In a lab group, there are 3 students taller than 62 inches and 2 students shorter than
62 inches.
The teacher selects 2 students at random.
What is the probability that both students are shorter than 62 inches?

To construct the parallelogram ABCD, follow these steps:

The diagram of the parallelogram ABCD is shown below:

      D - - - - -C

     /            |

   /              |

A - - - - - - - B

Note that AB is parallel to CD and AD is parallel to BC, and opposite sides of the parallelogram are congruent.

The balances and the running total, given the checking account record is :

The balance on the 14 th of February would be:

= Balance forward - Amount of check

= 299. 88 - 90. 48

= $ 209. 40

The balance on 2 / 15 :

= 209. 40 - 65

= $ 144. 40

The balance on 2 / 17 :

= 144. 40 + 381.33 which is a deposit

= $ 525.73

The balance and running total on 2 / 22 :

= 525. 73 - 54.47

= $ 471.26

The balance on 2 / 22 after the National Mortgage deduction is:

= 471. 26 - 375.99

= $ 95.27

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Answer: For x < -2.5:

y = |2x + 5| - |2x - 5|

y = -(2x + 5) - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 < 0 for x < -2.5)

y = -2x - 5 + 2x - 5

y = -10

For x > 2.5:

y = |2x + 5| - |2x - 5|

y = 2x + 5 - (2x - 5) (since 2x - 5 < 0 and 2x + 5 > 0 for x > 2.5)

y = 10

For -2.5 ≤ x ≤ 2.5:

y = |2x + 5| - |2x - 5|

y = 2x + 5 - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 > 0 for -2.5 ≤ x ≤ 2.5)

y = 4x

Step-by-step explanation:

Answer:The total number of cubes required is the product of the dimensions in cube-lengths: 3×4×2 = 24 cubes.

Step-by-step explanation:

Another way to figure this is to compute the prism volume in the given dimensions (cm³) and the cube volume in the same dimensions, then find the number of cube volumes in the prism volume.

Answer:

√3/2

Step-by-step explanation:

sin(10°) • cos(50°) + cos(10°) • sin(50°)

= sin(10 + 50)

sin(60°) = √3/2

The sequence of the transformation are - translation, then rotation, then reflection

Congruent refers to having the same size and shape. Congruent hence involves comparing two numbers, and equivalent denotes the equality of two expressions. Hence, to state two line segments are congruent implies that the two lines have equal measurements.

Angle measure is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees. The angles of a regular polygon will always be congruent, regardless of its size or scale.

here, from given figure we have triangle ABC ,where

ABC is translation,

A'B'C' is rotation of triangle ABC

A''B''C'' is reflection  ,

so,

the sequence of the transformations of triangle ABC is translation, then rotation, then reflection.

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Answer:

D

Step-by-step explanation:

Edge

Answer:

Step-by-step explanation:

The sequence starts with 4 and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the equation to describe the sequence is:

aₙ = 4(-3)^(n-1)

where aₙ represents the nth term in the sequence.

Using this equation, we can find the values of the first few terms in the sequence as follows:

a₁ = 4(-3)^(1-1) = 4(1) = 4

a₂ = 4(-3)^(2-1) = 4(-3) = -12

a₃ = 4(-3)^(3-1) = 4(9) = 36

and so on.

Note that the index n starts at 1, but in some contexts it may start at 0, in which case we would need to adjust the exponent accordingly.

The answer is 369,072. This is the total number of copies sold to date.

An expression that uses symbols to represent the relationship between two or more values.

This is calculated by solving the equation 9.7% × x = 35,800, where x is the total number of copies sold to date.

To solve this equation, we first need to convert the percentage to a decimal.

To do this, we divide 9.7 by 100, giving us 0.097.

We can then multiply both sides of the equation by this decimal, giving us 0.097x = 35,800.

We can then solve for x by dividing both sides of the equation by 0.097. This gives us x = 369,072. This is the total number of copies sold to date.

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Using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, the Pythagorean formula is as follows:

c = √a² + b²

Now, insert values as follows:

c = √a² + b²

c = √12² + 9²

c = √144 + 81

c = √225

c = 15 units

Therefore, using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

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Answer:

Got you bro

Step-by-step explanation:

The two-dimensional shape appears to be a semi-circle, and it is being rotated about a line to form a three-dimensional shape. The resulting shape is a sphere.

Answer:

Step-by-step explanation:

The two-dimensional shape appears to be a semi-circle, and it is being rotated about a line to form a three-dimensional shape.

The resulting shape is a sphere.

Answer:A complex number will, in general, have five(5) fifth complex roots./

Step-by-step explanation:

The product of 3.18 × 16 is 50.88 in decimal form.

A number system is a way to represent numbers using symbols or digits. The most commonly used number system is the decimal or base-10 system, which uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent any quantity.

Other common number systems include:

Binary or base-2 system, which uses two digits (0 and 1) to represent numbers

Octal or base-8 system, which uses eight digits (0, 1, 2, 3, 4, 5, 6, 7) to represent numbers

Hexadecimal or base-16 system, which uses sixteen digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) to represent numbers

Knowing that;

3.18 × 16

After multiplying, we now have;

3.18 × 16 = 50.88

Thus, the product of 3.18 × 16 is 50.88 in decimal form.

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Two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. For example, the probability of rolling a 6 on a fair dice is 1/6, or approximately 0.167.

In probability theory, events are often expressed as sets of possible outcomes, and probabilities are calculated based on the number of outcomes in the event relative to the total number of possible outcomes. For example, the probability of rolling an even number on a fair dice is 3/6, or 0.5, because there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

Since the event E is the event of getting an even number, the possible outcomes are 2, 4, 6, or 8.

Out of these, only 4 is a perfect square. Therefore, P(S/E) = 1/4.

These two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.

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The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex]

A hyperbolic is a U-shaped symmetry curve that is created when a plane and a cone collide. The parabola has the characteristic that the distance between any point on the curve and a fixed point (referred to as the focus) is identical to the distance between that point and a telephone service (called the directrix). Equation y = ax2 + bx + c, at which a, b, and c are constants, gives the conventional form of a parabola. The parabola opens either upwards or downwards depending on the sign of coefficient a. The arc opens upwards if an is positive and downwards if an is negative.

given

A parabola with a vertex at (h, k) and a vertical axis of symmetry has the following standard form equation:

[tex](x - h)^2 = 4p(y - k) (y - k)[/tex]

where p is the separation between the vertex and the directrix or focus.

In this instance, the vertex's coordinates are (h, k) = since it is located halfway between the focus and directrix (-4, 4). As the directrix is a horizontal line with the coordinates y = 5, the separation between it and the vertex is p = 1.

When we enter these values into the equation in standard form, we obtain:

[tex](x + 4)^2 = 4(1)(y - 4) (y - 4)[/tex]

If we simplify, we get:

[tex](x + 4)^2 = 4y - 16[/tex]

The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex] .

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Margo will pay an interest of $29.75 on her loan.

The population will exceed 2458 after approximately 10.1465 units of time, where the time unit depends on the context of the problem (e.g., hours, days, etc.).

A statement proving the equality of two expressions is known as an equation. It can include variables, integers, and mathematical operations like addition, subtraction, multiplication, and division. It also incorporates mathematical symbols. In mathematics and science, equations are frequently used to illustrate connections between quantities. The equals sign (=) is typically used in equations to denote that the expressions on each side of the sign have the same value. For instance, the formula 2 + 3 = 5 demonstrates that the total of 2 and 3 equals 5. Equations can be solved to determine a variable's value or to determine if a certain value meets the connection that the equation describes.

To estimate when the population will exceed 2458, we can set up an inequality using the equation for the population growth:

p(t) > 2458

Substituting the given equation for p(t), we get:

[tex]1100e^0.12t[/tex] > 2458

Dividing both sides by 1100, we get:

[tex]e^0.12t > 2.23545[/tex]

Taking the natural logarithm of both sides, we get:

0.12t > ln(2.23545)

Solving for t, we get:

t > ln(2.23545)/0.12

Using a graphing calculator to evaluate this expression, we get:

t > 10.1465

Therefore, the population will exceed 2458 after approximately 10.1465 units of time, where the time unit depends on the context of the problem (e.g., hours, days, etc.).

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Answer: To simplify the expression, we need to follow the order of operations, which is to perform the division first, then addition.

1/3 ÷ 7/6 + 1/5

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:

1/3 ÷ 7/6 = 1/3 × 6/7 = 2/7

Now we can substitute this value back into the original expression:

2/7 + 1/5

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 35:

2/7 × 5/5 = 10/35

1/5 × 7/7 = 7/35

Now we can add the two fractions:

10/35 + 7/35 = 17/35

Therefore, the simplified expression is 17/35.

Step-by-step explanation:

The probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.

What is probability?

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.

We can use the standard normal distribution to solve this problem by standardizing the variable using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that a conversation lasts longer than 6 minutes, so x = 6, μ = 5, and σ = 0.7. Substituting these values into the formula, we get:

z = (6 - 5) / 0.7 = 1.43

Next, we can use a standard normal distribution table or a calculator to find the probability that a standard normal random variable is greater than 1.43. Using a standard normal distribution table, we find that this probability is approximately 0.0764.

Therefore, the probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.

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Therefore , the solution of the given problem of equation comes out to be  rounded to three decimal places, is 17.483 grams.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Think about the information that y + 7 provides. When accompanied by generate y + 7, increasing results in b + 7 in this case rather than another method that could split 12 into two separate components.

Here,

We must enter t = 110 into the equation for y and solve for y in order to determine how much of the original mass is still present after 110 years:

=> y = 20(1 - 2^(-t/30))

=> y = 20(1 - 2^(-110/30))

=> y ≈ 2.517

As a result, there are roughly 2.517 grams of cesium-137 left after 110 years. We can deduct this amount from the original mass of 20 grams to determine how much of the initial mass is still present:

=> 20 - 2.517 ≈ 17.483

Thus, roughly 17.483 grams of the original 20 grams of cesium-137 are still present after 110 years.

The number, rounded to three decimal places, is 17.483 grams.

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[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(B)}{7}=\cfrac{\sin(30^o)}{6}\implies \sin(B)=\cfrac{7\sin(30^o)}{6} \\\\\\ B=\sin^{-1}\left[ \cfrac{7\sin(30^o)}{6} \right]\implies B\approx 35.69^o[/tex]

Make sure your calculator is in Degree mode.

Answer: it must be EXPONENTIAL as values are increasing exponentially

Step-by-step explanation:

After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.

The law of cosines is a trigonometrical rule that links the lengths of a triangle's sides to the cosines of one of its angles, whether the triangle is spherical or flat. When two sides and the angle between them are known, it can be used to determine the length of a side or the angle of a triangular. There are two versions of the law of cosines: one for spherical triangles and one for planar triangles.

We can use the Law of Cosines to solve for the length of BC (denoted by a) in triangle ABC, since we know two sides and the included angle.

[tex]\rm a=\sqrt{c^{2}+b^{2}-2 c b \cdot \cos A}[/tex]

[tex]\rm a=\sqrt{4^{2}+3^{2}-2(4)(3) \cdot \cos(32^{\circ})}[/tex]

[tex]\rm a=\sqrt{16+9-24\cdot \cos(32^{\circ})}[/tex]

[tex]\rm a=\sqrt{1 \cdot \cos(32^{\circ})}[/tex]

a = 2.155654

a ≈ 2.2

Thus, After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.

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The formula for finding the volume of a cone is [tex]\pi[/tex][tex]r^{2}[/tex] [tex]\frac{h}{3}[/tex]

Please note the following:

Radius: 5 in

Height: 13 in

(1): Substitute the radius and height into the equation.

[tex]\pi[/tex][tex](5^{2})[/tex][tex](\frac{13}{3} )[/tex]

(2): Using a calculator, solve the equation.

[tex]\pi[/tex][tex](5^{2})[/tex][tex](\frac{13}{3} )[/tex] = 340.33

(3): Round

If you were to round 340.33 to the next two decimal places, you'd get 340 as your final answer.

With that being said, the answer to your question is 340 in.

Answer:

$67,000 after 15 years.

Step-by-step explanation:

You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in the account in 15 years? account will have $67,000 in it after 15 years

Answer:

The slope of a line represents the rate of change, which in this case is the rate at which the skydiver is falling. The rate of falling is 4,800 feet in 4 seconds, which simplifies to 1,200 feet per second, therefore, the graph that has a slope of 1,200 best represents this rate.

Therefore, the absolute maximum value of f(x) over (-2, 3) is 201 and it occurs at x = -2. The absolute minimum value of f(x) over (-2, 3)is -98 and it occurs at x = 3.

We must identify the crucial points of the function within the period in order to determine the function's absolute maximum and minimum values.

Define critical point?

The critical points are those where the function's derivative is zero or undefinable. The function is then assessed at these pivotal points as well as the interval's endpoints.

Absolute maximum and lowest values are represented by the largest and smallest values, respectively.

The derivative of f(x) = 3x⁴ - 4x³ - 12x² + 1 over (-2, 3) is initially found as follows:

f'(x) = 12x³ - 12x²- 24x

If we set f'(x) to 0, we obtain:

12x³ - 12x² - 24x = 0

By multiplying both sides of this equation by 12x, we may simplify it to:

x²- x - 2 = 0

The answer to this quadratic equation is:

x = -1, x = 0, x = 2

Now we evaluate f(x) at these critical points and at the endpoints of the interval:

f(-2) = 201

f(-1) = -6

f(0) = 1

f(2) = 49

f(3) = -98

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PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations.

PEMDAS rule states that the order of operation starts with the parentheses first or the calculation, which is enclosed in brackets. Then, the operation is performed on exponents(degree or square roots), and later, we do operations on multiplication & division and at last addition and subtraction.

PEMDAS is the order that you solve a problem.

PEMDAS stands for:

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.

In the equation

2 + 3 * 5,

first you would do 3 * 5 because multiplication is before addition.

2 + 15

Then you would do the addition to get the answer:

17.

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The required statement is "The sky is clear if and only if the plane is on time."

The statement "Q<->P" is a logical statement that uses the biconditional operator "<->" which means "if and only if." This operator connects two propositions in such a way that both propositions are true or false together.

In this case, the propositions are "Q" and "P" which are defined as "The sky is clear" and "The plane is on time," respectively. Therefore, the statement "Q<->P" can be translated into words as "The sky is clear if and only if the plane is on time."

This means that the truth of the proposition "Q" (the sky is clear) is dependent on the truth of proposition "P" (the plane is on time) and vice versa.

If the plane is on time, then the sky must be clear, and if the sky is clear, then the plane must be on time. If either of these propositions is false, then the bi-conditional statement is false as well.

Thus, required statement is "The sky is clear if and only if the plane is on time."

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