Think of 5 positive integers that have a
mode of 3 and 4, a median of 4 and a
mean of 6.

Must assume positive values

f is above this line outside [a, b]

So,  f(x)f′′(x)<0 cannot hold for all x.

Given,

In the question:

Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x.

Now, According to the question:

Assume that :

f"(0) > 0

Then, f(0) < 0 and as neither factor can change sign.

f"(x) > 0 > f(x) for all x ∈ R and f is strictly convex.

Pick a < b with f(a) ≠ f(b).

Then the line through (a f(b)) and (b f(b)) intersect the x - axis.

By convexity, f is above this line outside [a, b],

Hence, Must assume positive values

f is above this line outside [a, b],

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By defining the SAS theorem of congruency, we have proved that SAS is congruent.

Congruency;-

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Here,

We have to prove that SAS is congruent.

For that, lets consider the SAS theorem of congruence,

According to the side-angle-side (SAS) theorem of congruence, two triangles are congruent if their corresponding two sides and their included angles are precisely equivalent to those of the first triangle.

That is,

We proved by the definition SAS is congruent

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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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x=1, -29+√337/2 and -29-√337/2 are zeros of function f(x)=x²-3x³-27x² - 13x +42

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

We need to find zeros of f(x)=x²-3x³-27x² - 13x +42

f(x)=-3x³-26x²-13x+42

Use division method

1   -3    -26   -13     42

    0      -3     -29   -42

    -3     -29   -42     0

-3x²-42x-42=0

x=1 is a zero

Now use the quadratic formula to find zeros

x=42±√(42)²-4(-3)(-42)/-6

x=-29+√337/2

and x=-29-√337/2

Hence, x=1, -29+√337/2 and -29-√337/2 are zeros of function f(x)=x²-3x³-27x² - 13x +42

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Answer:

-3,-2,1,7

Step-by-step explanation:

That's what Acellus said it was <3

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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Imani uses less flour in her cookies than Vic because vic uses 25 / 17 g of flour while Imani uses 25 / 21 g of flour.

How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.

A substance's density is a measurement of how heavy it is in relation to its size. When placed in water, an object will float if its density is lower than that of the water, whereas it will sink if its density is higher.

if we see Vic's recipe:

170 g of butter = 250 g of flour

1 g of butter = 250 ÷ 170

= 25 / 17 g of flour

and Imani's recipe:

630 g of butter = 750 g of flour

1 g of butter = 750 ÷ 630 = 25 / 21 g of flour

Compare:

25 / 21 < 25 / 17

so Imani uses less flour in her cookies than Vic

moreover imani's cookies are more dense.

Therefore, we get that Vic uses more flour than imani.

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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.

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.

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

Step-by-step explanation:

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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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]

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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Categorical data are the sort of variable that would need utilizing a population proportion hypothesis test rather than a population mean hypothesis test.

Data that cannot be easily gathered by counting is referred to as categorical data, which is another name for qualitative data. Hypothesis testing may be used with this type of data. Data are used in hypothesis testing to draw conclusions about population characteristics.

The findings are reached after first proposing a null hypothesis. Therefore, for qualitative or categorical data, a hypothesis test of the population is performed rather than a numerical test of the population mean.

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The equation of a line passing through the point (a,0) and parallel to the y-axis is x = a

The equation of line parallel to y axis is of the form x = a, and it cuts the x-axis at the point (a, 0). Here all the points on this line parallel to the y-axis will have the same x coordinate of a. Further the equation of line parallel to y-axis and cutting the x-axis at point (a, 0) is at a perpendicular distance of 'a' units from the y-axis

The equation of line parallel to the y axis and cutting the positive x-axis passes through the first and the fourth quadrant. And the equation of line parallel to the y axis and cutting the negative x-axis passes through the second and the third quadrant of the coordinate axes.

To find the equation of line passing through the point and parallel to y-axis:

Let Line cut the x-axis at point a .

So , the equation of line will be x = a

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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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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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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!

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 speed of bullet just before the impact would be 1.28 x 10^3 meter per second.

Let the speed of the bullet before impact be 'V₀.'

According to the question, we are given the mass of the rod 'M' = 4 kg. Length of the rod 'l' = 0.5 meter. The angle of the bullet's path 'Θ' = 60 degree and the angular velocity 'ω' = 10 rad/s.

   For bullet, the mass 'M' = 3 g = 3 x 10^3 kg. and the velocity is V₀.

  According to the law of conservation of momentum, we get

L(bullet) = l (bullet + rod)

mV₀ (l/2 sinΘ) = Iω

mV₀ x (l/2 sinΘ) = [ ml²/ 12 + m (l/2) ²] x ω

By cancelling the like terms, we get the equation as,

V₀ = (m +3m) x l/6m sin Θ

  By calculating the above equation, we get,

V₀ = 1.28 x 10^3 meter per second.

  Therefore, the speed of bullet before the impact is 1.28 x 10^3 meter per second.

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Answer:

12

Step-by-step explanation:

Number of outcomes for a coin = 2

Number of outcomes of a die = 6

2*6 = 12

Some calculations of degrees of freedom with multiple number of parameters or relationships use the formula

Df = N - P,

where P is the number of different parameters or relationships.

For example, in a 2-sample t-test, N - 2 is used because there are two parameters to estimate.

What Are Degrees of Freedom?

The formula to determine degrees of freedom is:

Df = N − 1

where:

Df =degrees of freedom

N=sample size

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