6−7. (5)(4)
8-9. d9 - d5
10-11. 780​

Answer:

9d+3

Step-by-step explanation:

(6D+5)-(2-3D);next step I disributed the negative sign into parenthesis wil resulted in no paranthesis.

6d+5-2+3d

9d+3

Consequently, the measurement between points AA and BB is roughly 14092.3 feet, rounded to the closest hundredth of a foot.

A pair of rays (half-lines) with such a shared termination are combined to form an angle. The latter is referred to as the angle's vertex, and the beams are sometimes referred to as the angle's legs and other times as its limbs.

Let's call the distance from point AA to the lighthouse/beacon light as "d" and the distance from point BB to the lighthouse/beacon light as "x".

We can use the tangent function to relate the angles of elevation to these distances:

tan(14°) = h/d, where h is the height of the lighthouse/beacon light above sea level

tan(5°) = h/x

We can eliminate h from these equations by solving for it in terms of d and x. Rearranging the first equation, we get:

h = d tan(14°)

This is what we get when we enter it into the second equation:

tan(5°) = (d tan(14°))/x

Solving for x, we get:

x = d tan(14°)/tan(5°)

Substituting the given value of d (1246 feet), we get:

x = 1246 tan(14°)/tan(5°) ≈ 14092.3 feet

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The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.

The exact value of sin(pi/3) can be determined using trigonometric properties and identities.

First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.

To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.

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The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.

given

The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.

Calculating the sample proportion is necessary:

The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:

P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031

Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:

\(z = (0.476 - 0.34) / 0.031 = 4.39\)

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

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Answer:

  30.0 ft

Step-by-step explanation:

You want the length of a pole whose shadow is 20 ft long when the angle of elevation of the sun is 62° and the pole is tilted 8° away from the sun.

Referring to the attached diagram, we see that the interior angle at B of triangle ABC is 90° -8° = 82°. This makes the interior angle at A ...

  A = 180° -82° -62° = 36°

The law of sines tells us side lengths are proportional to the sines of the opposite angles:

  c/sin(C) = a/sin(A)

  c = a×sin(C)/sin(A) = 20×sin(62°)/sin(36°) ≈ 30.043 . . . feet

The length of the pole is about 30.0 feet.

Answer:

b.) Analyzing the number of hours that freshman, sophomores, juniors, and seniors study in a semester as well as the number of hours of sleep each group gets at night.

Step-by-step explanation:

Analysis of Variance could be referred to as a form of statistical test which is used to evaluate the average or mean changes of a continous dependent variable based on the different combination of the input levels of TWO independent or predictor variables. From the options given, the option selected, the analysis is based on TWO independent, predictor variables which are hours of study in a semester and the number of sleeping hours for 3 different levels or categorical groups of students (Freshman, sophomore, Junior and Seniors) get at night.

Since, we can identify two distinct independent variables, then it is fit for analysis using a 2 - way ANOVA.

Answer:

The answer is simple, you have 72 calories as 3/4 of a cup. So you calculate 1/4 of a cup by dividing 72 by 3. We get 24, now we get a total of 96 calories in one cup. Now we have 96x4 which is 384.

P.S. I am a middle schooler in 7th grade

Step-by-step explanation:

So, the most precise classification of quadrilateral LMNP is a kite.

In mathematics, an equation is a statement that two mathematical expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in many areas of mathematics, science, and engineering to model relationships between quantities and to solve problems.

Here,

To classify the quadrilateral LMNP, we need to calculate the length of all four sides using the distance formula and then use those values to determine the shape of the quadrilateral.

The distance formula is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using this formula, we can calculate the length of each side of the quadrilateral as follows:

LM = √[(4 - (-1))² + (9 - 7)²] = √[5² + 2²] = √29

MN = √[(8 - 4)² + (-1 - 9)²] = √[4² + (-10)²] = √116

NP = √[(3 - 8)² + (-3 - (-1))²] = √[(-5)² + (-2)²] = √29

PL = √[(-1 - 3)² + (7 - (-3))²] = √[(-4)² + 10²] = √116

Now, we can use the values we have calculated to determine the shape of the quadrilateral. We can see that LM = NP and MN = PL, which means that opposite sides are congruent. Also, LM and MN are not equal to PL and NP, which means that opposite sides are not parallel. Therefore, LMNP is a kite.

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Discuss measures that can be taken to develop the spirit of hard work

The requried equation of the diagonals for which WXYZ will be rhombus is y = -x + 12 and y = x + 12.

A rhombus is a parallelogram with all sides of equal length. This means that the diagonals of a rhombus bisect each other at right angles.

Let's first find the length of the diagonals of rhombus WXYZ using the distance formula:

WY = \(\sqrt{[(9-1)^2 + (11-3)^2]]}\) = 8√2

Since the diagonals of a rhombus bisect each other at right angles, we can use the midpoint formula to find the midpoint M of the diagonal WY:

Midpoint M = ((1+9)/2, (3+11)/2) = (5, 7)

The slope of the line passing through W and Y is:

slope WY = (11-3)/(9-1) = 8/8 = 1

Therefore, the slope of the line perpendicular to WY is -1/1 = -1.

Using the point-slope form with point M and slope -1, we get:

y - 7 = -1(x - 5)

y = -x + 12

So, the equation of the line passing through M with a slope perpendicular to the line passing through W and Y is y = x + 12 equation for XZ will be the same but the slope will be +1 so the equation is y = x + 1.

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Answer:

c

Step-by-step explanation:

got it from my math book

Answer:

=x?15

Step-by-step explanation:

Answer:

hhhhh

Step-by-step explanation:

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

3a. An equation in slope-point for this line is y + 2 = 1/2(x - 0).

3b. The equation in slope-intercept form is y = 1/2(x) - 2.

4a. An equation in slope-point form to represent this function is y - 3875 = -1/695(x - 19375).

4b. The cost of operating a car that has been driven 31250 km is $3892.086.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part 3.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(4 - 0)

Slope (m) = 1/2

At data point (0, -2) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1/2(x - 0)

y = 1/2(x) - 2

Part 4a.

Based on the information provided about Jay's business, we would determine the slope of the line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3900 - 3875)/(2000 - 19375)

Slope (m) = 25/-17375

Slope (m) = -1/695

At data point (19375, 3875) and a slope of -1/695, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3875 = -1/695(x - 19375)

Part 4b.

For the cost when x = 31250 km, we have:

y - 3875 = -1/695(31250 - 19375)

y = 17.086 + 3875

y = $3892.086.

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The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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A complete set of probabilities will always add up to 1 (option c).

Probability is a fundamental concept in many fields, including mathematics, statistics, and science. It helps us to understand the likelihood of an event occurring, and it is expressed as a number between 0 and 1, inclusive.

The correct answer to the question is "1." A complete set of probabilities will always add up to 1. This means that if we have a set of mutually exclusive events, where only one of them can occur, the sum of their probabilities will be 1.

The other options presented in the prompt, such as 100%, 0.1, and 1%, are not correct. If we express a probability as a percentage, it should be converted to a decimal number between 0 and 1 before adding it to other probabilities.

So, the correct option is (c).

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Answer:

Yes, as for each trial there are only two possible outcomes, the trials are independent, and the number of trials is fixed.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they respond favorably, or they do not. The probability of a student responding favorably is independent of any other student, and the number of trials is fixed. Thus, this probability experiment represents a binomial experiment.

There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.

In Mathematics, the average of these quiz scores can be calculated by using the following formula:

Average = Sum of quiz score/Number of quiz scores

Note: Let the variable q represent the student's score on the third (3rd) quiz.

Substituting the given parameters into the formula, we have the following;

Average = (75 + 83 + q)/3

Average = (158 + q)/3

This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:

85 ≤ (158 + q)/3 ≤ 90

Multiplying all through by 3, we have the following:

255 ≤ (158 + q) ≤ 270

Subtracting 158 from both sides of the inequality, we have the following:

97 ≤ x ≤ 112

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Answer:

b

Step-by-step explanation:

it is b because it is pointing at that angle

The total volume taken by the coins is 88.47 cubic inches, so the correct option is D.

The coins are cylinders with a radius of 1.4 inches and a height of 0.0625 inches.

Remember that the volume of a cylinder is given by:

volume = (height)*pi*(radius)^2

Where pi = 3.14

Then here the volume of each coin is:

V = (0.0625 in)*3.14*(1.4 in)^2 = 0.384 in³

And there are 230 coins, so the total volume is:

V = 230*0.384 in³ = 88.47 in³

So the correct option is D.

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Answer: D: 88.47 in³​

Step-by-step explanation: So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h

Take 1.4 and times it by itself

1.4 x 1.4 = 1.96

Now multiply 1.96 by 0.0625

1.96 x 0.0625 = 0.1225

And times 0.1225 by pi, or in this case, 3.14

0.1225 x 3.14 = 0.38465

Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.

0.38465 x 230 = 88.4695 in³
Now round it to the nearest hundredth: 88.47 in³

That is your answer.

Also I took the same test and I picked 88.47 inches cubed and got it right.

Proof:

Have a good day :)))

The inverses of the following block matrices i 0 c i , a 0 c d , and 0 i i d (assuming they exist) are correct.

To find the inverse of a block matrix, we need to use the following formula:

[A B]

[C D] ^ -1 = 1 / (AD - BC) * [D -B]

[-C A]

where A, B, C, and D are matrices of appropriate sizes and AD - BC is the determinant of the matrix [A B; C D]. If the determinant is zero, the matrix is singular and has no inverse.

(a) [i 0; c i]

The determinant of this matrix is i * i - 0 * c = -c. Since the determinant is non-zero for any non-zero value of c, the matrix has an inverse. Using the formula, we have:

[ i 0 ]

[ c i ] ^ -1 = 1 / (-c * i - 0 * 0) * [ i 0 ]

[-c i ]

= -1 / c * [ i 0 ]

[-c i ]

= [ -1/c 0 ]

[ 0 -1/c ]

To check this inverse, we need to multiply the matrix by its inverse and see if we get the identity matrix:

[ i 0 ]

[ c i ] * [ -1/c 0 ] = [ 1 0 ]

[ 0 1 ]

and

[ i 0 ]

[ c i ] * [ 0 -1/c ] = [ 0 1 ]

[-1 0 ]

So the inverse is correct.

(b) [a 0; c d]

The determinant of this matrix is ad - 0 * c = ad. Since the determinant is non-zero for any non-zero values of a and d, the matrix has an inverse. Using the formula, we have:

[ a 0 ]

[ c d ] ^ -1 = 1 / (ad - 0 * c) * [ d 0 ]

[ -c a ]

= 1 / ad * [ d 0 ]

[ -c a ]

To check this inverse, we need to multiply the matrix by its inverse and see if we get the identity matrix:

[ a 0 ]

[ c d ] * [ d/ad -c/ad ] = [ 1 0 ]

[ 0 1 ]

and

[ a 0 ]

[ c d ] * [ 0 1/ad ] = [ 0 1 ]

[ 0 0 ]

So the inverse is correct.

(c) [0 i; i d]

The determinant of this matrix is 0 * d - i * i = -1. Since the determinant is non-zero, the matrix has an inverse. Using the formula, we have:

[ 0 i ]

[ i d ] ^ -1 = 1 / (-1) * [ d -i ]

[-i 0 ]

= [ -d -i ]

[ i 0 ]

To check this inverse, we need to multiply the matrix by its inverse and see if we get the identity matrix:

[ 0 i ]

[ i d ] * [ -d -i ] = [ 1 0 ]

[ 0 1 ]

and

[ 0 i ]

[ i d ] * [ i 0 ] = [ 0 1 ]

[-1 0 ]

So the inverse is correct.

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Answer:

m > 9

Step-by-step explanation:

-8m<-72

Divide each side by -8, remembering to flip the inequality

-8m/-8>-72/-8

m > 9

Answer:

what's the answer

Step-by-step explanation:

megaboom thank you

Volume is a three-dimensional scalar quantity. As per the Cavaleri's principle the volume of both the figures will be the same.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

According to Cavalieri's principle, if two figures have the same height and cross-sectional area throughout each point along that height, they have the same volume.

The height of both the objects is 16 cm, also the base area of both the objects is 96 cm². As it can be observed that for both the object there base area is the same through out their height.

Hence, as per the Cavaleri's principle the volume of both the figures will be the same.

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The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

The amount of space or volume inside the box but outside the basketball is 6589.44 cm³.

We have to find the volume of the box and volume of the basketball to determine the space outside it.

Box is in rectangular shape.

Volume of the box = 24 × 24 × 24

                                = 13824 cm³

Basketball is spherical in shape.

Volume of the sphere = 4/3 π r³

                                     = 4/3 π (12)³

                                     = 2304π

                                     = 7234.56 cm³

Amount of space inside the box but outside the basketball is,

13824 cm³ - 7234.56 cm³ = 6589.44 cm³

Hence the required space is 6589.44 cm³.

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