It takes  algebra books (all the same thickness) and  geometry books (all the same thickness, which is greater than that of an algebra book) to completely fill a certain shelf. Also,  of the algebra books and  of the geometry books would fill the same shelf. Finally,  of the algebra books alone would fill this shelf. Given that  are distinct positive integers, it follows that  isSolution

9514 1404 393

Answer:

Step-by-step explanation:

The midline is half the length of the parallel base.

  2(2x +36) = 3x +57

  4x +72 = 3x +57 . . . . . . eliminate parentheses

  x = -15 . . . . . . . . . . subtract 72+3x from both sides

Then the length of GH is ...

  GH = 2x +36 = 2(-15) +36 = -30 +36

  GH = 6

_____

The calculation steps are shown above. The strategy is to take advantage of the relation between the lengths of a midline and the corresponding base segment.

Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Answer:

median

Step-by-step explanation:

(median is used to measure the middle)

you just line up all the numbers from least to greatest, then pick the middle number, IF there are NO numbers in the middle, you add the the 2 middle numbers up, then divided by 2

Answer:

Median, because there is 1 outlier that affects the center

Step-by-step explanation:

"The median is the middle number of the data set. It is exactly like it sounds. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. If there is an odd number of data points, then you will have just one middle number."

Answer:

2

Step-by-step explanation:

The option that is NOT a condition/assumption of the chi-square test for two-way tables is: d. Random sample(s) of individuals that fall into just one cell of the table.

In the chi-square test for two-way tables, it is not required that the sample consists of individuals who fall into just one cell of the table. The chi-square test analyzes the association between two categorical variables in a contingency table. The conditions/assumptions for the chi-square test are:

a. Large enough expected counts: The expected frequency for each cell in the table should be at least 5 or higher. This ensures that the chi-square test statistic follows the chi-square distribution.

b. Normal data or large enough sample size: The chi-square test is based on an asymptotic distribution and works well for large sample sizes. However, it is not dependent on the assumption of normality.

c. None of these options: all three conditions/assumptions are necessary: This is an incorrect option because the assumption of normality is not necessary for the chi-square test. The other two conditions (large enough expected counts and random sample) are indeed necessary for the validity of the test.

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Answer:

Step-by-step explanation:

Option A

9.21 * 10³ = 9,210 ≠ 921

Option A is FALSE.

Option B

9.21 * 10¹ = 92.1

Option B is TRUE.

Option C

0.921 * 100 = 92.1 ≠ 921

Option C is FALSE

Option D

0.921 * 10⁴ = 9,210

Option D is TRUE

Option E

0.0921 * 10² = 9.21

Option E is TRUE

Answer:

tom

Step-by-step explanation:

The value of the expression is 284 5/ 9

A fraction can be defined as the part of a whole.

Some types of fractions are;

Given the fraction;

-13(21 4/9)

First, we convert the mixed fraction in the bracket to a proper fraction

- 13( 197/ 9)

Now, let's expand the bracket

-2561/ 9

Find the quotient

284 5/ 9

Thus, the value of the expression is 284 5/ 9

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There is a 0.25 and a 0.5 chance that the flight will arrive no more than 5 and 10 minutes late, respectively. 130 minutes is the estimated flight time.

Probability density function: It can take on any value and is used to define the random unknown probability falling inside a specific range of values.

For its flights from Cincinnati to Tampa, Delta Airlines reports a flight duration of 2 hours and 5 minutes.

Let's say we think the range of real flight timings is 2 hours to 2 hours and 20 minutes.

a)Between 120 and 140 minutes, the probability density function for a continuous uniform random variable is given as

\(f(x)=\left \{ {{\frac{1}{140-120},120 \leq x\leq 140}\\ \atop {0.o.e}} \right.\)

b)The likelihood that the flight will arrive no later than five minutes late is

integration from 130 to 125 of 1/20dx=5/20=1/4=0.25

c)There is a 10% chance that the flight will arrive no more than 10 minutes late.

integration from 135 to 125 of 1/20dx=10/20=0.5

d)The anticipated duration of the flight, in minutes, is

integration from 140 to 120 of x/20dx=(5200*5)/(2*20)=130

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The value of x in the quadrilateral is 23.

A quadrilateral is a polygon with 4 sides. The sum of interior angles in a quadrilateral is 360 degrees.

The sum of external angles of any polygon, irrespective of the number of sides is 360∘.

Therefore, the value of x of the quadrilateral can be found as follows:

6x + x + 16 + 3x - 1 + 5x = 360

combine like terms

6x + x + 3x + 5x + 16 - 1 = 360

15x = 360 - 15

15x = 345

divide both sides by 15

x = 345 / 15

x = 23

Therefore, the value of x is 23.

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Answer:

He should use the computer less.

Step-by-step explanation:

It is bad for mathews eyes.

The domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}. (Option A).

Now,

In the given function {(-3,4),(0,6),(2,-2),(1,-3),(6,-7),(3,2)},

Thus, According to the definition of domain and range,

Hence, Option A is correct, i.e., the domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}.

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Answer:

1/10

Step-by-step explanation:

2.50-2=0.5

0.5/2=0.25

0.25+2=2.25

2.5-2.25=0.25

0.25/2.5= 0.1

0.1 = 1/10

Answer:

$840 dollars

Step-by-step explanation:

Divide 540 by 9 to get the cost of 1 book then multiply it by 14

Answer:

$840

Step-by-step explanation:

\(\frac{14}{9}: \frac{y}{540}\)

y × 9 = 540 × 14

9y = 7560

9y ÷ 9 = 7560 ÷ 9

y = 840

The uniform continuous probability for the interval (25 < x < 45) within the uniform distribution U(15, 65) can be found by calculating the proportion of the total range that falls within that interval.

To calculate the probability, we need to determine the length of the interval (45 - 25) and divide it by the length of the entire range (65 - 15).

Length of the interval: 45 - 25 = 20

Length of the entire range: 65 - 15 = 50

Now, we divide the length of the interval by the length of the entire range to obtain the probability:

Probability = (Length of interval) / (Length of entire range) = 20 / 50 = 0.4

Therefore, the uniform continuous probability for p(25 < x < 45) within the uniform distribution U(15, 65) is 0.4, rounded to one decimal place.

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Answer:

384 cubic inches

Step-by-step explanation:

For this problem, we simply need to apply the volume formula for a box. The volume is length times width times height.

We are given length = 12 inches

We are given width = 8 inches

We are given tall(height) = 4 inches

So let's Calculate the volume.

Volume = Length * Width * Height

Volume = 12 inches * 8 inches * 4 inches

Volume = 384 cubic inches

Hence, the volume of the box is 384 cubic inches.

Cheers.

The mean and standard deviation for the number of correct answers for such students is; μ = 6.5 and σ = 1.802776

Given there is a surprise​ true/false test with 13​ questions.

Thus, the probability of correctly guessing the answer is; p=0.5

Let "X' be the answers correctly guess by a student.

The formula for the binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

A) The mean of the binomial distribution is given by the formula;

μ = np

μ = 13 * 0.5

μ = 6.5

The formula for standard deviation is:

σ = √(np(1 - p))

σ = √(13 * 0.5(1 - 0.5))

σ = 1.802776

B) The probability that the student getting at least 11 correct​answers is given by:

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13)

Using online binomial probability calculator, we have;

P(X ≥ 11) = 0.01123

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Complete question is;

Several psychology students are unprepared for a surprise​true/false test with 13 ​questions, and all of their answers are guesses.

a. Find the mean and standard deviation for the number of correct answers for such students.

b. Would it be unusual for a student to pass by guessing​ (which requires getting at least 11 correct​ answers)? Why or why​not?

Answer:

989cm

Step-by-step explanation:

103, 131, 149, 111

Bottom length = 103 + 149 = 253

Left height = 131 + 111 = 242

103 + 131 + 149 + 111 + 253 + 242 = 989

Answer: 36034 is the answer

Step-by-step explanation:

838

x 43

----------

When multiplying by larger numbers with two digits or more, use one placeholding zero when multiplying by the tens digit, two placeholding zeros when multiplying the hundreds digit, three zeros when multiplying by the thousands digit, and so forth.

Answer:

36034

Step-by-step explanation:

As a child, Mary despised her stringent upbringing;

however, as she grew older she began to appreciate

her grandmother’s strict  discipline.

The correct option is B.

Discipline - despised is the past tense of despise meaning - to feel contempt or a deep repugnance for something or someone. Discipline, on the other hand, is the process of teaching people to follow rules while using punishment to enforce compliance.

Although flexibility is not typically considered a benefit of discipline, being disciplined now will result in flexibility later. However, being rigid will result from being strict. Build the proper systems in your life by working hard to do so, but realize that the system itself won't ultimately matter.

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As a result οf answering the given questiοn, we may state that Varda equatiοn may thus mοw 20 lawns in 8 hοurs if she keeps the same mοwing rate.

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides separated by an equals sign (=). Fοr example, the equatiοn "2x + 3 = 9" argues that the expressiοn "2x + 3" is equal tο the value "9". The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that make the equatiοn true.

Simple οr cοmplex equatiοns, linear οr nοnlinear, and invοlving οne οr mοre variables are all pοssible. Fοr example, the quadratic equatiοn "x² + 2x - 3 = 0" invοlves the variable x raised tο the secοnd pοwer. Equatiοns are utilised in many areas οf mathematics, such as algebra, calculus, and geοmetry.

We can use the fοllοwing fοrmula:

rate = time / wοrk

where rate is Varda's mοwing speed, wοrk is the number οf yards she mοws, and time is the amοunt οf time she spends mοwing.

Varda is said tο mοw 10 lawns in 4 hοurs, hence her rate is:

10 lawns / 4 hοurs = 2.5 lawns per hοur

We can use the similar fοrmula tο determine hοw many lawns Varda can cut in 8 hοurs:

rate * time = wοrk

When we substitute the values we knοw, we get:

wοrk = 2.5 lawns each hοur multiplied by 8 hοurs = 20 lawns

Varda may thus mοw 20 lawns in 8 hοurs if she keeps the same mοwing rate.

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Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Hey there!

-y - (-3) = 7

-y + 3 = 7

-y = 7 - 3

-y = 4

=> y = -4

Hope it helps ya!

The labor hours required for the eighth satellite are calculated to be 51,200 based on a learning curve value of 0.5120 and an expected improvement curve of 80%.

The learning curve concept suggests that as the cumulative production doubles, the labor hours required to produce each unit decrease by a certain percentage. In this case, the learning curve value for the eighth unit is given as 0.5120, which means that the labor hours needed for the eighth satellite is 51.20% of the labor hours required for the first unit.

To calculate the actual number of labor hours, we multiply the learning curve value by the total labor hours required for the first unit. Given that the total labor hours for the first unit is 100,000, we can calculate the labor hours for the eighth satellite as follows: 0.5120 * 100,000 = 51,200.

Therefore, based on the given learning curve value and the expected improvement curve of 80%, the number of labor hours for the eighth satellite is determined to be 51,200.

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Answer:

The answer is 103 + h

Step-by-step explanation:

The sum of 103 and h

i.e., 103 + h

Thus, The answer is 103 + h

-TheUnknownScientist

Answer:

x > 5.5

Step-by-step explanation:

4(x - 3) - (2x - 1) > 0

4x - 12 - 2x + 1 > 0

4x - 2x - 11 > 0

2x - 11 > 0

2x - 11 + 11 > 0 + 11

2x > 11

2x ÷ 2 > 11 ÷ 2

x > 5.5

Answer:

x>13/2

Step-by-step explanation:

4x-12-2x-1>0

2x-13>0

2x>13

X>13/2

Answer:

B

Step-by-step explanation:

cut tghe shape into one rectangle and a two cimi circles

area of a rect. is b x h --> 7x14 = 98ft^2

now make the two cimi circles a whoal and find the area of a circle

pie r^2 --> 3.14x3.5^2 = 38.48

add both getting about 136.48

Answer:

136.48 ft^2 (B)

Step-by-step explanation:

First, we need to find the area of a rectangle.

A(rectangle) = l * w

  = 14 ft * 7 ft

  = 98 ft^2

Next we need to find the area of the two semicircles.

A(semicircle) * 2 = πr^2/2 * 2

                           = π(3.5 ft)^2

                           = 12.25π ft^2

                           = 38.48 ft^2

Finally, you add the two areas:

98 ft^2 + 38.48 ft^2 = 136.48 ft^2

Hope this helps!

Answer: A

Step-by-step explanation:

To solve for x, we can set the expression equal to 24√47 and solve for x.

24√47 = x√47

24 = x

Therefore, the value of x that makes the expression equivalent to 24√47 is x = 24, which corresponds to the answer choice A.