The ratio of donuts to bagels eaten by teachers in the morning is 4:5. If there were 25 bagels eaten, how many donuts were eaten?

a. This statement is true. We can write b = ak and d = cl for some integers k and l. Then, b + d = ak + cl = a(k + l). Since a|b, we know a must divide ak and thus a also divides ak + cl. Therefore, a + d = a(k + l) is divisible by a.

b. This statement is also true. Similar to part a, we can write b = ak and d = cl for some integers k and l. Then, bd = akcl = (ac)(kl). Since a|b and c|d, we know that a and c must divide ak and cl respectively. Therefore, ac must divide akcl = bd.

c. This statement is false. Consider a = 2, b = 4, c = 2, and d = 6. We have a|b and b|c, but a does not divide c. Therefore, the statement does not hold for all integers a, b, c, and d.

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a. This statement is true. We can write b = ak and d = cl for some integers k and l. Then, b + d = ak + cl = a(k + l). Since a|b, we know a must divide ak and thus a also divides ak + cl. Therefore, a + d = a(k + l) is divisible by a.

b. This statement is also true. Similar to part a, we can write b = ak and d = cl for some integers k and l. Then, bd = akcl = (ac)(kl). Since a|b and c|d, we know that a and c must divide ak and cl respectively. Therefore, ac must divide akcl = bd.

c. This statement is false. Consider a = 2, b = 4, c = 2, and d = 6. We have a|b and b|c, but a does not divide c. Therefore, the statement does not hold for all integers a, b, c, and d.

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Answer:

Step-by-step explanation:

You want the dimensions of a rectangle if adding 2 m to its width makes it a square with an area of 36 m².

The area of a square is the square of its side length, so the side length of the square is ...

  A = s²

  s = √A = √(36 m²) = 6 m

The problem statement tells you this dimension is 2 m more than the width of the rectangle. Hence that width is ...

  6 m - 2m = 4 m

The rectangle is 4 m wide and 6 m long.

Check

The length is 2 m less than twice the width: (2)(4 m) -2 m = 6 m, the value we show above.

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Answer: x= 7191.509 ft

Step-by-step explanation:

Sin9/1 = 1125/x

X/1 = 1125/sin9

Answer:

$10285.29

Step-by-step explanation:

The idea is to solve for the final amount when $7000 is invested and compounded

given data

principal= $7000

rate= 8%= 0.08

time =5years

We know that the expression for the final amount is

\(A = P(1 + {r)^{t}\)

A = 7000(1 + {0.08)^5

A=7000(1.08)^5

A=7000(.469328)

A= 10285.29

They have available to spend on that vacation $10285.29

Answer 15c3d−7c2d2

Step-by-step explanation:

The data does not suggest that the true average total body bone mineral content during postweaning exceeds that during breastfeeding by more than 25g.

1. Hypotheses:

  - Null hypothesis (H0): The true average total body bone mineral content during postweaning is not more than 25g higher than during breastfeeding.

  - Alternative hypothesis (H1): The true average total body bone mineral content during postweaning exceeds that during breastfeeding by more than 25g.

2. Test statistic and significance level:

  - We will use a t-test to compare the means of the two groups.

  - The significance level is given as 0.05.

3. Calculate the test statistic:

  - Subtract the bone mineral content during breastfeeding (B) from the bone mineral content during postweaning (P) for each subject.

  - Calculate the mean difference and standard deviation of the differences.

  - Compute the t-test statistic using the formula: t = (mean difference - 25) / (standard deviation / √n), where n is the number of observations.

4. Degrees of freedom (df):

  - The degrees of freedom for this test is equal to the number of observations minus 1.

5. P-value:

  - Use a statistical computer package to calculate the P-value associated with the obtained test statistic and degrees of freedom.

6. Decision:

  - Compare the P-value to the significance level.

  - If the P-value is less than the significance level (0.05), reject the null hypothesis.

  - If the P-value is greater than or equal to the significance level, fail to reject the null hypothesis.

In this case, the conclusion is based on the calculated P-value. If the P-value is less than 0.05, we would reject the null hypothesis, indicating that the true average total body bone mineral content during postweaning does exceed that during breastfeeding by more than 25g. If the P-value is greater than or equal to 0.05, we would fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude that the average bone mineral content during postweaning is significantly higher than during breastfeeding by more than 25g.

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The equations which are sums of perfect cubes are as follows;

\(\rm 8x^6+27x^9+1\)

\(\rm x^6+x^3\)

\(\rm 27x^9+x^{12}\)

Perfect cubes are the numbers that are the triple product of the same number.

We have to determine

Which are sums of perfect cubes?

1. The given equation is \(\rm 8x^6+27x^9+1\).

The equation can be written as;

\(\rm 8x^6+27x^9+1\\\\2^3(x^2)^3+3^3(x^3)^3+1^3\)

All the terms in the expression are can be represented as perfect cubes.

2.  The given equation is \(\rm 81x^3+16x^6\).

The equation can be written as;

\(\rm 81x^3+16x^6\\\\9^2x^3+4^2(x^2)3\)

In this, all the terms are not perfect cubes, some of them are squares.

3. The given equation is \(\rm x^6+x^3\).

The equation can be written as;

\(\rm x^6+x^3\\\\(x^2)^3+x^3\)

All the terms in the expression are perfect cubes.

4.  The given equation is \(\rm 27x^9+x^{12}\).

The equation can be written as;

\(\rm 27x^9+x^{12}\\\\3^3(x^3)^3+(x^4)^3\)

All the terms in the expression are perfect cubes.

5.   The given equation is \(\rm 9x^3+27x^9\).

The equation can be written as;

\(\rm 9x^3+27x^9\\\\3^2x^3+3^3(x^3)^3\)

In this, all the terms are not perfect cubes, some of them are squares too.

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Answer:

A,B,D,E

Step-by-step explanation:

Got it right on the assignment

We randomly take a card, if it is not a, then the probability that it is b, is 1/4.

We have to find the the probability that it is a card of b, if it is not a.

We have total number of cards = 20

The cards of a = 10

The cards of b = 5

The cards of c = 5

We don't select the card a, then;

The probability of choosing card b = The total number of card b/total number of cards

The probability of choosing card b = 5/20

The probability of choosing card b = 1/4

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Answer:

a + c = 29

10a + 6c = 222

Step-by-step explanation:

Admission for each adult costs $10. Admission for each child costs $6.

A group of 29 people attended the zoo.

The total admission fees paid by the group was $222.

Answer:

$222=a x $10 + c x$6

Step-by-step explanation:

I don't think the question is complete though

The total length of the movie was 120 minutes.

Let's assume the total duration of the movie is represented by 'M' minutes. According to the given information, Newton and his friends watched 30% of the movie before taking a break. This means they watched 0.3M minutes of the movie.

After the break, they watched the remaining portion of the movie, which is 100% - 30% = 70% of the total duration. This can be represented as 0.7M minutes.

We are given that the duration of the remaining portion after the break is 84 minutes. Therefore, we can set up the following equation:

0.7M = 84

To solve for M, we divide both sides of the equation by 0.7:

M = 84 / 0.7

M = 120

Therefore, the total duration of the movie was 120 minutes.

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If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.

This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.

The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.

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Answer:

So if theres two people who can have a drink thats the same and a dessert thats different, then there are 40 different ways you can have one drink with a different dessert.

Step-by-step explanation:

Drinks: 4

Desserts: 10

There are ten desserts for every drink.

10*4, or 10 times 4, equals 40.

For Quadrilateral ABCD is similar to quadrilateral A'B'C'D' the missing lengths can be solved using option 1 and option 3.

A transformation is a method for changing the two-dimensional position of a polygon or other object on a plane or coordinate system. Two-dimensional figures can move across a plane or coordinate system via mathematical transformations.

The shape in two dimensions before any alteration is known as a preimage or inverse image. The transformed figure is depicted in the picture.

When two figures are similar then the ratio of their segments are equal.

This statement is correctly represented by:

A'B' / AB = A'D' / AD

and

AB / A'B' = AD / A'D'

Hence, for Quadrilateral ABCD is similar to quadrilateral A'B'C'D' the missing lengths can be solved using option 1 and option 3.

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\(\huge\color{purple}\boxed{\colorbox{black}{Answer ☘}}\)

in ∆ABE

\( \tan(theta) = \frac{p}{b} \\ \tan(60) = \frac{h}{x} \\ \sqrt{3} = \frac{h}{x} \\ h = \sqrt{3}x\)

Now, in ∆CDE

\( \tan(theta) = \frac{p}{b} \\ \tan(30) = \frac{h}{80 - x} \\ \frac{1}{ \sqrt{3} } = \frac{ \sqrt{3}x }{80 - x} (from \: (1)) \\ = > 3x = 80 - x \\ 4x = 80 \\ x = 20\)

distance of pole CD from E = 80 - x = 60m

distance of pole AB from E = x = 20m

\(h = \sqrt{3} x = 20 \sqrt{3}m\)

Step-by-step explanation:

well, we have several right-angled triangles here.

the main one from the point in the street to the 2 tops of the poles.

and the 2 side ones of the poles to the point on the street.

we know the angle above the point in the street is 90 degrees, because the other 2 angles of the main triangle are 30 and 60 degrees. and the sum of all angles in a triangle must always be 180 degrees.

as the angles up are 30 and 60 degrees, so are their mirrored twins at the tops of the poles as part of the main triangle.

the Hypotenuse of the main triangle is the connection between the tops of the poles, and is also 80m long.

so, now that we have established the "picture", we can use the law of sine to get all the other side lengths.

a/sin(A) = b/sin(B) = c/sin(C)

where the sides are always opposite of the correlated angles.

so, we know,

80/sin(90) = 80 = a/sin(30) = 2a = b/sin(60)

a = 80/2 = 40m (the connection from the point in the street to the top of the pole under 60°)

b = 80×sin(60) = 69.2820323... m (the connection from the point in the street to the top of the second pole under 30°).

now we use the same principle on the side lengths of the 2 side triangles. their Hypotenuses are the 2 sides we just calculated.

let's start with the one with the round number as Hypotenuse : 40m

40/sin(90) = street distance / sin(30) = 2× street distance

street distance = 40/2 = 20m

that means the street distance of the point in the street to the other pole is 80-20 = 60m

for the pole height(s) we now just use regular Pythagoras

c² = a² + b²

with c being the Hypotenuse.

40² = 20² + pole height²

1600 = 400 + pole height²

1200 = pole height²

pole height = 34.64101615... m

Answer:

i think 18

Step-by-step explanation:

The inverse Laplace transform of 1/(s^4-36) is (1/6)sin(6t).

We can use Theorem 7.2.1 to find the inverse Laplace transform of 1/(s^4-36). According to this theorem, if F(s) has partial fraction expansion F(s) = (A/(s-p1)) + (B/(s-p2)) + ... + (N/(s-pn)), where p1, p2, ..., pn are distinct complex numbers and A, B, ..., N are constants, then the inverse Laplace transform of F(s) is given by:

ℒ^(-1){F(s)} = Aℒ^(-1){1/(s-p1)} + Bℒ^(-1){1/(s-p2)} + ... + Nℒ^(-1){1/(s-pn)}

In this case, the denominator s^4-36 can be factored as (s^2+6)(s^2-6). We can rewrite the expression 1/(s^4-36) as 1/[(s^2+6)(s^2-6)]. The roots of s^2+6 are ±i√6, and the roots of s^2-6 are ±√6.

To find the inverse Laplace transform, we need to calculate ℒ^(-1){1/(s^2+6)} and ℒ^(-1){1/(s^2-6)} separately.

ℒ^(-1){1/(s^2+6)} = (1/√6)sin(√6t)

ℒ^(-1){1/(s^2-6)} = (1/√6)sin(√6t)

Using Theorem 7.2.1, the inverse Laplace transform of 1/(s^4-36) is given by:

ℒ^(-1){1/(s^4-36)} = (1/√6)sin(√6t) + (1/√6)sin(√6t)

Simplifying the expression, we get:

ℒ^(-1){1/(s^4-36)} = (2/√6)sin(√6t)

Further simplifying, we find:

ℒ^(-1){1/(s^4-36)} = (1/6)sin(6t)

Therefore, the inverse Laplace transform of 1/(s^4-36) is (1/6)sin(6t).

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Answer:

HIHI! The correct answer you're looking for is 11pi/6 =) & I took the test too

Step-by-step explanation:

h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

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Answer:

y = (1/3)x + 7

Step-by-step explanation:

The general structure form of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.

The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.

m = 1/3

x = -3

y = 6

y = mx + b                                  <----- Slope-intercept form

6 = (-3)(1/3) + b                           <----- Insert values

6 = -1 + b                                    <----- Multiply -3 and 1/3

7 = b                                           <----- Add 1 to both sides

Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.

y = (1/3)x + 7

Answer:

Total time: 67 minutes

Step-by-step explanation:

35m + 4(8m) = 67m

Answer:

READING TIME :- 35 MINUTES

GAME TIME. :- 32 MINUTES

HOPE IT HELPS U!!!!

Answer:

8 maybe

Step-by-step explanation:

22! / 20! × 2!

\(21 \times 11 = 231 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

Answer:

68

Step-by-step explanation:

\(4+\left(11-3\right)^2\\(11-3)=8\\=4+8^2\\=4+64\\=68\)

Answer:

Step-by-step explanation:

x+2

degree is 1  

\(x^{1} +2\)

and has two terms so is a binomial

Answer:

165000

Step-by-step explanation:

simple interest

PV(1+it)

150000(1+5*.02)

=165000

if you need it then the interest earned would just be 165000-150000= 15000

The principal of account A is $20.83 and the principal of account B is $58.33. Account 2 earned the most interest rate in the first​ month.

The formula to calculate Simple interest, Simple interest = Principal × rate of interest × time.

The principle for Account A would be,

2 = Principal × 3.2% × 3

So, the principal is $20.83

The principle for account B would be,

38.50 = Principal × 2.2% × 30

So, the principal is $58.33,

The interest rate for both accounts is now as follows:

For account 1

= $20.83 × 3.2%

= $0.67

And, for account 2

= $58.33 × 2.2%

= $1.28

Account 2 has the greatest interest rate, thus it is taken into account.

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Measure of arc MLK is 270°

Angle MKL = 135 degrees

We are looking for the measure of the arc MLK

The diagram shows an angle formed by a chord (MK) and tangent

The relationship between angle formed by a chord and tangent:

Measure of arc MLK:

Answer:

2(17+8)

Step-by-step explanation:

2*17 is 34 and 2*8 is 16