use the unique factorization theorem to write the following integers in standard factored form. (a) 504 (b) 819 (c) 5,445

Leo has 48 toy soldiers.

What is the key concept is used to solve the question ?

This problem involves finding a number that satisfies certain conditions related to division with remainders. Specifically, the number must be divisible by 4 with no remainder, must leave a remainder of 6 when divided by 7, and must leave a remainder of 3 when divided by 5.

Calculating the number of toy soldiers :

Let's start by using the first condition to narrow down the possibilities for the number of toy soldiers. We know that the number must be divisible by 4 with no remainder, and it must be between 27 and 54. The multiples of 4 in this range are 28, 32, 36, 40, 44, 48, and 52.

Next, we can use the second condition to eliminate some of these possibilities. If we divide each of these numbers by 7, we get the following remainders:

28 ÷ 7 = 4 remainder 0

32 ÷ 7 = 4 remainder 4

36 ÷ 7 = 5 remainder 1

40 ÷ 7 = 5 remainder 5

44 ÷ 7 = 6 remainder 2

48 ÷ 7 = 6 remainder 6

52 ÷ 7 = 7 remainder 3

The only number in our list that leaves a remainder of 6 when divided by 7 is 48, so we can tentatively conclude that this is the number of toy soldiers.

Finally, we can check the third condition to make sure that 48 leaves a remainder of 3 when divided by 5. Indeed, 48 ÷ 5 = 9 remainder 3, so all of the conditions are satisfied.

Therefore, we can confidently say that Leo has 48 toy soldiers.

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Answer:

51 + 31

Step-by-step explanation:

To compare which quotient is greater between 51+31 and 5 1/4 ÷ 2 1/2, we can use estimation.

First, we can estimate 51+31 to be around 80.

Then, for the second quotient 5 1/4 ÷ 2 1/2, we can convert the mixed numbers to improper fractions to get 21/4 ÷ 5/2. We can then multiply the divisor (5/2) by 2/2 to get a common denominator of 10. This gives us 21/4 ÷ 5/2 = 21/4 ÷ 5/10. We can then invert the divisor and multiply to get 21/4 x 10/5 = 21/2 or 10.5.

Since 80 is greater than 10.5, we can conclude that 51+31 is greater than 5 1/4 ÷ 2 1/2.

Answer:

Ben knows that a line passes through the point (-3, 8) and has a slope of -3/4, but he needs to find the equation of the line. Therefore, he should substitute 8 for_______

and he should substitute -3 for _________, and he should substitute -3/4 for __________ into the Point-Slope Formula. He will need to __________ and simplify before solving for y = mx + b form.

Step-by-step explanation:

To use the Point-Slope formula to find the equation of the line, Ben should substitute the following values:

Substitute 8 for y, since the point (-3, 8) has a y-coordinate of 8.

Substitute -3 for x, since the point (-3, 8) has an x-coordinate of -3.

Substitute -3/4 for m, since the line has a slope of -3/4.

The Point-Slope formula is:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 8 = (-3/4)(x - (-3))

Simplifying the right-hand side, we get:

y - 8 = (-3/4)(x + 3)

To get the equation in y = mx + b form, we can start by distributing the (-3/4) to the x and the 3:

y - 8 = (-3/4)x - 9/4

Adding 8 to both sides, we get:

y = (-3/4)x + 23/4

So the equation of the line is y = (-3/4)x + 23/4.

Answer: 240

You multiply them. 6x4x10 :)

The number of different outfits made by Alyssa as per the given number of shirt , skirts and shoes is equal to 240 outfits.

To find the number of possible outfits Alyssa can make, you multiply the number of choices for each item of clothing:

Number of shirts = 6

Number of skirts = 4

Number of pairs of shoes = 10

Substitute the values and multiply with each other

Total number of possible outfits

= 6 (shirts) × 4 (skirts) × 10 (shoes)

= 240 outfits.

Therefore, Alyssa can make 240 different outfits using her 6 shirts, 4 skirts, and 10 pairs of shoes.

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Answer:

Use the quadratic formula to solve. Show work describe solution.

Step-by-step explanation:

The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.

For example, let's say we have the equation 2x^2 + 5x - 3 = 0.

Here, a = 2, b = 5, and c = -3.

Plugging these values into the quadratic formula, we get:

x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)

Simplifying the expression inside the square root:

x = (-5 ± sqrt(49)) / 4

x = (-5 ± 7) / 4

We get two solutions:

x = (-5 + 7) / 4 = 1/2

x = (-5 - 7) / 4 = -3

So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.

These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.

The graph οf g(x) is the same as its reflectiοn acrοss bοth the y-axis and the x-axis.

What is a graph?

A graph is a structure amοunting tο a set οf οbjects in which sοme pairs οf the οbjects are in sοme sense "related". The οbjects cοrrespοnd tο mathematical abstractiοns called vertices and each οf the related pairs οf vertices is called an edge.

Tο reflect a functiοn acrοss the y-axis, we replace x with -x in the functiοn. This gives us:

f(-x) = 1/4(8) = 2

This functiοn represents the reflectiοn οf f(x) acrοss the y-axis. Tο reflect this functiοn acrοss the x-axis, we replace f(-x) with -f(-x). This gives us:

-f(-x) = -2

Therefοre, the functiοn that results frοm reflecting f(x) = 1/4(8) acrοss the y-axis and then acrοss the x-axis is:

g(x) = -2

This is a hοrizοntal line that intersects the y-axis at -2. The graph οf g(x) is a straight line parallel tο the x-axis, and it dοes nοt change when reflected acrοss the y-axis οr x-axis. Sο, the graph οf g(x) is the same as its reflectiοn acrοss bοth the y-axis and the x-axis.

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The equation which results from applying the loop rule to loop akledcba is Ia + Ik + Il + Ie + Id + Ic + Ib + Ia

The current going through the top is 2.71 A.

Itop = 65 A - (24.0 V/0.10 Ω) - (5.0 Ω * 2) - (48.0 V/20 Ω) - (40 Ω * 0.50 Ω) - (36.0 V/6.0 Ω) - (10.05 Ω * 0.20 Ω) - (78 Ω * 0.20 Ω) = 2.71 A.

For Part (a), the equation resulting from applying the loop rule to loop akledcba is:

Iakledcba = Ia + Ik + Il + Ie + Id + Ic + Ib + Ia

For Part (b), if the current going through the centre of the loop is 65 A, then the current going through the top in amps is:2.71 A.

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The data suggest that females suffer more from asthma than males.

The null and alternative hypotheses for this problem are:
H0: p1 - p2 = 0; HA: p1 - p2 ≠ 0
The value of the test statistic is 3.7775 and its associated p-value is 0.0002. At the 5% significance level, the conclusion is that we reject the null hypothesis, and therefore we can say that the data suggest that females suffer more from asthma than males.

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Answer:

x=8

Step-by-step explanation:

x-3=5

+3=+3(cancel 3)

_____________

x=8

The best interpretation of the mean is A) "Every shipment of 25 bowls will have 23.75 undamaged bowls."

The question states that the company claims that 95% of their shipments arrive undamaged. This implies that the probability of a bowl being damaged in a shipment is 0.05.

Since the random variable G follows a binomial distribution with n=25 (number of shipments) and p=0.05 (probability of a shipment having a damaged bowl), the mean of G is given by np = 25 x 0.05 = 1.25.

However, the question asks about the number of undamaged bowls in a shipment, which is simply the number of bowls in a shipment minus the number of damaged bowls.

Therefore, the mean number of undamaged bowls in a shipment is 25 - 1.25 = 23.75. This means that on average, a shipment of 25 bowls will have 23.75 undamaged bowls.

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The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).

The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.

Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.

To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:

P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)

= (1/4) x (12/51)

= 3/52

Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex]  , or approximately [tex]0.0588[/tex] (rounded to four decimal places).

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First term in a geometric sequence is 5, and common ratio is 2. The sum of the first n terms of the sequence is 163,835.

The following formula can be used to calculate the sum of the first n terms of a geometric sequence:

Sn = a (1 - rn) over (1 - r),

where

a is the first term,

r is the common ratio, and

n is the number of terms.

So, Sn = a (1 - rn) over (1 - r) => 163835 = 5 (1 - 2n) over (1 - 2).

Simplifying it, we have

   163835 = 5 (1 - 2n) over (-1)

=> 163835 = -5 + 10n

=> 163840 = 10n

  => n = 16,384.

Therefore, the value of n is 16,384.

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In a right triangle, the trigonometric ratio x must be positive. There isn't an x solution that meets the requirements. The cosine and sine function values given are incompatible with a correct right triangle. x = -0.40

A right triangle is one with a 90 degree inner angle. The two arms of a right angle are made up of height and base.

The sum of the angles B and C's measurements in a right triangle is 90 degrees (since angle A is 90 degrees).

So we have:

B + C = 90

And since sin C = 3x + 0.31, we know that:

C = sin⁻¹(3x + 0.31)

B + sin⁻¹(3x + 0.31) = 90

Subtracting sin⁻¹(3x + 0.31) from both sides, we get:

B = 90 - sin⁻¹(3x + 0.31)

Now we can use the fact that cos B = x - 0.49:

cos(90 - sin⁻¹(3x + 0.31)) = x - 0.49

Using the identity cos(90 - θ) = sin(θ), we can rewrite this as:

sin(sin⁻¹(3x + 0.31)) = x - 0.49

Simplifying the left side using the inverse sine function, we get:

3x + 0.31 = x - 0.49

Subtracting x and 0.31 from both sides, we get:

2x = -0.80

Dividing both sides by 2, we get:

x = -0.40

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Answer:

Step-by-step explanation:

To find the product of (7-8x)(3x^3-2x^2+x), we need to use the distributive property of multiplication over addition/subtraction.

First, let's distribute the 7 across the second factor:

(7)(3x^3) - (7)(2x^2) + (7)(x)

This simplifies to:

21x^3 - 14x^2 + 7x

Next, we need to distribute the -8x across the second factor:

(-8x)(3x^3) + (-8x)(-2x^2) + (-8x)(x)

This simplifies to:

-24x^4 + 16x^3 - 8x^2

Now, we can combine the two simplifications:

(7-8x)(3x^3-2x^2+x) = 21x^3 - 14x^2 + 7x - 24x^4 + 16x^3 - 8x^2

Finally, we can combine like terms to simplify the expression:

-24x^4 + 37x^3 - 22x^2 + 7x

Therefore, the product of (7-8x)(3x^3-2x^2+x) is -24x^4 + 37x^3 - 22x^2 + 7x.

All of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders include the following:

A. The data are evenly distributed between 7 hours and 9 hours.

D. There is no outlier in the data.

In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

Mathematically, the range of a data set can be calculated by using the following mathematical equation;

Range = Highest number - Lowest number

By critically observing the double box-and-whisker plots or box plot for the variation in the hours slept by eighth graders, we can logically deduce that there is no outlier in the data because they are evenly distributed and centered about the mean.

In conclusion, the box-and-whisker plot or box plot is symmetrical.

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Answer:

Step-by-step explanation:

Yeah what the other guy said

Answer:

80 degrees

Step-by-step explanation:

Remember that corresponding angles are equal!

angle CBD and angle BFH are obviously corresponding angles.

(SEE ATTACHMENT IF YOU DON'T UNDERSTAND)

So, angle CBD = angle BFH = 100 degrees.

The angles of a line add to 180 degrees

angle BFH is 100 degrees and one part of this line. So the other part (aka angle x) is 180 - 100 = 80 degrees.

Thus, x is 80 degrees.

The square root of 138 is between 11 and 12. We can determine this by observing that 11 squared is 121, which is less than 138, and 12 squared is 144, which is greater than 138.

Therefore, the square root of 138 must lie between 11 and 12. Another way to approach this problem is to use estimation. We can start with the closest perfect square to 138, which is 12 squared (144).

Then we can divide the difference between 138 and 144 by twice 12, which gives us (144-138)/(2*12) = 6/24 = 1/4. This means that the square root of 138 is approximately 12 - 1/4 = 11.75, which is between 11 and 12.

In summary, the square root of 138 lies between 11 and 12, as 11 squared is less than 138 and 12 squared is greater than 138. Alternatively, we can estimate the square root of 138 as 11.75, which is also between 11 and 12.

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The following table shows how many hot cocoas Mei Mei would likely sell if the day's high temperature was 42 oF:

58.

How is a linear function defined?

The following is the definition of a linear function's slope and intercept:

y = mx + b.

The slope, or m, indicates the rate of change.

The value of y at x=0 is represented by the intercept, b.

At y = 100, where the function meets the y-axis, the intercept b is defined as follows:

b = 100.

As y decays to 94 when x rises to six, the slope m is calculated as follows:

m = (94 - 100)/(6 - 0) (6 - 0)

m = -1.

As a result, the function that forecasts how much hot chocolate will be sold at a high temperature.

Lack of Information

The graphic provided at the end of the response provides the linear function's graph.

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Answer:

P(A n B) = 1/4

Step-by-step explanation:

We know that:

P(A U B) = P(A) + P(B) - P(A n B)

Substituting the given values, we get:

3/8 = 1/2 + 3/4 - P(A n B)

Simplifying, we get:

P(A n B) = 1/4

Answer: P ( A n B ) = 7/8

Step-by-step explanation:  P ( A U B ) = P(A) + P(B) - P( A n B )

                                                         3/8   =   1/2  + 3/4 - P( A n B )

                                                         3/8   =   5/4 - P ( A n B )

                                               P ( A n B )  =  5/4 - 3/8

                                               P ( A n B )  =   7/8

Answer:

-1/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

Answer: Pie is the unofficial food of Pi Day; its symbol, π, is often carved into pie crusts.

Step-by-step explanation:

Answer:

You can divide and divide, but with pi, you never reach the end of the digits after a decimal point.

Step-by-step explanation:

This is why most people know pie as 3.14. It also means that the circumference is a bit more than 3 times the size of the diameter. It doesn't matter what circle you measure—the relationship will always be the same.

There is sufficient evidence tο say that the mean lifetime οf car engines οf a particular type is greater than 220,000 miles.

The cοnclusiοn οf the hypοthesis test shοuld be the same whether using the critical value apprοach οr using the p-value apprοach. Mοst οf the time the p-value is used tο test a hypοthesis and it is alsο knοwn as the mοdern apprοach.

Hο: μ ≤ 220000

Ha: μ > 220000

Upper Tail

The significance level,

α = 0.01

The sample mean,

¯x = 226450

The sample standard deviation,

s = 11500

The sample size,

n=23

Test statistics:

[tex]$t={\frac{{\bar{x}}-\mu}{{\frac{s}{\sqrt{n}}}}}$[/tex]

[tex]$={\frac{226450-2220000}{\dfrac{11500}{\sqrt{23} y} }$[/tex]

≈ 2.69

Decision rule:

Reject the null if,

p-value ≤α

Decision rule:

Reject the null if,

|Calculated t |≥|Critical t|

Degrees of freedom:

Df = n−1

=22

We can use a t-distribution table, an online tool, or the following excel command to calculate the p-value using excel =TDIST(2.69, 22, 1):

p-value = P(t>2.69)

≈0.0067

Critical value of t using excel: =TINV(0.02, 22)

t(critical) = tα,

df = t(0.01,22)

≈2.51

Decision:

p-value ≈0.0067<α =0.0100

Reject the null.

Conclusion:

There is sufficient evidence to say that the mean lifetime of car engines of a particular type is greater than 220,000 miles.

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Complete question:

Answer:

5 less than or equal to x

Step-by-step explanation:

make x subject

Answer:Let be a random variable with the following probability distribution

Value x of X / P (X=x)

20 / 0.05

30 / 0.05

40 / 0.35

50 / 0.20

60 / 0.35

Find the expectation of E(X) and variance Var (X) of X.

(A) E (x) = ?

(B) Var (X) =?

Step-by-step explanation:

 The study collected data from a random sample of 400 police reports on single persons. The data revealed that 120 individuals in the sample had been involved in at least one automobile accident in the previous three-year period.                

The research department at the home office of automobile accidents has conducted a study to understand the characteristics of drivers who are more likely to be involved in automobile accidents.

The study collected data from a random sample of 400 police reports on single persons. The data revealed that 120 individuals in the sample had been involved in at least one automobile accident in the previous three-year period. This finding is significant because it suggests that a significant proportion of drivers are at risk of being involved in accidents. The study provides valuable insights into the factors that may contribute to automobile accidents, such as driver behavior, age, and experience.

The study may help policy makers and law enforcement agencies develop targeted interventions to reduce the incidence of automobile accidents. For example, the study may suggest that more targeted driver education programs or increased enforcement of traffic laws may be necessary to improve road safety.   Overall, the study conducted by the research department at the home office of automobile accidents provides valuable insights into the incidence and causes of automobile accidents. The findings may inform policies and interventions that can help reduce the risk of accidents and improve road safety.

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The number 2 is the first even counting number,4 is the second even number, 6 is the third even number, and so forth. the sum of the first 25th even counting numbers is 650.

Since we are given that the first even counting number is 2 and each subsequent even counting number can be obtained by adding 2 to the previous one. so  by using the formula for finding the 25th term of an arithmetic series  which :

an=a+(n-1)d, where the nth term d is a common difference and a is the first term so, the  25th term is 2 + (25-1)*2 = 2 + 48 = 50. Now for finding the sum of the first 25 even counting numbers, we use the formula which is Sn = n /2 * (a1 + an),  where Sn is the sum of the first n terms of the series, a1 is the first term, and an is the nth term. since in this  n=25, a1=2 and an=50, so  after substituting the  values we get  S25 = 25/2 * (2 + 50) = 25/2 * 52 = 650

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The probability of leaving it in any given class is 1/4, the probability of leaving it in the 5th class is 1/4, or[tex]0.250 (25.0%).[/tex]

The probability that the student left her iClicker device in the 5th class is 0.250 (25.0%). This is because the probability of leaving it in any given class is 1/4, and as she attends 5 different classes,

there is 5/4 or 1.25 chances of her leaving it in the 5th class.

To explain further, the probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes. In this case, the event is leaving the iClicker device in the 5th class, and the total number of possible outcomes is 5 (for the 5 classes).

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Answer:

The diver descends:

50 seconds x 5 feet/second = 250 feet

The diver ascends:

54 seconds x 4.4 feet/second = 237.6 feet

Therefore, the total change in elevation is:

250 feet (descent) - 237.6 feet (ascent) = 12.4 feet

So, the diver's final elevation is:

0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet

Therefore, the diver ends up 12.4 feet below sea level.

Answer:

it is 1

Step-by-step explanation:

its is 1 2 3 hsvs jafsnsjhd jsusgsmsi jshsbjdg