(1 point) in how many ways can 5 different novels, 3 different mathematics books, and 1 biology book be arranged on a bookshelf if (a) the books can be arranged in any order? answer: 362880 (b) the mathematics books must be together and the novels must be together?

Answer:

A

Step-by-step explanation:

Proofs attached to answer

hope you understood the answer

Answer:

The correct answer is Option A, (x | 57 < x < 67}. This means that Darnell could spend any amount of time between 57 and 67 minutes on homework one day, give or take 5 minutes.

Step-by-step explanation:

The expected grade for a student working six hours on the project is given as follows:

b) 90.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function that predicts the grade of a student working x hours in the project is given as follows:

y = 5x + 60.

Hence, for a student working six hours, the expected grade is given as follows:

y = 5(6) + 60

y = 90.

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The sum of 1/6 and 1/4 is greater than 1/2.

The sum of 1/6 and 1/4 is greater than 1/2. This can be demonstrated with a simple formula and calculation.

To begin, the fraction 1/6 can be written as the decimal 0.1667, and the fraction 1/4 can be written as the decimal 0.25. When these two decimals are added together, the sum is 0.4167. This number can then be converted back into a fraction. 0.4167 can be written as 41/99. When simplified, this fraction is 41/99, which is greater than 1/2 when written as a fraction.

This can be demonstrated with a formula as well. The sum of 1/6 and 1/4 can be written as the equation 1/6 + 1/4 = x. When this equation is solved, the sum is x = 5/12. This fraction can be simplified to 41/99, which is greater than 1/2.

In conclusion, the sum of 1/6 and 1/4 is greater than 1/2. This can be shown with a simple calculation and formula.

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Answer: La edad de Andrés, Carlos y Rodolfo son respectivamente 35, 31 y 24 años

Step-by-step explanation:

Datos:

A la edad de Andrés,

C la edad de Carlos

R la edad de Rodolfo

Explicación:

Se plantean las siguiente ecuaciones:

La suma de las edades de Andrés Carlos y Rodolfo es de 90 años

Ec. 1 : A+C+R= 90

La edad de Andrés excede en 4 años a la edad de Carlos

Ec. 2: A= C+4 → C= A-4

La edad de Andrés excede en 11 años a la edad de Rodolfo

Ec. 3: A= R+11 → R= A-11

Se reemplaza Ec. 2 y Ec. 3 en Ec. 1:

A+C+R= 90

A+A-4 +A-11 = 90

3A-15= 90

3A=105

A=105/3

A=35

Se reemplaza el valor de A en Ec.2 y Ec. 3:

C= A-4

C= 35-4

C=31

R= A-11

R=35-11

R=24

The sοlutiοns tο x² + 8x - 3 = 0 using the cοmpleting-the-square methοd are x = -4 ± √19.

A square is a geοmetric shape with fοur equal sides and fοur equal angles. In algebra, the term "square" is οften used tο refer tο raising a number tο the pοwer οf 2, οr multiplying a number by itself.

Tο sοlve the quadratic equatiοn x² + 8x - 3 = 0 using the cοmpleting-the-square methοd, we fοllοw these steps:

Mοve the cοnstant term tο the right-hand side οf the equatiοn:

x² + 8x = 3

Cοmplete the square by adding the square οf half the cοefficient οf x tο bοth sides οf the equatiοn:

x² + 8x + (8/2)² = 3 + (8/2)²

x² + 8x + 16 = 25

Rewrite the left-hand side οf the equatiοn as the square οf a binοmial:

(x + 4)² = 25

Take the square rοοt οf bοth sides οf the equatiοn, remembering tο cοnsider bοth the pοsitive and negative square rοοts:

x + 4 = ±5

Sοlve fοr x by subtracting 4 frοm bοth sides οf each equatiοn:

x = -4 ±5

Sο, the sοlutiοns tο the equatiοn x² + 8x - 3 = 0 are:

x = -4 + 5 = 1

x = -4 - 5 = -9

Therefοre, the sοlutiοns tο the equatiοn are x = 1 and x = -9.

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This means that there is a 25% chance that the salesperson will make no more than 3 sales in an hour.

A salesperson is a professional who works to solicit and close sales with customers. They typically work in retail stores, warehouses, or other businesses where customers come to purchase goods or services. Salespeople focus on providing excellent customer service and developing relationships with potential and existing customers. They must be able to build trust with their customers and understand their needs in order to make successful sales. They must also be able to use different techniques to present products, services, and solutions to customers.

The probability of making no more than 3 sales in an hour is calculated by dividing the total number of possible outcomes with 3 or fewer sales (in this case, 4) by the total number of possible outcomes (16). This gives us a probability of 4/16, or 25%. This means that there is a 25% chance that the salesperson will make no more than 3 sales in an hour.

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By the end of the hour he will have made no more than 3 sales and the probability is  25%  or 1/4.

What is probability?

Probability means possibility of something or some incident. In this part of mathematics we deals with the occurrence of a random event. The value is in between zero and one.

The probability of making no more than 3 sales in an hour is calculated by dividing the total number of possible outcomes with 3 or fewer sales.

twenty minutes into the hour, the salesperson has made his first sale.

here the occurrence of 3 or fewer sales is 4

and the total number of possible outcomes is 16

so the probability is 4/16= 1/4

that is 25%.

Hence, there is a 25% chance that the salesperson will make no more than 3 sales in an hour also the probability is 1/4.

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Answer:

x = y = 5

Step-by-step explanation:

This triangle and its markings show that the acute angles are equal. Given that it is a right triangle, this is a 45-45-90 triangle. This also means that the values of x and y are equal. Note that for any triangle, if two angles are equal, then their corresponding side lengths are also equal. The side lengths for this type of triangle follow the pattern s - s - s√2 where the first two are side lengths and last value is the length of the hypotenuse. (s represents the length of a side)

We want to find x and y, so we need the value of s.

s√2 = 5√2
s = 5

Therefore, x = 5, y = 5.

Answer: y=mx+c

m is the gradient, and c is the y-intercept.

lmk if u want me to try to solve it::} (try)

Step-by-step explanation:

The volume of the rectangular prism is 8 cubic meters when it takes 8 blocks with a side lengths of one fourths meter to fill a rectangular prism.

If it takes 8 blocks with a side length of one fourths meter to fill a rectangular prism, we can assume that the volume of each block is:

[tex](1/4)^3 = 1/64m^3[/tex]

To find the volume of the rectangular prism, we need to know its dimensions. We can express its volume as one of the given options:

One eights cubic meters: This means the volume is 1/8 cubic meters. We can find the number of blocks needed to fill this volume by dividing the total volume by the volume of each block:

(1/8) ÷ (1/64) = 8 blocks

This doesn't match the given information, since we were told that it takes 8 blocks to fill the prism, not that the volume of the prism is 8 times the volume of a block.

One fourths cubic meters: This means the volume is 1/4 cubic meters. We can find the number of blocks needed to fill this volume in the same way:

(1/4) ÷ (1/64) = 16 blocks

This also doesn't match the given information.

Half cubic meters: This means the volume is 1/2 cubic meters. We can find the number of blocks needed to fill this volume:

(1/2) ÷ (1/64) = 32 blocks

Since it takes 8 blocks to fill the prism, this option doesn't match either.

One cubic meter: This means the volume is 1 cubic meter. We can find the number of blocks needed to fill this volume:

1 ÷ (1/64) = 64 blocks

This matches the given information, since it takes 8 blocks to fill the prism, which means there are 8 layers of 8 blocks each. Therefore, the dimensions of the prism are:

length = 8 × (1/4) = 2 meters

width = 8 × (1/4) = 2 meters

height = 8 × (1/4) = 2 meters

So the volume of the rectangular prism is:

volume = length × width × height = 2 × 2 × 2 = 8 cubic meters.

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The distance between her house and her mother's house =135 miles

Let the entire distance be 3x

Normally that takes 180 minutes

speed would be  (3x)/180  =  x/60   miles per minute

It would take 60 minutes to go the first distance of x and 276-60 = 216 minutes to the next 2x miles

She hits a bad snowstorm and reduces her speed by 20 miles per hour.

So her speed would be, (x - 20)/60 miles

for given situation we formulate an equation,

(x - 20)/60 = 2x/216

(x - 20)/10 = x/18

18x - 360 = 10x

8x = 360

x = 45 miles

So, the total distance would be:

3x = 3 × 45

    = 135 miles

Therefore, the required distance is 135 miles

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The solution to the equation is x = 4 when the given equation in the question is 24 + 0.44x = 19 + 1.69x.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by collecting the x terms on one side and the constant terms on the other side, as follows:

24 + 0.44x = 19 + 1.69x

Subtract 0.44x from both sides:

24 = 19 + 1.25x

Subtract 19 from both sides:

5 = 1.25x

Divide both sides by 1.25:

4 = x

Therefore, the solution to the equation is x = 4. To check our answer, we can substitute x = 4 back into the original equation and verify that both sides are equal:

24 + 0.44(4) = 19 + 1.69(4)

26.76 = 26.76

This confirms that x = 4 is indeed the solution to the equation.

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Answer is correct. Maximum vertical distance between the line y = x + 6 and the parabola y = x² for -2 ≤ x ≤ 3 is 6.25.

Follow these steps:

1. Subtract the equation of the line from the equation of the parabola to find the difference between their y-values: (x²) - (x + 6).

2. Simplify the expression: x² - x - 6.

3. Now we need to find the maximum value of this expression in the given interval. To do this, find the vertex of the parabola formed by the expression.

4. The vertex of a parabola with the form y = ax² + bx + c is given by the formula x = -b/(2a). In this case, a = 1 and b = -1, so the x-coordinate of the vertex is x = 1/2.

5. Since 1/2 is within the interval -2 ≤ x ≤ 3, the maximum vertical distance occurs at this x-coordinate.

6. Substitute x = 1/2 into the expression x² - x - 6 to find the maximum vertical distance: (1/2)² - (1/2) - 6 = 1/4 - 1/2 - 6 = -6.25.

7. Since we're looking for the maximum vertical distance, we need to consider the absolute value of the difference: |-6.25| = 6.25.

So, the maximum vertical distance between the line y = x + 6 and the parabola y = x² for -2 ≤ x ≤ 3 is 6.25.

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Answer:

Step-by-step explanation:

Mason subtracted 5 from each side instead of adding 5.

x - 5 < 11

x - 5 + 5 < 11 + 5

x < 16

The number line will have an open circle at 16 since it does not include

16.  It will be shaded to the left from that open circle as it includes

all values less than 16.  

Two positive consecutive even integers such that the square of the smaller integer decreased by five times the larger integer is 536 are 22 and 24.

Let's start by using algebra to solve the problem.

Let x be the smaller of the two consecutive even integers. Then the larger integer is x+2.

According to the problem statement, we have:

x² - 5(x+2) = 536

Expanding the left side, we get:

x² - 5x - 10 = 536

Moving all the terms to one side, we have:

x² - 5x - 546 = 0

We can solve for x using the quadratic formula:

x = (5 ± √(5² - 4(1)(-546)))/ (2(1))

x = (5 ± √(2201)) / 2

x ≈ 23.52 or x ≈ -18.52

Since we are looking for positive even integers, we can discard the negative solution and round the positive solution down to the nearest even integer, which is 22. Therefore, the two consecutive even integers are 22 and 24.

We can check that these numbers satisfy the original equation:

22² - 5(24) = 484 - 120 = 364

And indeed, 364 is 536 less than 900 (which is 30²).

Therefore, the two positive consecutive even integers that satisfy the given condition are 22 and 24.

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Answer:

43.9

Step-by-step explanation:

Complementary angles add to 90 degrees.

x  + 46.1 = 90

x = 90-46.1

x =43.9

The complementary angle is 43.9.

Answer: x = 8

Step-by-step explanation:

As you can see 15 is divided by 3 and so is 9 so you divide 24 by 3 and you get 8 because 24 divided by 3 = 8

Step-by-step explanation:

Based on the information you provided, an actuary earns $94,740 per year while a nurse practitioner earns $89,960 per year. The difference in their annual salaries is $4,780. Over 20 years, an actuary would earn $95,600 more than a nurse practitioner (20 years * $4,780/year = $95,600).

The coordinates of Point V, given the base of the triangle and the coordinates of the triangle is  (4, 3).

To find the coordinates of point V, which is the intersection of the height YV and the base XZ, we first need to find the equation of the line XZ and then the equation of the perpendicular line YV.

First, find the slope of XZ:

m_XZ = (y2 - y1) / (x2 - x1) = (1 - 5) / (6 - 2) = (-4) / (4) = -1

We can plug in the coordinates of point X (2, 5) to find b:

5 = -1 x 2 + b

5 = -2 + b

b = 7

So the equation of line XZ is:

y = -x + 7

The equation of line YV is:

y = x - 1

To find the intersection point V, we need to solve the system of equations:

y = -x + 7

y = x - 1

-x + 7 = x - 1

7 = 2x - 1

x = 4

Now plug x back into either equation to find y. We'll use the second equation:

y = 4 - 1

y = 3

So the coordinates of point V are (4, 3).

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the ratio of the height of the model to the height of the actual Arch is 0.0024.

To find the ratio of the height of the model to the height of the actual Arch, we need to divide the height of the model by the height of the actual Arch. We can convert the height of the actual Arch from feet to inches to make the units consistent.

First, we convert 630 feet to inches by multiplying by 12 (since there are 12 inches in a foot):

630 feet * 12 inches/foot = 7,560 inches

Next, we can simply divide the height of the model by the height of the actual Arch:

Ratio = Height of Model / Height of Actual Arch

Ratio = 18 inches / 7,560 inches

Ratio = 0.0024

So the ratio of the height of the model to the height of the actual Arch is 0.0024.

This means that for every 1 inch of height in the model, there are 416.67 inches of height in the actual Arch (1 / 0.0024 = 416.67). In other words, the model is 416.67 times smaller than the actual Arch in terms of height.

This ratio can be useful in determining the scale of other objects or models that relate to the Gateway Arch. For example, if we wanted to create a model of the Gateway Arch's surrounding park, we could use the same ratio to ensure that the scale is consistent with the model of the Arch itself.

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The amount of radioactive goo that will remain after 29 minutes is approximately 58.862 grams.

To solve this problem, we need to use the formula for radioactive decay

N(t) = N0 × e^(-λt)

Where

N(t) is the amount of radioactive material at time t

N0 is the initial amount of radioactive material

λ is the decay constant

t is the time elapsed

We can find λ using the half-life of the substance. Let's assume that the half-life of the radioactive goo is 25 minutes. This means that after 25 minutes, half of the initial amount will remain, and after another 25 minutes, half of that remaining amount will remain, and so on.

To find λ, we can use the formula

λ = ln(2) / half-life

λ = ln(2) / 25

λ = 0.0278 (rounded to four decimal places)

Now we can use the formula for N(t) to find the amount of radioactive material after 29 minutes

N(29) = 132 × e^(-0.0278 × 29)

N(29) = 132 × e^(-0.8072)

N(29) = 132 × 0.4465

N(29) = 58.862 grams (rounded to three decimal places)

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The given question is incomplete, the complete question is:

At the beginning of an experiment, a scientist has 132 grams of radioactive goo. After 75 minutes, her sample has decayed to 2.0625 grams . How many grams of goo will remain after 29 minutes?

a. The minimum number of dogs which could have a mass of more than 26 kg is of: 5.

b. The maximum number of dogs that could have a mass of more than 26 kg is of: 16.

The frequency table shows the number of times that each value, or values in each range, appears in the data-set.

A number of 11 weights are between 20 and 30, hence:

Full words "The table shows information about the masses of some dogs.

a) Work out the minimum number of dogs that could have a mass of more than 26 kg

b) Work out the maximum number of dogs that could have a mass of more than 26 kg

Mass, x (kg)  Frequency

0≤x≤10    4

10≤x≤20    8

20≤x≤30   11

30≤x≤40   5

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The x-intercepts of the quadratic function shown is (−2, 0) and (2, 0). Hence, option D is correct.

A quadratic equation is a second-degree polynomial equation of the form [tex]\rm ax^{2} + bx + c = 0[/tex], where x is the variable and a, b, and c are constants, with a ≠ 0.

Quadratic equations can have one, two, or no real solutions depending on the values of the constants a, b, and c. The solutions of a quadratic equation can be found by using the quadratic formula.

None of the given options are correct as they all describe x-intercepts that lie on either the x-axis or y-axis.

For a quadratic function in standard form, [tex]\rm y = ax^{2} + bx + c[/tex], the x-intercepts can be found by setting y = 0 and solving for x using the quadratic formula.

a. (0, −2) and (0, 1),

Here x - intercepts is 0 as x vale in both points are 0

b. (0, −2) and (0, 2)

Here x - intercepts is 0 as x value in both points are 0

c. (−2, 0) and (2, 0)

x - intercepts are -2 and 2 and is the correct answer.

d.  (−2, 0) and (1, 0)

x - intercepts are -2 and 1 and is the incorrect answer.

Thus, the x-intercepts of the quadratic function shown is (−2, 0) and (2, 0). Hence, option D is correct.

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What are the x-intercepts of the quadratic function?

(graph in attachment)

a. (0, −2) and (0, 1)

b. (0, −2) and (0, 2)

c. (−2, 0) and (2, 0)

d. (−2, 0) and (1, 0)

The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.85, 0.976).

Rhythm is the pattern of regular or irregular pulses or beats in music or poetry. It is the underlying structure in music, the beat or pulse that provides the framework for a musical composition. It is also the sense of movement created by the alternation of different sounds and silences.  Rhythm can be described as a fundamental element of all forms of music and art, as it is the primary way in which music is perceived and experienced.

This can be calculated using the following formula:
p ± (Z *√( p * (1- p ) ) /√n )
Where:
p = sample proportion = 85/125 = 0.68
Z = z-score for 99% confidence interval = 2.575
n = sample size = 125
The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.85, 0.976).

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The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.783, 0.577).

A confidence interval is the mean of an estimate minus the variability of that estimate. This is the range of values ​​within which the estimate will fall within a certain level of confidence when the test is repeated. Confidence is an alternative way of expressing probability in statistics.

This can be calculated using the following formula:

p ± (Z ×√( p × (1- p ) ) /√n )

Where:

p = sample proportion

p = 85/125

p = 0.68

Z = z-score for 99% confidence interval

Z = 2.575

n = sample size

n = 125

Now, substitute the values:

0.68 ± (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )

For 0.68 + (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )

= 0.783

For 0.68 - (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )

= 0.577

The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.783, 0.577).

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Answer: No

Step-by-step explanation:

If you added 11 + 24 + 25 you would get 60.

A right angle is 90 degrees and you can tell if it's a right angle or not if it forms an "L".

Hint:

Try drawing a square where the 2 lines in the word "L" meet if you can draw a square then that means it's a right angle and that it equals 90 degrees.

Answer:

the answer will be: C. 1/25

Step-by-step explanation:

There are five possible values for each coupon, so there are 5 x 5 = 25 possible combinations of food and pharmacy coupons. Each combination is equally likely, so the probability of getting any particular combination is 1/25.

There is only one combination that gives a $0.25 food coupon and a $0.40 pharmacy coupon, so the probability of getting this combination is 1/25.

Therefore, the probability that a customer receives a $0.25 food coupon and a $0.40 pharmacy coupon at the checkout is 1/25 or 0.04 (4%).

In this case, we are given a coupon-printing machine at the checkout of a grocery store prints one food coupon and one pharmacy coupon for each customer: $0.25, $0.30, $0.40, $0.45, or $0.50. It is asked in the problem to give the probability that a customer receives a $0.25 food coupon and a $0.40 pharmacy coupon at the checkout. Since the customer chose the $0.25 food coupon and a $0.40 pharmacy coupon,

Then the probability is 2/5. this is equal to 40%.

Answer:

Step-by-step explana add