There are 4 toys in the first box and 7 toys in the second box. what is the ratio of the number of toys in the second box to the total of toys in both boxes

Answer:

The volume is 1474.45 mm^2

Step-by-step explanation:

First, you have to find the radius. To do this, you divide the diameter by 2. This means that the radius is 8.

Then you use the formula V=3.14*r^2*(h/3)

V=3.14*8^2*(22/3)=1474.45 mm^2

Answer:

Step-by-step explanation:

The first roll can be any number from 1 to 6, since there are no earlier rolls to compare it to.

For the second roll, the probability of rolling a number greater than the first roll is 1/2, since there are only three numbers left on the die that are greater than the first roll.

Similarly, the probability of rolling a number greater than the first two rolls on the third roll is 1/3, and the probability of rolling a number greater than the first three rolls on the fourth roll is 1/4.

Therefore, the probability of rolling four numbers that are at least as high as the previous rolls is:

1 x 1/2 x 1/3 x 1/4 = 1/24

So the probability of rolling four numbers that are at least as high as the previous rolls is 1/24.

The probability of rolling each number higher than the previous number when a die is thrown four times is 1/3.

To calculate this probability, we must first understand the concept of a combination. A combination is a way of selecting items from a set, such that the order of selection does not matter. In this case, the set is the numbers 1-6.

The probability of rolling each number higher than the previous number is equal to the probability of selecting four numbers from a set of six without repeating any of them.

We can calculate this probability by dividing the number of desired combinations by the total number of possible combinations.

The number of desired combinations is equal to the number of ways we can choose the first number from the set (6 choices), multiplied by the number of ways we can choose the second number from the remaining five (5 choices), and so on.

Therefore, the number of desired combinations is 6*5*4*3, which is 360.

The total number of possible combinations is equal to the number of ways we can choose four numbers from a set of six, which is 6*5*4*3*2*1, or 720.

Therefore, the probability of rolling each number higher than the previous number when a die is thrown four times is 360/720, which is equal to 1/3.

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For a government published the above stem-and-leaf plot related to number of sloths at each major zoo in the country. The smallest of sloths at any one zoo was three.

A stem-and-leaf plot is a tool for presenting quantitative data in a graphical format, like as histogram for visualizing the shape of a distribution.

We have a stem-and-leaf plot present above and which showing the number of sloths at each major zoo in the country is published by government. Now, see the above plot carefully, thee smallest number in the stem-and-leaf plot is 03. We can get that by looking at the first stem value and the first leaf value. Hence, required number is 3.

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Complete question:

The government published the above stem-and-leaf plot showing the number of sloths at each major zoo in the country:pls answer fast if you can :

what was the smallest number of sloths at any one zoo?

The calculated value of the area of the circle with radius 7 feet is 153.93 square feet.

To find the area of a circle with radius 7 feet, we can use the formula A = πr^2, where A is the area and r is the radius.

Substituting the given value of radius, we get:

A = π(7)^2

Simplifying this expression, we get:

A = 49π square feet

Evauate the expression

So, we have

A = 153.93 square feet

Therefore, the area of the circle with radius 7 feet is 153.93 square feet.

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Complete question

Find the area.

Remember: A = πr²

Round to the nearest hundredth.

Use 3.14 for π

The finite population correction factor (FPC) is a factor used when the sample size is more than 5% of the population size. It corrects for the bias that can occur when taking a sample from a finite population.

Applying the FPC to the sample mean results in the standard error for the sample mean being equal to the population standard deviation divided by the square root of the sample size times the FPC.
In other words, the standard error for the sample mean is equal to:
Standard Error = Population Standard Deviation/√(Sample Size*FPC)
The FPC is calculated by taking the reciprocal of the following formula:
FPC = (N-n)/(N-1), where N is the population size and n is the sample size.
In conclusion, applying the FPC to the sample mean reduces the bias that can occur when taking a sample from a finite population, and the resulting standard error for the sample mean is equal to the population standard deviation divided by the square root of the sample size times the FPC.

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Answer:

When calculating the area of a triangle, you multiply the base by the height and then divide the result by 2. This is because a triangle is half of a parallelogram or a rectangle, and these shapes have an area equal to base times height. By dividing by 2, you are finding half of the area of the parallelogram or rectangle.

For a trapezoid, you can find the area by taking the average of the bases and multiplying it by the height. So the formula for the area of a trapezoid is A = (b1 + b2)h/2, where b1 and b2 are the lengths of the two parallel bases and h is the height. There is no need to divide the result by 2 because the formula already takes the average of the bases into account.

The probability of Felipe winning a prize is 1/5 or 0.2.

As per given equation:

Odds in favor of Felipe winning a prize is

Probability of an event is given by

P(event) = Number of favorable outcomes/ Total number of outcomes

In the given problem, the odds in favor of Felipe winning a prize are.

Hence, the probability of Felipe winning a prize is

P(win) = Number of favorable outcomes/ Total number of outcomes

Let us assume that there are x favorable outcomes and y total outcomes.

Then, according to the odds, we have x : y-x or x : y

There are two possibilities for x and y-x.

Thus, the total number of outcomes will be:

Total number of outcomes = x + (y - x) = y

Therefore, we have P(win) = x/y

Since the odds in favor of Felipe winning a prize are , we have x : y-x = :

That is, x:y-x = 1:4

This means that if x is 1, then y-x is 4.

So, the total number of outcomes is:

Total number of outcomes = x + (y - x) = 1 + 4 = 5

Hence, the probability of Felipe winning a prize is:

P(win) = x/y= 1/5

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The ratio of the surface area to the volume of the cylinder is 2/r + 1/9.

Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the formula for the surface area of a cylinder, we have;

Surface area (SA) of cylinder = (2 × π × r × 18) + 2πr²

Surface area (SA) of cylinder = 36πr + 2πr²

For the volume, we have:

Volume of cylinder = πr²h

Volume of cylinder = πr²(18)

Volume of cylinder = 18πr²

Now, we can determine the ratio;

Ratio = (36πr + 2πr²)/18πr²

Ratio = 2/r + 1/9

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Answer:

C

Step-by-step explanation:

A (- 6, - 8 ) and C (9, - 8 )

since the y- coordinates of both points are equal, both - 8

then AC is a horizontal line

the distance AC can be calculated by calculating the absolute value of the x- coordinates, that is

AC = | 9 - (- 6) | = | 9 + 6 | = | 15 | = 15 units

or

AC = | - 6 - 9 | = | - 15 | = | 15 | = 15 units

given 1 unit = [tex]\frac{1}{2}[/tex] mile , then

AC = 15 units = 15 × [tex]\frac{1}{2}[/tex] = 7.5 miles

Answer: m = 6/5

Step-by-step explanation:

Answer: m=6/5

Step-by-step explanation:

We use the formula I = Prt where I is the interest earned, P is the principal, r is the interest rate per year, and t is the time in years. Substituting the values, we find that it will take 4 years for a $5000 balance to reach $6500 with a 7.5% simple interest rate.

To solve this problem, we can use the formula for simple interest:

I = Prt

Where I is the interest earned, P is the principal (initial amount), r is the interest rate per year (as a decimal), and t is the time in years.

In this case, we know that the principal is $5000, the interest rate is 7.5% or 0.075, and we want to find the time required for the balance to reach $6500.

Substituting these values into the formula, we get:

I = $6500 - $5000 = $1500

P = $5000

r = 0.075

t = ?

Solving for t, we get:

$1500 = $5000 * 0.075 * t

t = $1500 / ($5000 * 0.075)

t = 4

Therefore, it will take 4 years for the balance of the account to be $6500 with a 7.5% simple interest rate.

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Answer:

The greatest common factor (GCF) of -16x^2 - 6x^4 is 2x^2.

To find the GCF, we can factor out the common factors of the two terms. In this case, both terms have a factor of 2 and a factor of x^2.

-16x^2 - 6x^4 = 2x^2(-8 - 3x^2)

So the GCF is 2x^2.

From the given information provided, the surface area and volume of cylinder is 1130.97 and 3816.85 respectively.

To find the surface area and volume of the cylinder, we can use the following formulas:

Surface Area = 2πr² + 2πrh

Volume = πr²h

Substituting the given values, we get:

Surface Area = 2π(9)² + 2π(9)(15) = 1130.97 square inches (rounded to the nearest tenth)

Volume = π(9)²(15) = 3816.85 cubic inches (rounded to the nearest tenth)

Therefore, the surface area of the cylinder is approximately 1130.97 square inches, and the volume is approximately 3816.85 cubic inches, both rounded to the nearest tenth.

Question - A cylinder has a height of 15 in and a radius of 9 in. Find area and volume. Round to the nearest tenth.

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Answer: b

Step-by-step explanation:

u just add them together

The inequality "w < 30" describes the weeks for which Halimah will put money in the bank instead of buying an oud. It means she must save for less than 30 weeks to have less than $300 saved.

Let's assume the number of weeks Halimah saves money is represented by the variable "w".

Halimah saves $10 per week, so the total amount of money she saves after "w" weeks is:

Total amount saved = $10 x w

According to the problem, Halimah will put the money in the bank instead of buying an oud if she saves less than $300. Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is:

$10 x w < $300

Simplifying the inequality:

w < 30

Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is "w < 30".

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Complete question:

Halimah saves $10 per week for w weeks to buy an oud. If she saves less than $300, she will put the money in the bank instead of buying an oud.

What inequality describes the number of weeks for which Halimah will put money in the bank?

The x² statistic for the goodness-of-fit test is approximately 104.15.

EXPLANATION:

In the given case, is the data assuming binomial distribution with a probability of 0.8 that a flight leaves on time. We have to find the x² statistic for the goodness-of-fit test.

The steps involved are:

Calculate the expected values for each category of data (in this case, the number of on-time departures) using the given probability and sample size

.Use the formula:

χ² = Σ [(observed value - expected value)² / expected value]

Here, Σ means sum over all the categories. Now, let's solve the given problem to find the x² statistic for the goodness-of-fit test.

Problem

Let p = probability that a flight leaves on time = 0.8

n = sample size = 200

Then, q = 1 - p = 0.2

The binomial distribution is given by B(x; n, p), where x is the number of on-time departures.

So, we can write:

B(x; 200, 0.8) = (200Cx)(0.8)x(0.2)200-x= (200! / x!(200 - x)!) × (0.8)x × (0.2)200-x

Now, we can calculate the expected frequency of each category using the above formula.

χ² = Σ [(observed value - expected value)² / expected value]

The observed value is the actual number of on-time departures. But, we don't have this information.

We are only given the sample size and the probability. Hence, we can use the expected frequency as the observed frequency.

The expected frequency is obtained using the formula mentioned above.

χ² = Σ [(observed value - expected value)² / expected value]

Let's calculate the expected frequency of each category.

Because the probability of success is 0.8 and there are two flights per day, the expected number of on-time departures per day is 1.6 (i.e., 2 × 0.8).

Hence, the expected frequency of each category is:0 on-time departures:

Expected frequency = B(0; 200, 0.8) = (200C0)(0.8)0(0.2)200-0 = (0.2)200 ≈ 2.56 on-time departures:

Expected frequency = B(1; 200, 0.8) = (200C1)(0.8)1(0.2)200-1 = 200(0.8)(0.2)199 ≈ 32.06 on-time departures:

Expected frequency = B(2; 200, 0.8) = (200C2)(0.8)2(0.2)200-2 = (199 × 200 / 2) (0.8)2 (0.2)198 ≈ 126.25

Similarly, we can calculate the expected frequency of all categories. After that, we can calculate the x² statistic as:

χ² = Σ [(observed value - expected value)² / expected value]

χ² = [(0 - 2.5)² / 2.5] + [(1 - 32.1)² / 32.1] + [(2 - 126.25)² / 126.25] + ... (all other categories)

χ² = 104.15 (approx)

Hence, the x² statistic for the goodness-of-fit test is approximately 104.15.

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The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. The periodic rate is 1.1867%

The finance charge is the cost of borrowing money, and it is typically expressed as a percentage of the outstanding balance. In the given scenario, the finance charge is the interest that is charged on the unpaid balance.

10) The unpaid balance is the previous balance minus the payment, which is:

Unpaid balance = Previous balance - Payment

                           = $678.98 - $150

                           = $528.98

Therefore, the unpaid balance is $528.98.

11) The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. Since the period is monthly, we divide the APR by 12. The periodic rate is:

Periodic rate = APR / 12

                     = 14.24% / 12

                     = 1.1867%

Therefore, the periodic rate is 1.1867%.

12) The finance charge is the unpaid balance multiplied by the periodic rate. The finance charge is:

Financial charge = Unpaid balance times the periodic rate

                            = $528.98 × 1.1867%

                            = $6.28 (rounded to the nearest cent)

Therefore, the finance charge is $6.28.

13) The new balance is the sum of the unpaid balance, the finance charge, and the purchases. The new balance is:

New balance = Unpaid balance + Finance charge + Purchases

                      = $528.98 + $6.28 + $147.20

                      = $682.46

Therefore, the new balance is $682.46.

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You need 1.8 lbs of the type of chocolate that sells for $2.50/lb and 6.6 lbs of the type of chocolate that sells for $3.60/lb.

A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these problems. The intersection of two lines represents the system of equations' solution.

let

x = lbs of the type of chocolate that sells for $2.50/lb

y = lbs of the another type of chocolate that sells for $3.90/lb

You would like to have 8.4 lbs of a chocolate mixture that sells for $3.60/lb

x + y = 8.4

2.50x + 3.90y = 8.4 x 3.60

2.50x + 3.90y = 30.24

Putting the value of x = 8.4 - y in equation 2.

2.50( 8.4 - y) + 3.90y = 30.24

21 - 2.5y + 3.9 y = 30.24

1.4y = 9.24

y = 6.6

Putting y in x equation we get,

x = 1.8

by solving the above system of equations we find:

x = 1.8 lbs

y = 6.6 lbs

Therefore, each chocolate will you need to obtain the desired mixture is 1.8 lbs and 6.6 lbs.

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The common difference of the arithmetic sequence -6, 10, 26, 42 is given as follows:

16.

The common difference of an arithmetic sequence is the constant value added or subtracted to each term in the sequence to get to the next term.

The sequence for this problem is given as follows:

-6, 10, 26, 42, . . .

The difference between consecutive terms is given as follows:

42 - 26 = 16, which is constant for the other terms of the sequence.

Hence 16 is the common difference of the arithmetic sequence -6, 10, 26, 42, . . . given in this problem.

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The wallpaper cost $40 to John.

To find the amount of wallpaper John purchased, we have to solve for x in the cost function equation.

First, let's write down the cost function c(x) using the given information.Cost function equationc(x) = 12x + 20.

Here, x is the amount of wallpaper needed in square meters, and c(x) is the total cost John has to pay, including the cost of wallpaper and delivery.

Now, let's use the given total cost of $500 and solve for x.c(x) = 12x + 20Since the total cost John paid is $500, we can write the following equation:12x + 20 = 500

To solve for x, we can isolate x on one side by subtracting 20 from both sides.12x = 480x = 40Therefore, John purchased 40 square meters of wallpaper.

Answer: 40

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Step-by-step explanation:

Probabilities

The question describes an event where two counters are taken out of a bag that originally contains 11 counters, 5 of which are white.

Let's call W the event of picking a white counter in any of the two extractions, and N when the counter is not white. The sample space of the random experience is Ω = {WW, W N, NW, N N}

We are required to compute the probability that only one of the counters is white. It means that the favorable options are A = {W N, NW}

Let's calculate both probabilities separately. At first, there are 11 counters, and 5 of them are white. Thus, the probability of picking a white counter is 5/11.

Once a white counter is out, there are only 4 of them and 10 counters in total. The probability to pick a non-white counter is now 6/10.

Thus, the option WN has the probability P(WN) = 5/11 x 6/10 = 30/110 = 3/11

Now for the second option NW. The initial probability to pick a non-white counter is 6/11.

The probability to pick a white counter is 5/10

Thus, the option NW has the probability P(WN) = 6/11 x 5/10 = 30/110 = 3/11

P(A) = 3/11 + 3/11 = 6/11.

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Karla paid 57.1% of the original price for an item that was originally priced at $350.

The explanation is that we can find the percentage that Karla paid by dividing the amount she paid by the original price and then multiplying by 100.

Percentage is a fraction out of 100. The formula for finding the percentage is as follows:  (part / whole) × 100.

So, if Karla paid $200 for an item that was originally priced at $350, we can find the percentage she paid as follows: (200/350) × 100 = 57.1%.

Therefore, Karla paid 57.1% of the original price. To round it to the nearest tenth of a percent, we can simply round the answer to one decimal place, which is 57.1%.

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The surface area of this rectangular prism is equal to 68 mm².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

SA = 2(WH + LW + LH)

Where:

By substituting the given parameters into the formula for the surface area of a rectangular prism, we have the following;

SA = 2(1 × 4 + 6 × 1 + 6 × 4)

SA = 2(4 + 6 + 24)

SA = 2(34)

SA = 68 mm².

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Answer:

The length of BD in its simplest radical form is [tex]\sf \sqrt{429}[/tex].

Step-by-step explanation:

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

[tex]\boxed{\sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}}[/tex]

Given values (see attached diagram):

To find the length of the altitude BD, substitute the values into the formula and solve for x:

[tex]\implies \sf \dfrac{BD}{AD}=\dfrac{DC}{BD}[/tex]

[tex]\implies \sf \dfrac{x}{33}=\dfrac{13}{x}[/tex]

[tex]\implies \sf x^2=429[/tex]

[tex]\implies \sf x=\sqrt{429}[/tex]

As the square root of 429 cannot be simplified any further, the length of BD in its simplest radical form is [tex]\sf \sqrt{429}[/tex].

Answer:

Step-by-step explanation:

nothing makes it true

Answer:

Step-by-step explanation:

# elements = 292 - 268 - 1 = 23 elements

G has 2^23 subsets = 8388608

G has 2^23 - 1 proper subsets = 8388607

Answer:

average rate of change on [-1,3] = 11

Step-by-step explanation:

avg rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

[tex]\frac{f(3)-f(-1)}{3-(-1)}[/tex]

1. find your y-values.

we are given the x values from the interval [-1,3]. Plug each into the equation to get the y-value of the coordinates.

[tex]f(-1)=4(-1)^2+3(-1)-4\\f(-1)=4(1)-3-4\\f(-1)=-3\\[/tex]

coordinate: (–1,3)

[tex]f(3)=4(3)^2+3(3)-4\\f(3)=4(9)+9-4\\f(3)=36+9-4\\f(3)=41[/tex]

coordinate: (3, 41)

2. plug into the slope formula

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{41-(-3)}{3-(-1)} \\m=\frac{41+3}{4} \\m=\frac{44}{4} \\m=11[/tex]

The polynomial 7x² - 4 + 6x³ - 4x - x⁴ in standard form is - x⁴ + 6x³ + 7x² - 4x - 4  

Given that

7x² - 4 + 6x³ - 4x - x⁴

The standard form of a polynomial is when the terms are arranged in decreasing order of degree

To rewrite 7x² - 4 + 6x³ - 4x - x⁴ in standard form, we need to rearrange the terms accordingly:

- x⁴ + 6x³ + 7x² - 4x - 4  

Now the terms are in decreasing order of degree, with the highest degree term first

This is the standard form of the polynomial.

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The probability that company will receive five or more objections in a single day is [tex]0.9951[/tex].

Probability is simply the possibility that something will happen. We may talk about the possibility with one result, or the probability of numerous outcomes, if we don't understand how such an occurrence will turn out. Statistical is the study of events that follow a probabilistic model.

Probability is typically considered as one of the most difficult mathematical concepts because probabilistic arguments can occasionally give results that seem inconsistent or nonsensical. The Monty Hill paradox and the anniversary problem are two examples.

Let [tex]X[/tex] be the random variable denoting the number of complaints received in a day. We need to find P(X ≥ 5).

Using the Poisson probability mass function,

P(X ≥ 5) = 1 - P(X < 5)

[tex]= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)[/tex]

[tex]= 1 - e^{(-7)(1 + 7 + 24.5 + 57.33 + 100.18)}[/tex]

[tex]= 1 - 0.0049[/tex]

[tex]= 0.9951[/tex]

Therefore, the probability that the firm receives [tex]5[/tex] or more complaints in a day is [tex]0.9951[/tex].

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Answer:

z=8

Step-by-step explanation:

Considering the triangle on the RHS,

Let the Unknown side be "x"

from pythagora's theorem,

x ^ 2 = 4 ^ 2 - 2 ^ 2 x = √(4 ^ 2 - 2 ^ 2)

x = √(16 - 4)

x = √12

cos alpha = 2/4 , alpha = arccos(2/4)

alpha = 60°

< ABC + theta + alpha = 180°

theta = 180 - alpha - <ABC

theta = 180 - 60 - 90

theta = 30°

Now Considering the triangle on the LHS,

tan 30 = (√12)/y

y = (√12)/(tan 30°)

y = 6

z = y + 2

z = 8