by the integrating factor. The partial derivatives ∂(e*cos(wx) + ew*sin(wx))/∂y and ∂(e²)/∂x are equal, so the equation is exact.

Integrating the first term with respect to x gives ∫(e*cos(wx) + ew*sin(wx))dx = e*sin(wx) + C(y), where C(y) is the constant of integration with respect to x.

Therefore, the general solution to the differential equation is e*sin(wx) + (1/3)*e³ + K = 0.

The corresponding particular solution is e*sin(wx) - (1/3)*e³ - 5 = 0.

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Answer:

The probability P that she selects a romance movie at random fromthe shelf is;

Explanation:

Given that;

On Dora's shelf are the following movies:

Adventure movies ---- 4

drama movies ----------6

romance movies-------6

Total number of movies = 4+6+6=16

So, the probability P that she selects a romance movie at random fromthe shelf is;

In reduced fraction, The probability P that she selects a romance movie at random fromthe shelf is;

The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

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The frequency of a class is the number of data points that fall within the class is 1.

To determine the frequency of each class in the table shown, we must first divide the data points into the respective classes. The classes are 1003, 1062, 1063, 1122, 1123, 1182, 1183, 1242, 1243, 1302, 1303, and 1362.

For the class 1003, the frequency is 1, since there is only one data point (1003) in this class.

For the class 1062, the frequency is also 1 since there is only one data point (1062) in this class.

For the class 1063, the frequency is also 1 since there is only one data point (1063) in this class.

For the class 1122, the frequency is 1 since there is only one data point (1122) in this class.

For the class 1123, the frequency is 1 since there is only one data point (1123) in this class.

For the class 1182, the frequency is 1 since there is only one data point (1182) in this class.

For the class 1183, the frequency is 1 since there is only one data point (1183) in this class.

For the class 1242, the frequency is 1 since there is only one data point (1242) in this class.

For the class 1243, the frequency is 1 since there is only one data point (1243) in this class.

For the class 1302, the frequency is 1 since there is only one data point (1302) in this class.

For the class 1303, the frequency is 1 since there is only one data point (1303) in this class.

For the class 1362, the frequency is 1 since there is only one data point (1362) in this class.

Therefore, the frequency of each class in the table shown is 1.

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To determine the degree of a polynomial function given in factored form, a good first step is to count the highest power of the variable in the factored expression.

In factored form, a polynomial function is expressed as the product of linear factors or irreducible quadratic factors.

Each factor represents a root or zero of the function.

The degree of a polynomial is determined by the highest power of the variable in the expression.

To find the degree of the function, examine each factor in the factored form.

For linear factors, the degree is 1 since the highest power of the variable is 1.

For irreducible quadratic factors, the degree is 2 since the highest power of the variable is 2.

By observing the highest power in the factored expression, you can determine the degree of the polynomial function.

If the highest power is 1, the polynomial has a degree of 1 (linear function). If the highest power is 2, the polynomial has a degree of 2 (quadratic function). And so on.

It's important to note that the degree of a polynomial corresponds to the highest power of the variable in the expression and not the number of factors.

The number of factors indicates the number of roots or zeros of the polynomial, but it doesn't determine the degree.

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Answer:

Least common denominator = L.CM. of 7 and 10

Therefore, least common denominator = 7 x 10 = 70.

Hope it helps you :D

2/7 and 3/10 fractions have a Least Common Denominator of 70.

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

We have to determine the Least Common Denominator of fractions 2/7 and 3/10.

We need to calculate the factors of the denominators 7 and 10

⇒ 7 = 7 × 1

⇒ 10 = 5 × 2 × 1

The LCD would be:

⇒ 7 × 5 × 2 × 1 = 70

Hence, 2/7 and 3/10 fractions have a Least Common Denominator of 70.

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The volume of the composite figure with a pentagon as its base is equal to 385.5 cubic inches.

Volume of prism = area of base × height

area of pentagon base = 1/2 × apothem × perimeter

apothem = 5in/[2×tan(180/5)] = 3.4 in

perimeter = 5 × 5in = 25 in

area of pentagon base = 1/2 × 3.4 in × 25 in = 42.5 in²

Volume of the top triangular prism = 42.5in² × 3in = 127.5 in³

Volume of pentagon base prism = 42.5in² × 6in = 255 in³

Volume of the composite figure = 127.5 in³ + 255 in³

Volume of the composite figure = 382.5 in³

Therefore, the volume of the composite figure with a pentagon as its base is equal to 385.5 cubic inches.

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the focus of all points Y that occur as midpoints of segments PX, where X lies on the given circle, is a circle with radius half of the original circle (R/2) and its center located at the midpoint M of segment OP.

Given a circle centered at point O and an arbitrary point P, let's consider the focus of all points Y that occur as midpoints of segments PX, where X lies on the given circle.
To show that this focus is a circle with radius half of the original circle, let's first analyze the properties of the midpoint Y. By definition, Y is the midpoint of segment PX, so PY = YX.
Let the radius of the original circle be R, and let OP = d. Using the law of cosines, we can derive the distance between X and P as follows:

PX² = OP² + OX² - 2(OP)(OX)cos∠POX.

Since OX = R, OP = d, and ∠POX = θ, we have:

PX² = d² + R² - 2dRcosθ.

Now, let's consider the distance between Y and P. Since Y is the midpoint of segment PX, we have:

PY² = (1/2PX)² = (1/4)(d² + R² - 2dRcosθ).

Now, let's find the locus of Y. To do so, we will fix the distance PY and let the angle θ vary. The locus of Y will be the set of all points equidistant from P with distance (1/2)PX. This forms a circle centered at a point M with radius half of the original circle (R/2).

To locate the center M of the locus, let's consider the midpoint of segment OP. Since Y lies on the line segment PX, and Y is the midpoint of PX, the locus of Y will be the set of all points equidistant from the midpoint of segment OP. This forms a circle centered at point M, where M is the midpoint of segment OP.

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Answer:

C-$5.00 per ticket

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

$75.00 / 15 = $5

Each ticket costs $5

We must first obtain the number in order to obtain the fraction. You can find the number by using an algebraic expression. The fraction is \(\frac{12}{30}\).

A fraction is a piece of the entire. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction contains a fraction. In mathematics, there are three different types of fractions. Proper fractions, wrong fractions, and mixed fractions are the three types that exist. Fractions are defined by their numerator and denominator terms. In the context of these two words, we describe its types.

Given fraction \(\frac{2}{5}\)

Let numerator is \(n\)

The denominator is \((n+18)\) and the numerator is \(18\) less, the fraction is \(\frac{n}{n+18}\)

To determine the answer, write the algebraic expression in the form of the question.

\(\frac{n}{n+18}=\frac{2}{5}\\n=12\)

Calculate the fraction.

\(\frac{n}{n+18}=\frac{12}{12+18}\\\frac{n}{n+18}=\frac{12}{30}\)

As a result, the fraction is \(\frac{12}{30}\)

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Answer:

0.56

it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%

The correct option (b) Negative skewness. it refers to longer or fatter tail on left side of the distribution.

Negative skewness is a type of distribution in which there are more values ​​to the left of the mean than to the right. it refers that mean > median and the tail of the distribution is on the left. This type of distribution is also referred to as left lean.

Negative skewness is caused by the presence of extreme values ​​or outliers on the left side of the distribution. All these extreme values ​​can cause the data to deviate from the mean that results in negative deviation. The presence of outliers can affect the variance of the data too. In the situations with high outliers, as  the outliers form the mean of most of the data therefore, the variance of data is higher than the normal.

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The steps for constructing the bisector of an angle by using a ruler and compasses are as follows:

Step 1:

Take a compass and place its point on the angle's vertex Q.

Step 2:

Adjust the compass to the medium wide setting. The exact width is not important.

Step 3:

Without changing the compasses' width, draw an arc across each leg of the angle.

Step 4:

Now, place the compass on the point where one arc crosses a leg and draw the arc in the interior of the angle.

Step 5:

Without changing the compass setting repeat for the other leg so that the two arcs cross.

Step 6:

Now by using a ruler draw a line from the vertex to the point where the arcs cross.

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For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.

Properties of circumcenter of triangle are:

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Answer:

7 x 2 + 3 = 17

7 - 2 + 3= 8

14 ÷ 2 + 3 = 10

14 ÷ 7 - 3  - 1

Step-by-step explanation:

The data being skewed and indicating higher wait times above 7 minutes due to a busy park is the most suitable description based on the given line plot.

The best description of the shape of the data is that it is skewed and might mean that the wait times were higher than 7 minutes because the park was busy.

Here's the explanation:

From the line plot, we can observe that there are 6 dots above 6, 5 dots above 7, 3 dots above 5, and 2 dots above 8.

The distribution is not symmetric, as the data points are not evenly spread around a central value.

The fact that there are more dots above 7 and 8 suggests that the wait times were higher than these values for a significant number of rides. This skewness in the data indicates that there were instances of longer wait times.

Additionally, the presence of dots above 5 and 6 suggests that there were some rides with shorter wait times as well.

However, the higher concentration of dots above 7 and 8 indicates that the park was likely busy, leading to longer wait times.

The option stating that the data is skewed and might mean that the wait times were higher than 7 minutes because the park was busy best aligns with the information provided by the line plot.

It acknowledges the skewness of the data towards higher wait times, suggesting that the park experienced increased demand and longer queues during the fair.

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The equation y = 2x² - 12x + 23 describes the function graph that includes a vertex at (3, 5) and passes through the point (5, 13).

The vertex of a parabolic equation is at the point and the vertex form is y = a(x - h)2 + k, where a, h, and k are constants (h, k).

Find the function whose graph has the vertex at (3, 5) and passes through the point in the question (5, 13).

Assuming it to be a parabolic function, we know that a parabolic equation's vertex form is y = a(x - h)2 + k, where a, h, and k are constants, and the vertex is located at the position (h, k).

As the vertex of the necessary function is at the position (3, 5), we may substitute h = 3 and k = 5 to obtain the following equation in the above equation:

y = a(x - 3)² + 5

Now that we know that the graph passes through the point (5, 13), we can change the original equation to read:

13 = a(5 - 3)² + 5,

or, 13 = 4a + 5,

or, 4a = 13 - 5 = 8,

or, a = 2.

We obtain the following from the equation y = a(x - h)2 + k by inserting a = 2, h = 3, and k = 5:

y = 2(x - 3)² + 5,

alternatively, y = 2(x² - 6x + 9) + 5,

alternatively, y = 2x² - 12x + 18 + 5,

Alternatively, y = 2x² - 12x + 23.

As a result, the function graph with the vertex at (3, 5) and the point of intersection (5, 13) yields the equation y = 2x² - 12x + 23.

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Answer:

-6, -5 ,-3 ,-1 ,1 ,4

Answer:

x = 32

Step-by-step explanation:

2x+1 + x-7 = 90

3x - 6 = 90

3x = 96

x = 32

The measure of the angle of x is 69.

In order to find the measure of one angle, given the measure of the other angle on the same straight line, you must use the relationship between the angles.

When two angles are on the same line and adjacent, they must add up to 180 degrees. This means that the two angles, x degrees and (2x-27) degrees, must add up to 180 degrees. We can use this to solve for x. We can set up an equation to represent this relationship:

x + (2x - 27) = 180

We can now use the distributive property to solve for x.

3x - 27 = 180

Adding 27 to both sides of the equation, we get:

3x = 207

Dividing both sides of the equation by 3, we get:

x = 69

Therefore, the measure of the angle is x = 69 degrees.

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Complete Question:

The measures of two adjacent angles on a straight line are x degrees and (2x-27) degrees. Find x

Answer:105 i believe so

Step-by-step explanation:

Answer:

105 members

Step-by-step explanation:

\(1.25 \times 84 = 105\)

Jill will have approximately $394,881.39 in her account when she reaches the age of 65.

To calculate the amount Jill will have in her account when she reaches the age of 65, we can use the formula for the future value of a series of monthly deposits compounded monthly.

Let's break down the given information:

- Jill deposited $300 at the end of each month from age 25 to 40, which means there are 15 years (40 - 25) of monthly deposits.

- The interest rate is 6% per year, compounded monthly. To calculate the monthly interest rate, we divide the annual interest rate by 12 and express it as a decimal. Therefore, the monthly interest rate is (6/12)/100 = 0.005.

Using the formula for the future value of a series of monthly deposits:

Future Value = Monthly Deposit * [((1 + Monthly Interest Rate)^(Number of Months) - 1) / Monthly Interest Rate]

Let's plug in the values:

Monthly Deposit = $300

Monthly Interest Rate = 0.005

Number of Months = 15 * 12 = 180 (15 years * 12 months/year)

Future Value = $300 * [((1 + 0.005)¹⁸⁰ - 1) / 0.005]

Calculating this expression will give us the future value of Jill's retirement account at age 65.

Future Value ≈ $394,881.39

Therefore, Jill will have approximately $394,881.39 in her account when she reaches the age of 65.

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