A sample of 21 of 30 students has a test score average above a b fine the critical value for a 95% confidence

A park, in the figure of a quadrilateral ABCD, has ∠C = 90°, AB = 9m, BC = 12 m, CD = 5 m, and AD = 8 m. The area is 65.49 m² ≈ 65.5m²

Join BD in "BCD," and receive BC and DC.

In order to compute BD, we can use Pythagoras's theorem.

[tex]& \Rightarrow \mathrm{BD}=\sqrt{\mathrm{BC}^2+\mathrm{CD}^2} \\[/tex]

[tex]& \quad=\sqrt{12^2+5^2}=\sqrt{144+25}=13 \mathrm{~m}=\mathrm{BD}[/tex]

Area of triangle ABD

[tex]$ =\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \text { (Heron's formula) } \\[/tex]

[tex]& \Rightarrow 2 \mathrm{~S}=9+8+13, \mathrm{~S}=\frac{30}{2} \\[/tex]

[tex]& \Rightarrow \mathrm{S}=15 \mathrm{~m} \\[/tex]

[tex]& \Rightarrow \text { Area of } \triangle \mathrm{ABD} \\[/tex]

[tex]& =\sqrt{15(15-9)(15-8)(15-13)} \\[/tex]

[tex]& =\sqrt{15 \times 6 \times 7 \times 2}=\sqrt{630 \times 2} \\[/tex]

[tex]& =6 \sqrt{1260}=35.49 \mathrm{~m}^2[/tex]

⇒ Area of Park = Quad ABCD

= 30+35.49

= 65.49 m² ≈ 65.5m²

The complete question is:

A park, in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

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The volume of the solid obtained by rotating the region enclosed by the graphs [tex]x=y^4[/tex] and [tex]x= y^1/4[/tex] about the y-axis over the interval [0,1] is 4π/7.

[tex]V = π ∫y^4 - y^1/4 dy[/tex]

 = π ∫[tex]y^7/4 dy[/tex]

 =[tex][4π/7*y^(7/4+1)]_0^1[/tex]

 = [tex]4π/7[/tex]

To find the volume of the solid obtained by rotating the region enclosed by the graphs[tex]x=y^4[/tex] and [tex]x= y^1/4[/tex] about the y-axis over the interval [0,1], we first use the formula for the volume of a solid of revolution: V = π ∫[tex]y^2 - y^1/4 dy.[/tex] Then, we rewrite the upper limit of the integral as [tex]y^7/4[/tex]and evaluate the integral from 0 to 1. This gives us the volume as 4π/7.

The volume of the solid obtained by rotating the region enclosed by the graphs [tex]x=y^4[/tex] and [tex]x= y^1/4[/tex] about the y-axis over the interval [0,1] is 4π/7.

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Answer:

F, M, J

Step-by-step explanation:

Step-by-step explanation:

then let's change that. you don't want to stay a dumdum, right ?

midpoint. what does that mean ? it is the point exactly in the middle between 2 other points.

what does that mean to be in the middle between 2 other things ?

well, it means that the distance is the same to both other things. otherwise it would not be the middle.

therefore,

4.

QS = 56 ft

exactly the same distance as PQ.

PS = PQ + QS

because Q is the point in the middle between P and S.

it is really that simple.

5.

the line segment PQ is bisected (cut in half) by the line segment MN at point R.

so, we know what the intersection of PQ and MN did to PQ (cut PQ in half). but this does not tell us what it did to MN. it could be also one of the ends of MN that cut PQ in half. we simply don't know.

therefore, we cannot say anything about the midpoint of MN.

and therefore the first 2 answer options are not generally correct. they COULD be correct, but they could be also wrong. therefore they are mathematically and logically not a true statement per se. for that the statement needs to be true unconditionally = in all possible cases.

R is the midpoint of PQ. yes, correct. that's what is meant by being bisected or cut in half at that point.

since the 3rd answer option is correct, the 4th answer option (none of these) is incorrect.

The complete binomial expression

40v³w + 135w = 5w {(2v + 3) ((4v² - 6v +9)}

Cubic equations are polynomials of degree3. That means the maximum degree of polynomial is three.

And the standard form of cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c and d are constant coefficients a ≠ 0.

Given:

An expression,

40v³w + 135w = (_) 5w(4v² - 6v +9)

To find the missing value:

Simplifying,

40v³w + 135w

= 5w (8v³ + 27)

= 5w {(2v)³ + (3)²}

= 5w {(2v + 3) ((4v² - 6v +9)}

Therefore, the missing expression is (2v + 3).

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The area of a rectangle is calculated by multiplying its two sides together. This is because a rectangle is a shape with four straight sides, and the area of a rectangle is the amount of space inside the rectangle.

A rectangle is a four-sided shape with four right angles and four equal sides. It is a type of quadrilateral, which means it has four sides. Rectangles are the most common type of shape and can be found in many areas of life, from art to architecture and engineering. Rectangles are sometimes referred to as geometric shapes and are used to define and measure space.

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The complete question is: How do you find an area with two sides?

Answer:

Step-by-step explanation: by using the formula, volume of cylinder= πr2h

The measure of the angle BCD is 60 degrees.

Ok, remember that the sum of the interior angles of a triangle is always equal to 180°.

And we can write the top angle at C as:

(5x + 10) + C = 180°

C = 180 - 5x - 10

Then the sum of the interior angles gives:

3x + 3x + (180 - 5x - 10) = 180

Now we can solve that for x to get:

6x -5x - 10 = 180 - 180

x - 10 = 0

x = 10

Then the measure of BCD is:

BCD = 5x + 10

BCD = 5*10 + 10 = 60

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It as 2.24m far from the origin. The location in polar coordinates is 26.6°.

The fly is located at the point having coordinates (2.00, 1.00) m

Cartesian and Polar Coordinates:

In the Cartesian system the coordinates are perpendicular to one another with the same unit length on both axes. A Polar coordinate system is determined by a fixed point, a origin or pole, and a zero direction or axis. Each point is determined by an angle and a distance relative to the zero axis and the origin.

If the cartesian coordinates of a point is given (x,y), the polar coordinates r,θ is given by the following relation

Take the wall as the xy plane so that the coordinates are x=2.00m and y=1.00m; and the fly is located at point P.

The distance between two points in the xy plane is

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

⇒d=[tex]\sqrt{(2-0)^{2}+(1-0)^{2} }[/tex]

⇒d=[tex]\sqrt{4+1} =\sqrt{5}[/tex]

⇒d=2.24 m

Therefore, 2.24m far from the origin.

(b).

⇒tanθ=[tex]\frac{y}{x}[/tex]

⇒θ=[tex]tan^{-1}(\frac{y}{x} )=tan^{-1}(\frac {1.00}{2.00})[/tex]

=26.6°

Therefore, the location in polar coordinates is 26.6°.

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A stem-and-leaf diagram separates each value of a data set into two parts: the stem and the leaf.

The stem is the first part of the number, typically the largest place value, and it is used to group similar values together. The leaves are the last part of the number, typically the smallest place value, and they provide the specific values within each group.

For example, consider a data set with the values 15, 19, 10, 11, 15. In a stem-and-leaf diagram, the stem for these values would be 1 and the leaves would be 5, 9, 0, 1, and 5, respectively.

The stem-and-leaf diagram would then look something like this:

This format allows for a quick visualization of the distribution of the data and can be useful for identifying patterns and relationships within the data set.

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The values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

The concept of the integral is a fundamental part of calculus and it is used to calculate the area under a curve or the volume of a 3-dimensional object. In this context, we will be exploring the integral of a two-dimensional set in the R^2 plane.

For every two-dimensional set C contained in R^2 for which the integral exists, the function Q(C) is defined as the double integral of the function (x^2 + y^2) over the set C. The double integral is a mathematical tool for finding the total volume under a surface.

Let's consider the three sets C1, C2, and C3 and find Q(C1), Q(C2), and Q(C3).

C1={(x,y) : −1 ≤ x ≤ 1, −1 ≤ y ≤ 1}

Q(C1) = ∬C1 (x^2 + y^2) dxdy = ∫^1_{-1}∫^1_{-1} (x^2 + y^2) dxdy = ∫^1_{-1} [(x^2 + y^2)/2]^1_{-1} dx = 4.

C2 ={(x,y):−1≤x≤1,−1≤y≤1}

Q(C2) = Q(C1) = 4.

C3 = {(x,y):x^2 + y^2 ≤1}

Q(C3) = ∬C3 (x^2 + y^2) dxdy = π.

In conclusion, the values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

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An equation of product form of 3 and b is, 3b

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Two terms,

3

And b

by multiplying both the terms,

⇒  3 × b

⇒  3b

Hence, the product is 3b

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Answer:

4√5.

Step-by-step explanation:

Treat the surd (√5) as a variable:

7x - 3x = 4x

So, 7√5 - 3√5

= 4√5

matrix organizational is most suited for aligned project accountability and authority, and for rapid reaction to customer needs

The true statement about a matrix organizational structure is that In a strong matrix organizational structure, the project manager controls the project budget and has moderate to high authority.

What is matrix organizational structure ?

A matrix organizational structure  can be regarded as workplace format where by, employees will be  reporting to two or more managers.

This system involves two managers overseeing every aspect of a project.

For instance, an employee could report to primary manager as well as other managers.

matrix organizational is most suited for aligned project accountability and authority, and for rapid reaction to customer needs

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The paragraph proof to show that VUTS is a parallelogram is as shown below.

Generally for parallelograms we know that;

A) If any one pair of opposite side is congruent and parallel, then the quadrilateral is parallelogram.

B) If two pair of opposite sides are parallel then it is a parallelogram.

Thus, the paragraph proof is as follows;

ΔSVX ≅ ΔUTX                      Given

SV // TU                                 Given

SV ≅ TU                                Corresponding part of congruent triangle

VUTS parallelogram               Definition of parallelogram.

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The equation that can be used to find the cost, c, of the pizza is c/5 = $3.25.

An equation is a mathematical statement that shows that two expressions are equal. Equations use an equals sign (=) to show that the values of the expressions on either side of the sign are equal.

Equations can include variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value of the variable that makes the equation true.

If they divide the cost of a meatball pizza evenly among 5 people and each person pays $3.25, then we can write the equation as

c/5 = $3.25

where c is the cost of the pizza

Plugging in the known value of p = $3.25, we get: c = 5($3.25) = $16.25.

So the cost of the meatball pizza at the Dancing Meatball is $16.25.

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Answer:

Step-by-step explanation:

The measurement of the angle 7 is,

[tex]5+6+7=180\\ 5+90+7=180\\58+90+7=180\\ 7=180-90-58\\ 7=32[/tex]

Therefore, the desired angle is 32.

In order to do well on BYU Calculus BC Explorations, you should have a solid understanding of the basic principles of calculus.

This includes understanding derivatives and integrals, as well as the fundamental theorem of calculus. Additionally, it is important to have a strong background in basic algebra and trigonometry, as these skills will be necessary for working with functions and equations. When solving problems, it is important to read the problem carefully and identify what type of calculus concept is being asked for. Once the concept is identified, you can use formulas and calculations to solve the problem. By working through problems in a systematic and logical way, you can make sure that you arrive at the correct answer.

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Complete question:What is the best way to do well on BYU Calculus BC Explorations?

Mowing Andre's uncle's lawn paid better than the other two jobs.

The job that paid better compared to the others is mowing Andre's uncle's lawn. He earned $30 for 1 hour of work, which is more than the $10 he earned for mowing a neighbor's lawn for 1 hour or the $15 he earned each hour for mowing the community's lawn for 2 hours.

The thinking behind this is basic. The rate of pay for mowing Andre's uncle's lawn was higher than the rate of pay for the other two jobs.

This is still up in the air by isolating the sum earned by the number of hours worked.

For the uncle's lawn, the rate was $30/1 hour = $30 each hour.

For the neighbor's lawn, the rate was $10/1 hour = $10 each hour. Furthermore, for the community center's lawn, the rate was $30/2 hours = $15 each hour.

Therefore, Mowing Andre's uncle's lawn paid better compared to the next two jobs.

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The value of the expression 42+6⋅52−33÷32 is 352.96

An expression is combination of variables, numbers and operators.

Remember the order of operations rules.BODMAS: parentheses first, then exponents, then multiplication, then division, then addition and subtraction is last.

= 42+6⋅52−33÷32

multiply first

= 42 + (6*52) - 33 ÷ 32

= 42 + 312 - 33 ÷ 32

division second

= 42 + 312 - 1.03125

addition next

= 354 - 1.03125

subtraction last

= 352.96875

Hence, the value of the expression 42+6⋅52−33÷32 is 352.96

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The correct answer is option c. 50%;

50% of scores in a normal distribution are above the mean.

A normal distribution is symmetrical, which means that the mean, median, and mode are all equal and that the percentage of scores below the mean is equal to the percentage of scores above the mean.

For a normal distribution with a mean of 40, exactly half of the scores (50%) will be above the mean, and the other half (50%) will be below the mean. This is true for any normal distribution, regardless of the standard deviation or any other characteristic of the distribution.

In a normal distribution, the data is symmetrically distributed around the mean. This means that if the mean is represented by a line, the same number of data points will be on either side of the line.

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Answer: [tex]ST=27[/tex]

Step-by-step explanation:

[tex]RU=\sqrt{29^2 -21^2}=20\\\\SU=\sqrt{52^2 -20^2} \implies ST=\sqrt{52^2 -20^2}-21 =27[/tex]

False. If the mean of "u" (unobserved ability) is independent of education, it only means that the average level of ability is not affected by the level of education. It does not imply that the average level of ability is the same for all levels of education.

In economics, "u" is often used to represent unobserved ability or talent, which can affect an individual's income or job performance. If the mean of "u" is independent of education, it means that the average level of ability is not affected by the level of education, i.e., the mean of "u" is the same for all individuals regardless of their level of education.

However, it does not imply that the average level of ability is the same for all levels of education.

For example, individuals with higher levels of education may have higher levels of "u" on average, due to factors such as better access to resources, more opportunities for learning and development, or self-selection of individuals with higher levels of "u" into higher levels of education.

In such a case, the mean of "u" would still be independent of education, but the average level of ability would not be the same for all levels of education.

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The amount of money received by Mary based on the mentioned information is 4.

Let the total amount of money be x. So, the amount received by Mary = 5/8x. The amount received by Donal = x - 5/8x

Performing subtraction on Right Hand Side of the equation

The amount received by Donal = (8x - 5x)/8

The amount received by Donal = 3x/8

Now, the amount received by Donal is 2.40. Size equating the two values -

3x/8 = 2.40

3x = 2.40 × 8

Performing multiplication on Right Hand Side of the equation

3x = 19.2

x = 19.2/3

Performing division on Right Hand Side of the equation

x = 6.4

Amount received by Mary = 5×6.4/8

Performing multiplication

Amount received by Mary = 32/8

Performing division

Amount received by Mary = 4

Thus, Mary received 4.

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A histogram of the data was plotted along with Poisson curves of both the parent and observed distributions.

a) The mean decay rate is 3.2 decays per minute and its standard deviation is 1.8 decays per minute. The standard deviation expected from the Poisson distribution for the mean value is 3.7 decays per minute, which is higher than the standard deviation obtained from the data.

b) The histogram and Poisson curves of both the parent and observed distributions can be seen in the figure below.

The mean decay rate of the source was found to be 3.2 decays per minute with a standard deviation of 1.8 decays per minute. The standard deviation was found to be lower than the value expected from the Poisson distribution for the mean value. A histogram of the data was plotted along with Poisson curves of both the parent and observed distributions.

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Answer:

$352

Step-by-step explanation:

David Gave 1/5 of his money to charity

$2640 / 5 = $528

$2640 - $528 = $2112

1/3 of it to his mom

$2112 / 3 = $704

$2112 - $704 = $1408

He shared the rest of it among his 4 sisters equally

$1408 / 4 = $352

So, each of his sisters get $352

m<6 = 125° ( m<4 & m<6 are corresponding angles)

m<5 = 180°-125° (angles on a straight line)

= 55°

m<8 = 125° (corresponding angles)

m<7 = 55° (angles on a straight line)