A rectangular picture is 7 inches by 5 inches and has a border of uniform width surrounding it. If the area of the picture and the border is 80 square inches find the width of the border

The measure of HI based on the given diagram is 70 units.

A triangle mid segment is the line joining the midpoint of any two sides of the triangle which is parallel to the third side and is also half of the length of the third side.

HI = 3x + 5

EF = -3x + 55

So,

HI = 1/2(EF)

3x + 5 = 1/2(-3x + 55)

3x + 5 = (-3x + 55) / 2

cross product

2(3x + 5) = -3x + 55

open parenthesis

6x + 10 = - 3x + 55

6x + 3x = 55 - 10

9x = 45

divide both sides by 9

x = 45/9

x = 5

Therefore, the measure of HI and EF are;

HI = 3x + 5

= 3(5) + 55

= 15 + 55

= 70

EF = -3x + 55

= -3(5) + 55

= -15 + 55

= 40

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(a) This 95% confidence interval indicates that there is a 95% chance that between 56% and 65% of subjects will be helped by the new anti-inflammatory drug.

(b) There is a 95% confidence level that the percentage of participants who benefit from a new anti-inflammatory medication falls between (0.56, 0.65).

(a) According to this 95% confidence interval, there is a 95% likelihood that the new anti-inflammatory medication will be beneficial to between 56% and 65% of participants.

(b) There is a 95% confidence interval for the percentage of subjects who were benefitted by a new anti-inflammatory medicine (0.56, 0.65).

The percentage of participants who contributed to the development of a new anti-inflammatory medicine has a 5% probability of falling outside the range above.

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Answer:

To find the annual growth rate percentage, we can use the formula:

annual growth rate = [(final value / initial value)^(1/number of years)] - 1

where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.

Using the given values, we have:

annual growth rate = [(148,000 / 108,000)^(1/20)] - 1

= 0.0226 or 2.26%

So the house appreciated at an annual growth rate of 2.26%.

To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:

value in 2010 = 148,000 * (1 + 0.0226)^5

= $175,465.11 (rounded to the nearest cent)

Therefore, the value of the house in the year 2010 was $175,465.11.

Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features.

When a researcher wants to report the average cost of college tuition from the 1950s until present time, descriptive statistics are the appropriate method to use. Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features. By using descriptive statistics, the researcher can calculate measures of central tendency, such as the mean, median, and mode, to determine the typical or average cost of college tuition over time. Additionally, measures of variability, such as the range and standard deviation, can be calculated to understand the spread of the data. Descriptive statistics are commonly used in many fields, including business, economics, psychology, and education, and can provide valuable insights into trends, patterns, and distributions within a dataset.

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Increasing the probability of a type I error generally leads to a decrease in the probability of a type II error, and vice versa.

If your data have statistical significance, this suggests that even if the null hypothesis is correct, they are extremely improbable to occur. You would then reject your null hypothesis in this situation. Yet occasionally, this may be a Type I mistake.

If your results are not statistically significant, the null hypothesis is likely to be correct and they have a high probability of occurring. As a result, your null hypothesis is not rejected. Yet occasionally, this may be a Type II mistake.

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The lowest frequency the tuba can produce is approximately 49 Hz.

The lowest frequency produced by the tuba is called its fundamental frequency, which corresponds to the longest wavelength that can fit in the tube. The wavelength of a sound wave is related to its frequency and the speed of sound by the equation

wavelength = speed of sound / frequency

In this case, the effective length of the tube is equal to half of the wavelength of the fundamental frequency (because the tube is open at one end and closed at the other), so we can write

wavelength = 2 × effective length = 7.00 m

Solving for the frequency using the above equation, we get

frequency = speed of sound / wavelength = 343 m/s / 7.00 m ≈ 49 Hz

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The equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).

To discover the equation of the tangent line to the curve sin( x y) = 8x- 8y on the point( π, π), we want to apply implicit differentiation to discover the pitch of the tangent line at that point.

We begin through differencing both sides of the equation with reference to xcos( x y)( 1 dy/ dx) = eight- 8dy/ dx

After, we can simplify the expression by isolating the terms beholding dy/ dx on one aspect

cos( x y) cos( x y) dy/ dx = 8- 8dy/ dx

8 cos( x y)) dy/ dx = 8- cos( x y)

dy/ dx = ( 8- cos( x y))( 8 cos( x y))

Now we're suitable to discover the pitch of the tangent line at the factor( π, π) by plugging in x = π and y = π into the expression we simply derived

dy/ dx = ( 8- cos( 2π))( 8 cos( 2π))

dy/ dx = ( 8- 1)/( 8 1)

dy/ dx = 7/ nine

Thus, the pitch of the tangent line to the curve sin( x y) = 8x- 8y at the factor( π, π) is7/9.

To find the equation of the tangent line, we can use the point- slope form of the equation

y- y1 = m( x- x1)

In which m is the pitch we simply set up, and( x1, y1) is the point( π, π). Plugging in the values, we get

y- π = ( 7/ nine)( x- π)

Simplifying, we get

y = ( 7/ nine) x-( 2π/ nine)

Thus, the equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).

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Answer:

  about 11.5 m

Step-by-step explanation:

You want the height of a tree when the angles of elevation to its top are 25° and 50° from points 15 m apart.

The tangent relation between angles and sides in a right triangle is ...

  Tan = Opposite/Adjacent

In the attached diagram, this means ...

  tan(25°) = TX/AX

  tan(50°) = TX/BX

The difference between AX and BX is known, so we can rearrange this to ...

  AX -BX = 15 = TX/tan(25°) -TX/tan(50°)

  15·tan(25°)·tan(50°) = TX(tan(50°) -tan(25°) . . . multiply by tan(25°)tan(50°)

  TX = 15·tan(25°)·tan(50°)/(tan(50°)-tan(25°) ≈ 11.5 . . . . meters

The height of the tree is about 11.5 meters.

__

Additional comment

The value of the height can be computed by finding each tangent only once if we use ...

  TX = 15/(1/tan(25°) -1/tan(50°))

You recognize 1/tan(x) = cot(x) = tan(90°-x), so this is ...

  TX = 15/(tan(65°) -tan(40°))

Answer:

Step-by-step explanation:

       12 ounces = 150 calories, so

12 x 2 ounces = 150 x 2 calories,

      24 ounces = 300 calories

Answer:

The student's z-score for mathematics is 0.75, which means that his score is 0.75 standard deviations above the mean. This puts him in the upper quartile of the class, indicating that he performed better than 75% of the class.

The student's z-score for economics is 1.5, which means that his score is 1.5 standard deviations above the mean. This puts him in the upper quintile of the class, indicating that he performed better than 80% of the class.

The student performed better in economics than in mathematics.

Using simple division we know that the acceleration per second is 11.54 m/s.

Multiplication is the opposite of division.

If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

The division is a mathematical process that includes dividing a sum into groups of equal size.

For instance, "12 divided by 4" translates to "12 shared into 4 equal groups," which would be 3 in our example.

So, to find the acceleration per second:

We need to perform division as follows:

= 27.7/2.4

= 11.54

Therefore, using simple division we know that the acceleration per second is 11.54 m/s.

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The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.

To find the solution to the initial value problem, we first need to solve the differential equation.

Taking the derivative of y(t), we get:

y'(t) = -2t + a

Taking the derivative again, we get:

y''(t) = -2

Substituting y''(t) into the differential equation, we get:

y''(t) + 2y'(t) + 10y(t) = 20sin(3t)

Substituting y'(t) and y(t) into the equation, we get:

-2 + 2a + 10(-2t + a) = 20sin(3t)

Simplifying, we get:

8a - 20t = 20sin(3t) + 2

Using the initial condition y(0) = 2, we get:

y(0) = -2(0) + a = 2

Solving for a, we get:

a = 2

Using the other initial condition y'(0) = 21, we get:

y'(0) = -2(0) + 2(21) + B = 21

Solving for B, we get:

B = -21

Therefore, the solution to the initial value problem is:

y(t) = -t^2 + 2t + 3sin(3t) - 1

Thus, we have e(t) = y(t) - 8, so

e(t) = -t^2 + 2t + 3sin(3t) - 9

and a = 2, B = -21.

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_____The given question is incomplete, the complete question is given below:

Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =

Jacobi get area of pizza is 52.987 in²

5 friends getting equally share each one area of pizza is 40.27 in²

Any point in a plane that is a certain distance away from another point forms a circle. The fixed point is known as the center of the circle and the fixed distance is known as the radius of the circle.

The formula for calculating a circle's sector's area is (∅/360°) ×π×r²

Jacobi get area of pizza =(75/360°) × π×9²=52.987in²

5 friends getting pizza with each central angle measuring=360°-75°/5

=57°

5 friends getting each one area of pizza = (57/360°) × π×9²

40.27in².

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Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

In response to the stated question, we may state that As a result, the equation's answer is x = 0.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

4x = 864x is the provided equation.

This equation may be simplified by deleting 4x from both sides:

[tex]860x = 0[/tex]

This equation may now be rewritten in factored form:

[tex]860x = 0 \sx(860) = 0[/tex]

We know from the zero-product principle that if the product of two elements is zero, then at least one of them must be zero. As a result, we may set each component to zero and solve for x:

x = 0 or 860 = 0 (which is impossible) (which is impossible)

As a result, the equation's answer is x = 0.

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The equation that models the position of the weight at time t seconds is y(t) = 2.5 sin (πt) + 2.5

The equation that models the position of the weight at time t seconds is

y(t) = 2.5 sin (πt) + 2.5

The position of the weight at time t seconds can be modeled by a sinusoidal function of the form

y(t) = A sin (ωt + φ) + C

where

A is the amplitude of the oscillation (half the distance between the highest and lowest points), which is 2.5 in.

ω is the angular frequency of the oscillation, which is 2π divided by the period (the time for one complete cycle), which is 2 seconds. So, ω = 2π/2 = π radians/second.

φ is the phase angle, which depends on the initial position of the weight. We can assume that the weight starts at the highest point (the crest), so φ = 0.

C is the vertical shift, which is the midpoint of the oscillation (half the distance between the highest and lowest points added to the starting point). So, C = 2.5 + 0 = 2.5 in.

Putting it all together, we get

y(t) = 2.5 sin (πt) + 2.5

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By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

the length of the base AB,

Area = (1/2) * base * height

[tex]CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\[/tex]

We also know that the area of the triangle is:

[tex]46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\[/tex]

[tex]8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\[/tex]

[tex]AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\[/tex]

Therefore, the length of the base AB is approximately 20.88 centimeters.

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By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion  [tex]"2x + 3 = 9"[/tex] states that the word  [tex]"2x + 3"[/tex] Corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations [tex]"x2 + 2x - 3 = 0[/tex]  ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.

Abby, according to the picture, spent:

She spends 25% of her time in school.

She spends 40% of her time at work and 15% of her time on other hobbies.

Therefore, Furthermore, she spends  [tex]20[/tex] of her time napping.

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Answer:

None of the options provided in the question accurately describe the behavior of f(t) = 7 over the interval from t = -4 to t = -3.

Step-by-step explanation:

he function f(t) = 7 is a constant function that does not depend on the value of t. Therefore, f(t) = 7 remains the same over the interval from t = -4 to t = -3. In other words, there is no change in the value of f(t) over this interval.

The statement that best describes the mode of selection depicted in the figure is (b) Directional Selection, changing the average color of population over time.

The Directional selection is a type of natural selection that occurs when individuals with a certain trait or phenotype are more likely to survive and reproduce than individuals with other traits or phenotypes.

In the directional selection of evolution, the mean shifts that means average shifts to one extreme and supports one trait and leads to eventually removal of the other trait.

In this case, one end of the extreme-phenotypes which means that the dark-brown rats are being selected for. So, over the time, the average color of the rat population will change.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

The figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?

(a) Disruptive Official, favoring the average individual

(b) Directional Selection, changing the average color of population over time

(c) Directional selection, favoring the average individual

(d) Stabilizing Selection, changing the average color of population over time

The total number of elements in either Set A or Set B is 156.

A set is a collection of unique items, but a subset is a set that contains only components that belong to another set, termed the superset. In other words, set A is a subset of set B if all of its items are also found in set B.

Given that, Set A contains 98 elements and Set B contains 93 elements.

Total number of elements in either Set A or Set B = number of elements in Set A + number of elements in Set B - number of common elements

Total number of elements in either Set A or Set B = 98 + 93 - 35

Total number of elements in either Set A or Set B = 156

Hence, the total number of elements in either Set A or Set B is 156.

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Some of the tips which is used to conduct a survey are:

Conducting a survey is an important tool for gathering information from a large and diverse group of people. Its allows allow researchers to obtain data from a representative sample of the population, which can then be used to make informed decisions, identify trends, and measure changes over time.

Also important, its can provide insight into people's attitudes, beliefs, and behaviors, which can be valuable in developing marketing strategies, designing programs and policies, and making important decisions.

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Answer: Zemāk

Step-by-step explanation:

1)

a. Le prix du manteau après la réduction de 15% est:

78€ - (15/100)*78€ = 66,30€

Le prix du manteau après la réduction est de 66,30€.

b. Soit x le prix initial du manteau.

Le prix du manteau après la réduction de 15% est:

x - (15/100)*x = 55,25€

Simplifions cette équation:

0,85x = 55,25€

x = 65€

Le prix initial du manteau était de 65€.

2)

Pour les lunettes, le prix initial est de 45€ et la réduction appliquée est de 20%:

45€ - (20/100)*45€ = 36€

Pour la montre, le prix initial est de 35,55€ et la réduction appliquée est également de 20%:

35,55€ - (20/100)*35,55€ = 28,44€

On constate que le pourcentage de réduction est le même pour les deux articles, donc Manu a tort.

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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The experimental probability that at least one of the first three customers that walks into the store will make a purchase is 60%.

It is determined by counting the number of times an event occurs in a given experiment and dividing the total number of trials by the number of successful outcomes.

The experimental probability that at least one of the first three customers that walks into the store will make a purchase is calculated by dividing the total number of customers who make a purchase by the total number of customers who enter the store.

In this case, there are 3 trials and 2 customers who make a purchase.

The experimental probability is 3 by 5 which is the total number of trials.

Thus, the experimental probability

=3/5

= 60%.

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The value οf v=3√2 and  w=√3/√2.

If a triangle has a straight angle (90 degrees), the hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides, accοrding tο the Pythagοras theοrem.

Keep in mind that BC² = AB² + AC²in the triangle ABC signifies this. This equatiοn uses the variables base AB, height AC, and hypοtenuse BC. It is impοrtant tο nοte that the hypοtenuse, οr lοngest side, οf a right-angled triangle is.

Here fοr sin(30)= v/3√2

1/2 = v / 3√2

v = 3√2

cοs(30)= w/3√2

w=3√2*√3/2

w=√3/√2

Hence the value οf v=3√2 and  w=√3/√2.

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The mean of the numbers 8, 2 and 2 when solved graphically is 4

The numbers in the dataset are given as

8, 2 and 2

The mean is also known as the average and is calculated by adding up all the values in a dataset and then dividing the sum by the total number of values.

To find the mean of 8, 2, and 2 graphically, we can use a number line.

The midpoint between 2 and 8 is 5, and the midpoint between 2 and 2 is also 2.

Therefore, the mean of 8, 2, and 2 is the average of the midpoints

Mean = (8 + 2 + 2)/3

Mean = 4

Hence, the mean is 4

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}[/tex]

[tex]\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4[/tex]