A rectangle is 1/2 feet long and 3/4 feet wide.



What is the area of the rectangle?



Enter your answer as a fraction in simplest form

The true statement about the figure is not represented in the options

From the question, we have the following parameters that can be used in our computation:

The triangle

The value of y can be calculated using the following Pythagoras theorem

y^2 = (3x)^2 + (4x)^2

Evaluate

y^2 = 25x^2

So, we have

y = 5x

The height is given as

Height = 100

This means that

4x = 100

So, we have

x = 25

For y, we have

y = 5x

y = 5 * 25

y = 125

For the area, we have

Area = 1/2 * 4x * 3x

Area = 1/2 * 4 * 25 * 3 * 25

Evaluate

Area = 3750

Hence, none of the options are true

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The lines CA and CD are tangents to the circle O, hence; EA = 4, AB = 15, m∠ABO = 90°, m∠ODC = 90°, and m∠EAB = 30°.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

If OB = 6 and AB = 8, then;

OA = √(8² + 6²) {by Pythagoras rule}

OA = √100

OA = 10

EA = OA - OE(radius)

EA = 10 - 6 = 4

If DE = 16 and EA = 9, then;

OA = (diameter/2) + EA

OA = 8 + 9 = 17

AB = √(17² - 8²)

AB = √225

AB = 15

OB is perpendicular to line CA tangent to the circle so m∠ABO = 90°

OD is perpendicular to the line CD tangent to the circle so m∠ODC = 90°

If m∠DOB = 120° then;

120° = m∠ABO + m∠EAB {exterior angle of a triangle is equal to the two opposite interior angles}

m∠EAB = 120° - 90°

m∠EAB = 30°

In conclusion, for the lines tangent to the circle, we have that;

EA = 4, AB = 15, m∠ABO = 90°, m∠ODC = 90°, and m∠EAB = 30°

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Answer:

x = 6/7, y = 33/7

Step-by-step explanation:

y = 2x + 3 ----eq(1)

3x + 2y = 12 ----eq(2)

Substituting value of "y" from eq(1) into eq(2)

3x + 2(2x + 3) = 12

3x + 4x + 6 = 12

7x = 12-6

x = 6/7 ---eq(3)

Substituting value of x or eq(3) into eq (1)

y = 2(6/7) +3

y = 12/7 + 3

y= 12 + 21/7

y= 33/7

Therefore, x = 6/7 and y = 33/7

The centripetal acceleration of the wooden block is 0.32 m/s^2.

The centripetal acceleration of an object moving in a circle with radius r and angular velocity ω (in radians per second) is given by the formula:

a = rω^2

In this problem, the wooden block is on the end of a string with a radius of 0.7 meters, and it makes 14 rotations in 20.7 seconds. The angular velocity ω can be calculated by dividing the number of rotations by the time:

ω = (14 rotations) / (20.7 seconds) = 0.676 radians/second

Plugging in the values for r and ω, we get:

a = (0.7 meters) × (0.676 radians/second)^2 = 0.32 m/s^2

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The given question is incomplete, the complete question is:

A group of students observes that a wooden block (m = 0.40 kg) on the end of a string with a radius of 0.7 meters makes 14 rotations in 20.7 seconds when twirled. Part A Calculate the centripetal acceleration of the wooden block?

Answer:

310cm

Step-by-step explanation:

The Total surface of cuboid is S=2(lb+bh+lh)  

l=length

b=breadth b means w (width)

h=height

S=2(50+70+35)

S=2(155)

=310cm

Answer:

260 cm²

Step-by-step explanation:

Bottom surface area = 5 x 10 = 50

Surface area of the 2 long sides = 2(10 x 7) = 140

Surface area of the 2 short sides  = 2(5 x 7) = 70

Total surface area = bottom + 4 sides = 50 + 140 + 70 = 260 cm²

The solution of the given problem of Test statistic comes out to be Using a table or calculator with 98 degrees of freedom, we find the value to be approximately 0.06.

The test statistic for anything akin to a Z-test has been the Z-statistic, which shows the ordinary normal neutral hypothesis is correct. Suppose you perform a 2 different X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also referred as a Z-value). 0.0124 is the value for the this Z-value.

Here,

: un - ud <= 0 (the mean GPA of night students is less than or equal to the mean GPA of day students)

H: un - ud > 0 (the mean GPA of night students is greater than the mean GPA of day students)

We will use a significance level of 0.05.

The test statistic is calculated as:

t = (xn - xd - 0) / √(s²/n + s²/n)

where xn and xd are the sample means, s and s are the sample standard deviations, and n is the sample size.

Plugging in the values from the problem, we get:

t = (2.91 - 2.87 - 0) / √0.08²/50 + 0.06²/50) = 1.57

The degrees of freedom for the t-distribution is

f = n₁ + n₂ - 2 = 50 + 50 - 2 = 98 (assuming equal variances).

Using a table or calculator with 98 degrees of freedom, we find the

value to be approximately 0.06.

Since the value (0.06) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.05 significance level.

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Answer: f=756

Step-by-step explanation:

f/28=7

multiply both sides of the equation by 28

28 x f/28=28 x 27

cancel out the greatest common factor 28

f=28 x 27

multiply 28 x 27

f=756

The sum of two opposite interior angles of a triangle is equal to the opposite exterior angle of a triangle

Therefore,

( 5x - 101 )° + ( x + 36 )° = ( 9x - 164 )°

5x + x - 106 + 36 = 9x - 164

6x - 65 = 9x - 164

6x - 9x = - 164 + 65

- 3x / - 3 = - 99 / - 3

x = 33

The first interior angle

= ( 5x - 101 )°

= ( 5 ( 33 ) - 101 ) °

= ( 165 - 101 )°

= 64°

The second interior angle

= ( x + 36 )°

= ( 33 + 36 )°

= 69°

The exterior angle

= ( 9x - 164 )°

= ( 9 ( 33 ) - 164 )°

= ( 297 - 164 )°

= 133°

Answer:

20000

Step-by-step explanation:

i think this is the right answer i could

A number greater than 5 is: P(odd or greater than 5) = 1/2 + 1/6 = 2/3

It depends on the context of the probability question. Here are a few possibilities:

If you're rolling a fair six-sided die, then the probability of rolling an odd or a number greater than 5 on a single roll is:

P(odd or greater than 5) = P(odd) + P(greater than 5) - P(odd and greater than 5)

P(odd) = 3/6 = 1/2 (because there are three odd numbers out of six possible outcomes)

P(greater than 5) = 1/6 (because there is only one number greater than 5)

P(odd and greater than 5) = 0 (because there is no number that is both odd and greater than 5)

So, the probability of rolling an odd or a number greater than 5 is:

P(odd or greater than 5) = 1/2 + 1/6 = 2/3

If you're dealing with a continuous random variable (like the height of people), then the probability of a value being odd or greater than 5 doesn't make sense. However, if you're dealing with a discrete random variable with a known distribution (like the number of customers who enter a store), you can calculate the probability of this event based on the distribution.

In general, it's important to define the context of the probability question and the underlying probability distribution to answer the question properly.

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The roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

Using the quadratic formula to solve the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex],we have

[tex]x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\[/tex]

Therefore, the two roots of the quadratic equation in exact square root form are:

[tex]x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\[/tex]

Thus, the roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

A quadratic equation is a second-degree polynomial equation in one variable of the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.

The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.

The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).

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Nico and Aditi are not correct in their approach to solving the problem.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and others. The goal of solving an equation is to find the values of the variables that make the equation true.

Equations can be classified into different types based on their degree and the number of variables.

Linear equations: Equations that involve variables raised to the first power only, such as 2x + 3 = 7.

Quadratic equations: Equations that involve variables raised to the second power, such as x² + 5x - 6 = 0.

Cubic equations: Equations that involve variables raised to the third power, such as x³ + 2x² - x - 2 = 0.

Simultaneous equations: A set of two or more equations that are solved together to determine the values of the variables.

Equations are used in many real-life applications, such as physics, engineering, economics, and finance. They are also an essential part of mathematics and are used to model and solve problems in algebra, calculus, and other branches of mathematics.

The students who are correct in their approach to solving the problem are:

Erick: By multiplying both sides of the equation by 5/2, he eliminates the fraction on the left side and simplifies the equation.

Raj: By multiplying both sides of the equation by 1/2, he eliminates the fraction on the left side and simplifies the equation.

Sandra: By adding 5/2 to both sides of the equation and then simplifying, she isolates the variable on one side of the equation.

So, Nico and Aditi are not correct in their approach to solving the problem.

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Answer:

yo

Step-by-step explanation:

C D E

The annual yield of the bond is 3.50%.

To calculate Mike's profit, we first need to determine the total cost of his investment, including the back-end load. The back-end load is calculated by multiplying the initial investment by the loading rate:

Back-end load = $14,000 * 5.5% = $770

So the total cost of Mike's investment is:

Total cost = $14,000 + $770 = $14,770

To determine the profit, we need to subtract the total cost from the total amount Mike received when he sold his shares:

Profit = ($21.85 - $20.00) * 14,000 - $770 = $2,730

Therefore, Mike made a profit of $2,730.

Note that the problem statement is exactly the same as the previous question. The answer is $2,730.

The annual rental income that Clara Teague needs to receive to achieve an annual yield of 8% can be calculated as follows:

Annual rental income = Total investment * Yield

where Total investment = $115,800 - $25,000 = $90,800

So the annual rental income that Clara Teague needs to receive is:

Annual rental income = $90,800 * 8% = $7,264

To determine the monthly rent, we divide the annual rental income by 12:

Monthly rent = $7,264 / 12 = $605.33

Therefore, Clara should charge a monthly rent of $605.33 to achieve an annual yield of 8%.

The annual yield of the bond can be calculated as follows:

Annual yield = (Annual interest payment / Bond price) * 100%

The annual interest payment is:

Annual interest payment = Bond face value * Annual interest rate = $25,000 * 3.7% = $925

The bond price is quoted at 105.7% of its face value, so the bond price is:

Bond price = Bond face value * 105.7% = $25,000 * 1.057 = $26,425

So the annual yield is:

Annual yield = ($925 / $26,425) * 100% = 3.50%

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The key features of this rational function include the following:

Domain: (-∞, -2) ∪ (-2, ∞)

Range: (-∞, -1) ∪ (-1, ∞)

Y-intercept: 2.

X-intercept: 1.

Vertical asymptote: x = -2.

Horizontal asymptote​: y = -1.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

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Answer:

it will take approximately 15.42 years for an investment of $567 at 4.5% continuous compounding to double to $1134.

Step-by-step explanation:

The formula for continuously compounded interest is:

A = Pe^(rt)

where A is the final amount, P is the initial principal, r is the annual interest rate, t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

We want to know how long it will take for an initial investment of $567 to double, so our final amount will be $1134. We know that the interest rate is 4.5% or 0.045 as a decimal. Substituting these values into the formula, we get:

1134 = 567e^(0.045t)

Dividing both sides by 567, we get:

2 = e^(0.045t)

Taking the natural logarithm of both sides, we get:

ln(2) = 0.045t

Solving for t, we get:

t = ln(2)/0.045

Using a calculator, we get:

t ≈ 15.42 years

Therefore, it will take approximately 15.42 years for an investment of $567 at 4.5% continuous compounding to double to $1134.

Answer:

it Will give it 15 years in as much as the previous comment is accurate to my answer

The length of median CP is 48.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

Since the triangles are congruent, corresponding sides are equal. So, we have:

AB = DE (corresponding sides)

BC = EF (corresponding sides)

Now, we can use the formula for the length of a median of a triangle, which states that the median to a side of a triangle is half the length of the side that it intersects. Thus, we have:

CP = (1/2) AB

FQ = (1/2) DE

Substituting the values we have for AB and DE, we get:

CP = (1/2) AB = (1/2) DE = FQ

So, we can equate the expressions for CP and FQ, and solve for x:

3x - 12 = 2x + 8

x = 20

Now that we know the value of x, we can substitute it back into either expression for CP or FQ to find the length of CP:

CP = 3x - 12 = 3(20) - 12 = 48

Therefore, the length of median CP is 48.

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The width of the olen river is 16 yards

From the question, we have the following parameters that can be used in our computation:

ABC, ~ EDC

The above means tha the triangles are similar triangles

Using the above as a guide, we have the following:

x : 32 = 20 : 40

Express as fraction

x/32 = 20/40

So, we have

x = 32 * 20/40

Evaluate

x = 16

Hence, the length is 16 yards

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The solution is, the value  of the function when x = -2 is -4.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Given the expression

h(x) = -x^2 +4x

h(-2) = (-2)^2 + 4(-2)

h(-2) = 4  + (-8)

h(-2) = 4 -  8

h(2) = -4

Hence the value of the function when x = -2 is -4.

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The number of boys more than girls altogether in the two programs is 6 boys

The number of boys and girls in the sport-studies program is :

= 30 x 60 %

= 18 girls

Boys in sport-studies program are:

= 30 - 18

= 12 boys

Boys in media tic program :

= 30 x 70 %

= 21 boys

Girls in media tic program:

= 30 - 21

= 9 girls

The difference is :

= ( 12 + 21 ) - ( 18 + 7 )

= 6 boys

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To find the expression for the nth term of the sequence, we need to first find the common difference.

The common difference is the difference between any two consecutive terms in the sequence. We can see that the difference between each pair of consecutive terms is 6. Therefore, the common difference is 6.

To find the nth term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Substituting the values we have:

a1 = 5

d = 6

So the expression for the nth term of the sequence is:

an = 5 + (n - 1)6

Simplifying:

an = 6n - 1

Answer:

Step-by-step explanation:

A frequency distribution is a table or graph that displays the number of times each value or range of values occurs in a dataset, while a probability distribution is a function that describes the likelihood of each possible outcome of a random variable in terms of its probability.

In other words, a frequency distribution describes the actual frequencies or counts of the values in a dataset, while a probability distribution describes the theoretical probabilities of the outcomes of a random variable. Frequency distributions are typically used in descriptive statistics, while probability distributions are used in inferential statistics to make predictions and test hypotheses.

Answer:

the odds of both events happening is 1 in 8 or 0.125.

Step-by-step explanation:

here are the step-by-step calculations to find the odds of both events happening:

The probability of the first event happening is 50%, which can be written as a decimal as 0.5.

The probability of the second event happening is 25%, which can be written as a decimal as 0.25.

To find the probability of both events happening, we multiply these probabilities together:

P(both) = P(first) x P(second)

= 0.5 x 0.25

= 0.125

We can also express this probability as odds by dividing the probability of both events happening by the probability of just one event happening (in this case, either the first or second event happening). The probability of one event happening is 0.5 + 0.25 = 0.75, since these events are mutually exclusive (only one of them can happen at a time). So the odds of both events happening is:

P(both) / P(one) = 0.125 / 0.75

= 1/8

Therefore, the odds of both events happening is 1 in 8 or 0.125.

Answer:

Para calcular las deformaciones asociadas en los puntos dados, es necesario calcular primero los componentes del tensor de deformación. Los componentes del tensor de deformación se pueden obtener a partir del gradiente del campo de desplazamiento utilizando la siguiente relación:

ε_ij = (1/2) * (∂u_i/∂x_j + ∂u_j/∂x_i)

donde ε_ij son los componentes del tensor de deformación y u_i es la i-ésima componente del vector de desplazamiento.

Calculando los componentes del tensor de deformación en los puntos (1, 1, 1) y (2, 2, 2), se obtiene:

En el punto (1, 1, 1):

ε_xx = 12 (10^-3)

ε_xy = 5 (10^-3)

ε_xz = 1 (10^-3)

ε_yx = 5 (10^-3)

ε_yy = 8 (10^-3)

ε_yz = 3 (10^-3)

ε_zx = 1 (10^-3)

ε_zy = 3 (10^-3)

ε_zz = 6 (10^-3)

En el punto (2, 2, 2):

ε_xx = 420 (10^-3)

ε_xy = 28 (10^-3)

ε_xz = 20 (10^-3)

ε_yx = 28 (10^-3)

ε_yy = 86 (10^-3)

ε_yz = 36 (10^-3)

ε_zx = 20 (10^-3)

ε_zy = 36 (10^-3)

ε_zz = 84 (10^-3)

Podemos ver que los valores de deformación son mayores en el punto (2, 2, 2) que en el punto (1, 1, 1). Esto sugiere que el campo de desplazamiento produce una mayor deformación en el punto (2, 2, 2) que en el punto (1, 1, 1). Además, podemos observar que los componentes de deformación son simétricos (es decir, ε_ij = ε_ji), lo cual es consistente con la teoría de la mecánica de materiales.

Step-by-step explanation:

espero te sirva

By using the greatest common factor of 84 and 48, the sum 84+48 can be written as the product 12 x (7 + 4).

To write the sum 84+48 as a product using their greatest common factor, we need to factor both numbers and find the largest common factor.

The prime factorization of 84 is 2 x 2 x 3 x 7, while the prime factorization of 48 is 2 x 2 x 2 x 2 x 3.

To find the greatest common factor, we need to identify the factors that both 84 and 48 have in common. We see that both numbers have two factors of 2 and one factor of 3 in common. So, the greatest common factor of 84 and 48 is 2 x 2 x 3 = 12.

Now, we can rewrite the sum 84+48 as a product of 12 and another sum, using the distributive property of multiplication:

84 + 48 = 12 x (7 + 4)

So, the sum 84+48 can be written as the product 12 x (7 + 4).

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Answer:

Step-by-step explanation:

here are the steps to solve this problem:

Draw a line segment MO and a point N on it, such that N is between M and O. Label the length of MN as 2x, the length of NO as x-2, and the length of MO as 2x-9.

Write the equation that relates the lengths of MN, NO, and MO. This equation is MO = MN + NO, since MO is the sum of MN and NO.

Substitute the given expressions for MN, NO, and MO into the equation from step 2. We get:

2x-9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x-9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

-x = 7

Divide both sides of the equation by -1 to isolate x. We get:

x = -7

Check the solution by plugging it back into the original equation. We get:

2(-7)-9 = -23

2(-7) + (x-2) = -16

The two sides of the equation are not equal, so x = -7 is not a valid solution.

Recheck the original problem to see if there was an error in the given values, or if the problem was written incorrectly. We notice that the values of MN, NO, and MO are all positive, so x cannot be negative. Therefore, we assume that there was an error in the given solution for MO, and that it should be 2x+9 instead of 2x-9.

Rewrite the equation from step 2 with the corrected value for MO. We get:

2x+9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x+9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

x = 11

Check the solution by plugging it back into the original equation. We get:

2(11) + (x-2) = 22 + 9 = 31

2(11) + (11-2) = 20 + 9 = 29

The two sides of the equation are not equal, so x = 11 is not a valid solution.

Recheck the original problem to make sure there are no other errors. We notice that the length of MN is given as 2x, but we haven't yet found the value of x. This means we need to solve the equation from step 11 for the value of 2x:

2x = 2(11) = 22

Therefore, the numerical length of MN is 22.

Answer:

a=35

Step-by-step explanation:

5a=25×7

5a=175

5a/5=175/5

a=35

The balance at the end of a year is $1051.56.

To find the balance at the end of a year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the balance after t years

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $1000, r = 0.05, n = 2 (since the interest is compounded semi-annually), and t = 1. Plugging these values into the formula, we get:

A = $1000(1 + 0.05/2)^(2*1)

= $1000(1.025)^2

= $1051.56

Therefore, the balance at the end of a year is $1051.56.

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