Which formula should be used to correctly calculate the monthly mortgage payment? m = p startfraction left-bracket r (1 minus r) superscript n baseline right-bracket over (1 r) superscript n baseline endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction r over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over (n r) endfraction

According to the given condition, for 8181 values of n, q + r is divisible by 11.

What does division algorithm states?

The division algorithm for integers states that given any two integers a and b, with b > 0, we can find integers q and r such that 0 < r < b and

a = bq + r.

According to the given question:

q + r  is divisible by 11 if and only if N is divisible by 11. This is because their difference is divisible by 11:

N − (q + r) = 100q + r − q − r = 99q = 11 x (9 x q) . So what you're asking is how many 5 -digit numbers are divisible by 11.

The first such number is  10010 = 910 x 11 because  ⌈10000/11⌉=910 .

The last such number is  99990 = 9090 x 11 because  ⌊100000/11⌋=9090 .

Therefore, in total there are 9090 – 910 + 1 = 8181 such numbers.

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The ratio of the depth of the liquid to the depth of the cup is 4/5.

Geometry and Ratio

The formula for the volume of a cone is:

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

where r is the radius of the base of the cone and h is the height of the cone.

When the conical cup is filled with water, there will be a difference in the radius of the water and the cup and a difference in the height of the water and the height of the cup (can be seen in the picture).

From the difference in radius and height of the water with the conical cup, a ratio can be made of similarity rule of triangle (see picture).

If the radius of water is [tex]r_{1}[/tex] and the height of water is [tex]h_{1}[/tex], radius of cup is [tex]r_{2}[/tex] and the height of cup is [tex]h_{2}[/tex], so:

[tex]\frac{r_{1} }{r_{2} } =\frac{h_{1} }{h_{2} }[/tex]

[tex]r_{1}[/tex] with [tex]r_{2}[/tex] and  [tex]h_{1}[/tex] with  [tex]h_{2}[/tex] have the same certain ratio. Let's assume the ratio is x, then it can be written:

[tex]r_{2}=x.r_{1} \\h_{2}=x.h_{1}[/tex]

The ratio of the volume of water to the volume of the conical cup is 64/125, meaning that 64 of the water in the conical cup with a volume of 125.

From here we can substitute it in the volume ratio:

[tex]\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi r_{2}^{2}h_{2}} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi (xr_{1})^{2}(x.h_{1})} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3}\pi r_{1}^{2}h_{1}x^{3} } =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{1}{x^{3}}=\frac{64}{125}\\ \frac{1}{x^{3}}=\frac{64}{125}\\\\x^{3}=\frac{125}{64} \\x=\frac{5}{4}[/tex]

The ratio between the radius and height of the cup and the water is 5/4. This means that the ratio between the radius and height of the water and the cup is 4/5.

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Answer:

1. Distribute

2. Combine like terms

3. Get all variable on one side and everything else on the other (Inverse operations: Add / subtract)

4. Solve for one of your variables (inverse operation: Multiple / Division

5. Simplify

Answer:

Step-by-step explanation:

6m+15=36-m

Plus m to both sides

7m+15=36

Minus 15 from both sides

7m=14

Divide by 2

m=2

Answer:

[tex]\huge\boxed{\sf x = \frac{y-14}{428} }[/tex]

Step-by-step explanation:

428x + 14 = y

Subtract 14 to both sides

428x = y - 14

Divide 428 to both sides

[tex]\displaystyle \boxed {x = \frac{y-14}{428} }[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

x = [tex]\frac{y-14}{428}[/tex]

Step-by-step explanation:

428x + 14 = y ( subtract 14 from both sides )

428x = y - 14 ( divide both sides by 428 )

x = [tex]\frac{y-14}{428}[/tex]

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\pounds 679\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3\\ \end{cases} \\\\\\ A=679(1 - 0.04)^{3} \implies A=679(0.96)^3\implies A \approx 600.74[/tex]

The value of the phone after 3 years is equal to £600.73

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, the present value of the phone is £679 and we are required to find the future value of the phone after 3 years when it depreciates every year by 4%

thus, FV= £679 × (1-4%)³

             =  £679 × 0.96³

             = £600.73

Hence The value of the phone after 3 years is equal to £600.73

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While the midpoints of a sides of a rectangle having area $a$ are united to produce a triangle with size $m$, the area of a new triangle equals $frac14$ the area of a original triangle.

A "area" is the size or length of an a double surface, which is frequently measured in square units. It is employed to describe a shape's or object's size, such as the length, width, or height of a side, a bit of land, or even a geometrical figure. By dividing a form's length by its breadth, the area of the form may be calculated. For instance, a rectangle with dimensions of 5 units in length and 3 units in width has a surface area of 15 square units. The area of a circle is calculated using the formula r2, wherein r is the ring's radius. A fundamental geometric concept known as "area" has several applications in the sectors of construction, real estate, and horticulture.

Assume that the original triangle has sides that are s1, s2, and s3. The triangle's area when the side's midpoints are united is [m=frac s 1s 2s 3 16]. This happens because the new triangle's area is $frac14$ the size of a original triangle since each side of a new triangle being half as long as the equivalent side of the old triangle.

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The number of sweets that Dave have equals to 18 sweets.

In mathematics, a ratio is a metric that shows how many times one number contains another. For instance, if we have 8 oranges and 6 lemons in a bowl of fruit, then, the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.

Given data

Dave and martin ratio = 2:3

Dave is given 15 sweets.

The number of sweets that dave have now is computed as follows:

2/5 = 0.4= 40%

3/5 = 0.6 = 60%

Dave sweets will equals to:

= 15 sweets + (15 sweets * 1/5)

= 15 sweets + 3 sweets

= 18 sweets.

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3x² - 7x + 9 is x² - 11x + 17 less than 2x² + 4x - 8.

The value of the expression, x² - 11x + 17, when x = 2 is: -1.

To find the value of an expression, simply replace the given value of the variable and solve to simplify.

To find how much less the expression, 3x² - 7x + 9 is less than 2x² + 4x - 8, subtract 2x² + 4x - 8 from 3x² - 7x + 9:

(3x² - 7x + 9) - (2x² + 4x - 8)

3x² - 7x + 9 - 2x² - 4x + 8

Combine like terms

x² - 11x + 17

Substitute x = 2 into the expression:

2² - 11(2) + 17

= -1.

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There is the not sufficient evidence that the average small business loan is different that the amount stated in the  investment blog.

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Here we have given that,

Claim: To check whether the average small business loan is different that the amount stated in the  investment blog.

The hypothesis is,

H0: μ= 20 thousand dollars  Versus  H0: μ ≠ 20 thousand dollars

We have given that,

n= Number of observation = 25

x bar  = sample mean =18.5

S= sample standard deviation =5

Here, population standard deviation is unknown, we use the one sample t test.

t - statistics = (x bar - μ) / (s / √n)

                   = (18.5 - 20) / (5 / √25)

                   = -1.342

we get,

the Test statistic is -1.342

Now we find the P-value

α = level of significance = 0.05

Degrees of freedom = n - 1 = 25 - 1 = 24

This is two tailed test as our interest is to show the population mean is equal or not equal to zero.

Now, we can find the P-value

P-value = 0.1922     Using EXCEL = TDIST( | t-statistics | = 1.342 , D.F=24, tail=2)

Hence, There is the not sufficient evidence that the average small business loan is different that the amount stated in the investment blog.

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Answer:

SSS: Side-Side-Side

AAS: Angle-Angle-Side

SAS: Side-Angle-Side

ASA: Angle-Side-Angle

Step-by-step explanation:

These are all used for triangles and proofs :)

The standard deviation of the data represented is 4.

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

From the question, We were given the terms,

4 8 12 24

The number of terms=5

We will obtain the mean value and then calculate the square of the difference between each term and the mean.

The mean=Sum of terms/Number of terms

Mean=(4+8+10+12+16)/5

=50/5

=10

Now, the difference between terms and the mean is as follows:

4-10= -6

8-10= -2

10-10=0

12-10=2

16-10=6

Squaring the obtained values and adding them,

=36+4+4+36

=80

The standard deviation of the terms=

Square root of the sum of squares of values divided by the number of terms

[tex]\sqrt{80/5}[/tex]

[tex]\sqrt{16}[/tex]

4

Hence the standard deviation is 4.

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The slope of line 2 is -2/9, The lines have the same slope & the two lines are parallel.

To find out whether the lines through the given points are parallel, perpendicular, or neither:

The slope of a line is calculated as:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

The slope of line 1 is:

[tex]m_1 = \frac{9-5}{-8-10} \\\\m_1 = \frac{4}{-18} \\\\m_1 = -\frac{2}{9}[/tex]

Hence, the slope of line 1 is -2/9.

The slope of line 2 is:

[tex]m_1 = \frac{-6--4}{11-2} \\\\m_1 = \frac{-2}{9} \\\\m_1 = -\frac{2}{9}[/tex]

Hence, the slope of line 2 is -2/9.

Hence the answer is, the slope of line 2 is -2/9, The lines have the same slope & the two lines are parallel.

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Rolle's Theorem can be applied on [tex]-x^2 + 9x[/tex] on [0, 9]

What is Rolle's Theorem?

Rolle's Theorem states that

1) If f is continuous on [a, b]

2) f is differentiable on (a, b)

3) f(a) = f(b)

Then there exist a point c in (a, b) such that [tex]f^{'}(c) = 0[/tex]

Here, f(x) = [tex]-x^2 + 9x[/tex]

f is continuous on [0, 9] as it is a polynomial function.

f is differentiable on (0, 9)

f(0) = [tex]-0^2+9\times 0 = 0[/tex]

f(9) = [tex]-9^2+9 \times 9 = 0[/tex]

f(0) = f(9)

So Rolle's Theorem has been applied here

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Taylor has to pay 0.7875 ounces for the macadamia nut.

What is the rule of multiplication?

If a, b, and c are three numbers given to us and any expression is expressed as [tex]a\frac{b}{c}[/tex] then it can be expressed as

                          [tex]a\frac{b}{c}[/tex]  = [tex]\frac{a*c + b}{b}[/tex]

It is given that, Taylor measures out [tex]1\frac{3}{4}[/tex] of macadamia nut.

                          [tex]1\frac{3}{4} = \frac{1*4 + 3}{4}\\\\ 1\frac{3}{4} = \frac{7}{4}[/tex]

                               = 1.75  macadamia nut.

Per ounce is at 0.45

then 1.75 macadamia nuts will cost her = 1.75 * 0.45

                                                                = 0.7875 ounces.

Hence, Taylor has to pay 0.7875 ounces for the macadamia nut.

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When one or more of the activities that make up each business's value chain offer chances for cross-business cooperation to develop important new resource strengths and competitive capabilities, there is a strategic fit between the firms.

Given,

Strategic fit between two or more businesses exists when one or more activities comprising their respective value chains present opportunities:

We have to find the correct definition from the options given;

Strategic Fit;-

The degree to which a business is aligning its resources and talents with the opportunities in the external environment is expressed by its strategic fit. The organization must therefore have the actual resources and competencies to implement and support the plan because the matching is done through strategy.

Here,

The correct answer is Option D;- For cross-business collaboration to build valuable new resource strengths and competitive capabilities

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Question is incomplete. Completed question is given below;

Strategic fit between two or more businesses exists when one or more activities comprising their respective value chains present opportunities:

A. to prevent the transfer of expertise or technology or capabilities from one business to another.

B. to independently preserve common brand names from cross-business usage.

C. to increase costs by combining the performance of the related value chain activities of different businesses.

D. for cross-business collaboration to build valuable new resource strengths and competitive capabilities.

E. to maintain business value chain activities separate and apart from one business to another to protect company independence.

Answer:

12

Step-by-step explanation:

Number of outcomes for a coin = 2

Number of outcomes of a die = 6

2*6 = 12

The fewest number of bags DeShawn must buy to cover Field A is 6.5 bags.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r², (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area. Area of a circle is equal to r² or d²/4, where = 22/7 or 3.14. A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given,

DeShawn needs grass seed to cover Field A. One bag of grass seed covers `5000` square feet.

Field A is a circular field with a `100`-foot radius.

Area of circular field:

Area = πr²

Where r = 100

Area = 3.14 × 100²

Area = 31400 square feet

Each bag seeds cover 5000 square feet,

So, dividing area by 5000

5000÷ 31400

6.28

The fewest number of bags DeShawn must buy to cover Field A is 6.5 bags.

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When the start fraction is 1 and the end fraction is 27, the value is a=-11/3.

A fraction is a part of a whole or, more broadly, any number of equal parts. In ordinary English, a fraction describes the number of components of a specific size and consists of a numerator displayed above a line (or before a slash like 12) and a non-zero denominator displayed below (or after) that line.

In addition to common fractions, numerators and denominators are used in rare fractions such as compound fractions, complex fractions, and mixed numerals.

Positive common fractions have natural integers as their numerator and denominator.

Here we need to find the value of n for which 9=(1/27)ᵃ⁺³

Now, we have to rewrite with a base of 3 we get,

3²=3⁻³.3ᵃ⁺³

2=-3(a+3)

2=-3a-9

=2+9=-3a

11=-3a

a=-11/3

Therefore, the values is a=-11/3

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Answer:

triangle

Step-by-step explanation:

a quadrilateral is a four-sided figure, but a triangle is three-sided, so a triangle isn't a quadrilateral.

The correct scenario represented by this graph will be;

''The temperature in Lanie's backyard drops steadily over time as a cold front moves in. The x-axis represents time; the y-axis represents the temperature.''

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph is shown in figure.

Now,

Let the x-axis represents time and the y-axis represents the temperature.

So, We can say that;

The temperature in Lanie's backyard drops steadily over time as a cold front moves in.

Thus, The correct scenario represented by this graph will be;

''The temperature in Lanie's backyard drops steadily over time as a cold front moves in. The x-axis represents time; the y-axis represents the temperature.''

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Quadratic functions are one type of non linear function.

Given,

We have to find whether quadratic function non-linear;

The graph is not a straight line if it is non-linear. A non-linear function has a curved line as its graph. A line that continuously changes in direction is said to be curved.

These are the so-called nonlinear functions, and they can take many various shapes. A quadratic function is one of these nonlinear functions, and its typical form is y = ax2 + bx + c. A parabola represents the graph of a quadratic function.

Therefore,

Quadratic functions are one type of non linear function.

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Answer: 7*[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

70 x 4

Step-by-step explanation:

To round to one significant figure we have to round each numbers to the first numbers greater than 0

To round 74.5 to 1sf we have to round it to the nearest 10. As the number next to it (4) is less than 5 we will round down to 70

To round 3.6 to 1sf we have to round to the nearest whole number. As the number next to it (6) is greater than 5 we will round up to 4

Hope this helps, have a great day!

The required value Z = 11.792 >1.96 at a 0.05 level of significance.,he null hypothesis is rejected,the alternative hypothesis is accepted at a 0.05 level of significance.

As the mean weight is less than 16 ounces.

Given that the mean of the Population = 16

Given that the standard deviation of the process

σ = 0.03 ounce

Given that the mean of the sample = 16.05 ounces

Null hypothesis: H₀:μ > 16 ounces

Alternative HypothesisH₁: μ <16 ounces

    Z = x-mean/SD/√n      

    Z = 16.05-16/0.03/√50

    Z =  11.792

Level of significance = 0.05

Z₀.₀₅ = 1.96

The required Z = 11.792 >1.96 at 0.05 significant level,null hypothesis is rejected and alternate hypothesis is accepted.

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The slope of the line in the simplest form is 1 / 2.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

The slope is rise over run.

The slope of the line can be found as follows:

m = slope = y₂ - y₁ / x₂ - x₁

Therefore, using (7, 0) and (3, -2)

Hence,

x₁ = 7

x₂ = 3

y₁ = 0

y₂ = -2

Therefore,

slope = - 2 - 0 / 3 - 7

slope = - 2 / -4

slope = 1 / 2

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Line y=6x−2 and line 6y=−x are perpendicular.

Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.

In the equation of line y=mx+c, m represents the slope of the line.

The given lines are

a: y=6x−2           (1)

b: 6y= -x            (2)

and c: y+6x=1     (3)

To determine lines are parallel or perpendicular,

Find the slope of the lines, use the standard equation of line is y=mx+c,

Compare the given equations with standard equation of line,

Slope of line (1) m₁= 6

Slope of line (2) m₂ = -1/6

Slope of line (3) m₃ = -6

By multiplying slope of line (1) and (2), gives -1

Implies that line (1) and (2) are perpendicular to each other.

Therefore, Line y=6x−2 and line 6y=−x are perpendicular.

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The central angle theorem states the ratio of arc length and its radius.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its centre. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the centre of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's centre subtends is known as the central angle.

According to the central angle theorem, we state that:

Theorem: An arc's angle at the circle's centre is twice as large as its angle at any other point along the circle's circumference.

OR

According to the central angle theorem, the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the centre of the circle.

Hence,

The central angle theorem states the ratio of arc length and its radius.

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A system of linear equations is a collection of two or more linear equations that have two or more variables each. All of these equations are considered at once.

Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations. There could be an unlimited number of solutions for some linear systems, whereas others might not have any. There must be at least as many equations as there are variables for a linear system to have a singular solution. However, this does not ensure an original answer. There is always one answer to a set of equations that makes sense. A consistent system, like the one we just examined, is said to be an independent system if it only has one solution. The two lines cross at one location in the plane and have different slopes. If the equations' slopes and y-intercepts match, the system is said to be consistent and considered a dependent system.

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