5. Arrange the following interest rates in ascending order (least to greatest):
4.72
4 1/4
4.168
4 1/5
4 1/6
4.22

There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

To learn more about integer: https://brainly.com/question/929808

#SPJ11

Answer: 8b^2 + 9b + 3y + 5 =

Step-by-step explanation:

8b^2 + 9b + 3y + 5 =

Answer:

2.5 cups of milk will make his ingredients proportional.

Step-by-step explanation:

Since he used five out of the three cups of flour he was supposed to use, you can use that as the fraction: 5/3.

Since 5/3 was used on the flour, it also has to be used on the milk

To apply it to the milk, you just multiply 5/3 × 1.5 cups of milk, which gets you 2.5 cups of milk

*Multiplying by a fraction also means of.

Example: 1/2 × 4 = 2 because two is 1/2 of 4

To find the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number, we can use the principle of inclusion-exclusion.

First, we find the total number of ways to pick a set of six balls from the bin, which is 21 choose 6 (written as C(21,6)) = 54264.

Next, we find the number of ways to pick a set of six balls from the bin in which all the balls have even numbers. There are only 10 even-numbered balls in the bin, so the number of ways to pick a set of six even-numbered balls is 10 choose 6 (written as C(10,6)) = 210.

Therefore, the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number is:

C(21,6) - C(10,6) = 54264 - 210 = 54054.

So there are 54054 ways to pick a set of six balls from the bin in which at least one ball has an odd number.e

learn more about odd here:brainly.com/question/29377024

#SPJ11

Answer:

385836

Step-by-step explanation:

Use a calculator, or do traditional multiplication by carrying over numbers. 8769 plus itself 44 times = 385836

Answer:

385836

Step-by-step explanation:

use calculator

The solution to the equation cos(2x + 45°) = 0.8 in the domain of 0° to 180° is x = 15° and X=139° or X=176 °

Because Cos (±37° +360k) = 0.8

0≤2X ≤ 360°

0+45°=2x+45° 360°+45° 45°≤ 2x+45°< 405°

50 2x+45° = 360°-37° or 2x+45° = 360° + 37°

{list the equation} 397° -45°=2X = 323-45°

2X = 323-45°. 2x=397° -45°

2x= 278°.         2x= 352°

X = 139°.          X=176°

So , x = 139° or x = 176°

To discover the solution set of an equation with a particular domain, first insert each domain value into the equation to obtain the associated range values. Make ordered pairs out of these values and put them down as a set. That set is your solution!

To learn more about Cos to refer

brainly.com/question/16498526

#SPJ1

Answer:

The club can continue to accept customers for 9.66 hours, after which they'll have exceeded 600.

Step-by-step explanation:

339 + 29h = 600

29h = 261

h = 9.66

The percentage of the sheets with no air bubbles is given as follows:

13.53%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

The mean for this problem is given as follows:

\(\mu = 2\)

The proportion of these sheets with no air bubbles is P(X = 0), hence it is given as follows:

P(X = 0) = e^-2 = 0.1353 = 13.53%.

More can be learned about the Poisson distribution at https://brainly.com/question/7879375

#SPJ1

Answer:

converges.

Step-by-step explanation:

We can use the ratio test to determine whether the series converges or diverges.

The ratio test states that for a series ∑aₙ, if the limit of the absolute value of the ratio of successive terms is less than 1, then the series converges absolutely. If the limit is greater than 1 or does not exist, then the series diverges.

Let's apply the ratio test to the given series:

lim k→∞ |(k^(2+1)−k+2) / (3(k+1)^(4)+2(k+1)^(2)+1) * (3k^(4)+2k^(2)+1) / (k^(2)−k+1)|

= lim k→∞ |(3k^(6) + 8k^(5) - 5k^(4) - 6k^(3) + 9k^(2) + 2k + 1) / (3k^(6) + 12k^(5) + 23k^(4) + 22k^(3) + 13k^(2) + 4k + 1)|

= 3/3 = 1

Since the limit of the absolute value of the ratio of successive terms is 1, the ratio test is inconclusive. We need to use another test.

Let's try the limit comparison test, where we compare the given series to another series whose convergence or divergence is known.

We can choose the series ∑[infinity]->k=1 1/k^(2). This series converges by the p-series test since p=2>1.

Now, let's find the limit of the ratio of the two series:

lim k→∞ [(k^(2)−k+1) / (3k^(4)+2k^(2)+1)] / (1/k^(2))

= lim k→∞ k^(4)(k^(2)-k+1)/(3k^(4)+2k^(2)+1)

= 1/3

Since the limit is a finite positive number, both series have the same convergence behavior. Therefore, the given series converges by comparison to the convergent series ∑[infinity]->k=1 1/k^(2).

Therefore, the given series converges.

The given series can be determined to be a convergent series using the Limit Comparison Test.

To apply the Limit Comparison Test, we need to find another series whose behavior is known. We can do this by simplifying the given series by dividing both the numerator and denominator by k^4. This gives us:

[(k^2/k^4) - (k/k^4) + (1/k^4)] / [3 + (2/k^2) + (1/k^4)]

Now, as k approaches infinity, all the terms containing k will approach zero, leaving us with:

[0 - 0 + 1/k^4] / [3 + 0 + 0]

Simplifying this expression further gives us:

1 / 3k^4

Now, we can compare this to the known convergent p-series, 1/k^2, by taking the limit of the ratio of their terms as k approaches infinity:

lim as k -> infinity of [(1/3k^4)/(1/k^2)] = lim as k -> infinity of (k^(-2))/3 = 0

Since the limit is a finite value, we can conclude that the given series is convergent by the Limit Comparison Test. Therefore, the series converges.

To learn more about Limit Comparison Test, visit:

https://brainly.com/question/30758037

#SPJ11

Allopurinol:

- Xanthine oxidase inhibitor

- Prevents the buildup of uric acid

- Prevents urinary/bladder/kidney stones

Answer:

a) (2x+7)(x-4)

b) x = -7/2 and x = 4

Step-by-step explanation:

a) (2x  ?)(x  ?)

set up the above and considered factors of 28 that, when paired with 2, would give me -1x and -28  → (1·28, 2·14, 4·7)

after trial-and-error, found that 4 and 7 worked (used un-FOIL)

b) 2x + 7 = 0

2x = -7

x = -7/2

*********

x-4 = 0

x = 4

One ounce of food contains average  about 28 grams of carbs.

One of the three macronutrients that the body needs for energy, carbohydrates can be found in a wide variety of foods. Sugar, starch, and fiber are the three elements that make up carbohydrates. Weight is measured in ounces, which weigh 28.35 grams. As a result, one ounce of food contains about 28 grams of carbs. Carbohydrates are crucial for supplying the body with the 4 calories per gram of energy it needs to function, fuel physical activity, and help with digestion. Foods like fruits, vegetables, grains, nuts, and dairy products all naturally include ounces of carbs. It is crucial to remember that there are several kinds of carbs, some of which are healthier than others.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

The complete question is

How many grams of carbs in an ounce of food ?

Answer:

A

Step-by-step explanation:

Answer:

88.5

Step-by-step explanation:

First you multiple 9.5 and 8 and you should get 76.0

last you add 12.5 and 76.0 and you should get 88.5

and make sure you line up the decimals when adding.

hope this helps

The natural logarithm of 0 is undefined, this initial condition does not satisfy the solution to the differential equation. Please check the given initial condition or the differential equation for any errors.

To solve the given initial value problem, we need to find the solution to the differential equation and then apply the initial condition.

The differential equation is given as:

dy/dx = 2xy + y²

To solve this differential equation, we can use separation of variables. Let's separate the variables and integrate both sides:

(1/(2xy + y²)) dy = dx

Integrating both sides:

∫(1/(2xy + y²)) dy = ∫dx

To evaluate the integral on the left side, we can make a substitution. Let's substitute u = 2xy + y²:

d(u) = (d(2xy) + d(y²))

d(u) = (2xdy + 2ydy)

d(u) = 2x dy + 2y dy

d(u) = 2xy dy + 2y² dy

The integral becomes:

∫(1/u) d(u) = ∫dx

ln|u| = x + C1, where C1 is the constant of integration.

Substituting back u = 2xy + y²:

ln|2xy + y²| = x + C1

Now, we need to apply the initial condition y(1) = -2 to find the value of the constant C1. Substituting x = 1 and y = -2 into the equation above:

ln|2(1)(-2) + (-2)²| = 1 + C1

ln|-4 + 4| = 1 + C1

ln|0| = 1 + C1

know more about differential equation here;

https://brainly.com/question/32645495

#SPJ11

Answer:

The answer is the first choice and the last choice.

Step-by-step explanation:

The first one is already solved for y, so when you plug 9 into the equation in the x spot since 9 is the x-coordinate of the point, you get -2, which is correct because it is the corresponding y-value.

The second one is a mess when trying to solve and it clearly doesn't yield the right answer.

For the last one, when you solve for y and then plug in 9 for x, you get -2, the y-value making it correct.

Smallpox is a highly contagious disease transmitted through direct skin contact with skin crusts. It is characterized by symptoms such as fever, prostration, rash, and potential toxemia and shock. The virus can become dormant in the ganglia of sensory neurons, leading to recurrent episodes known as shingles.

Smallpox is primarily transmitted through close contact with infected individuals, specifically through direct skin-to-skin contact or by inhaling respiratory droplets from an infected person. The disease manifests with initial symptoms of high fever, severe fatigue, and body aches, leading to a characteristic rash that covers the body. Smallpox can also cause toxemia, resulting in a severe systemic illness with potential complications like shock.

Additionally, the virus responsible for smallpox, variola virus, has the ability to establish latent infection. After the acute infection subsides, the virus can enter a dormant state and reside in the ganglia of sensory nerves. If reactivated, typically due to a weakened immune system or other factors, the virus can cause a recurrent episode known as shingles. Shingles is characterized by painful, blistering rashes that typically follow the distribution of sensory nerves and can occur years after the initial smallpox infection.

In conclusion, smallpox is indeed a disease that can be transmitted through direct skin contact with skin crusts. It presents with symptoms such as fever, prostration, rash, and potential toxemia and shock. Moreover, the variola virus responsible for smallpox can become latent in the ganglia of sensory neurons, leading to recurrent episodes known as shingles.

Learn more about high here: https://brainly.com/question/13807620

#SPJ11

The values of x that solve the equation g(x) = 0 are x = -3, 1, 5 and 7 and there are four values of x that solve the equation g(x) = 2

The graph represents the given parameter

(a) Evaluate g (-2), g(0), g (3) and g (7)

To do this, we take the function value at the given value of x

The function g(-2) means

x = -2

So, we have

When x = -2, g(x) = -3

This means that g(-2) = -3

The function g(0) means

x = 0

So, we have

When x = 0, g(x) = -3

This means that g(0) = -3

The function g(3) means

x = 3

So, we have

When x = 3, g(x) = 4

This means that g(3) = 3

The function g(7) means

x = 7

So, we have

When x = 7, g(x) = 0

This means that g(7) = 0

On the graph, we have the following values of x at g(x) = 0

x = -3, 1, 5 and 7

Hence, the values of x that solve the equation g(x) = 0 are x = -3, 1, 5 and 7

See attachment

Using the line in (c), the line crosses the curve four times at y = 2

Hence, there are four values of x that solve the equation g(x) = 2

Read more about functions at

https://brainly.com/question/1415456

#SPJ1

Amount of gift wrap to cover the entire box = total surface area of rectangular box = 1,048 in.².

The total surface area of a rectangular box is the area of all the faces of the box = 2(wl + hl + hw).

Therefore, to find the material that will cover the whole rectangular box, Demarcus should find its total surface area, given the following dimensions:

Plug in the values into TSA = 2(wl + hl + hw):

Total surface area of rectangular box = 2(8×20 + 13×20 + 13×8) = 1,048 in.²

Learn more about total surface area of rectangular box on:

https://brainly.com/question/24448247

Answer:

-549/8 as mixed number

Answer:

62

Step-by-step explanation:

4x + 6

4(14) + 6 (substituting x = 14)

56 + 6

62

Answer:

y=3x+4.8 would be the incorrect answer

Step-by-step explanation:

1234567 ate ine tan

Answer:

the correct answer is A. y= 4.8x + 3 on Edge

Answer:

43.6 (approximately)

Step-by-step explanation:

Diagonal measures of the screen is,

√(35²+26²)

= √(1901)

= 43.6 (approximately)

Answered by GAUTHMATH

We calculate the dioglonal using the Pythagorean theorem

\(\displaystyle\ C^2=A^2+B^2=> C=\sqrt{A^2+B^2} \ then \\\\C=\sqrt{26^2+35^2} =\sqrt{1225+676} =\sqrt{1901} \approx43.6\\\\Answer : the \:diagonal \:\:length is \:\underline{43.6}\)

To prove that (6,1) is a solution to the system, we have to evaluate it in each equation, if it satisfies both equations, then it's a solution to the system.

EVALUATING (6,1) IN THE FIRST QUESTION.

As you can observe, the given coordinated pair satisfies the first equation.

EVALUATING (6,1) IN THE SECOND EQUATION.

The pair also satisfies the second equation.

The expression is simplified to F⁸. Option C

To determine the value, we have that;

Index forms are described as forms used in the representation of numbers that are too small or large.

Other names for index forms are scientific notation and standard forms.

From the information given, we have that

F² by the power of 4

This is represented as;

(F²)⁴

To simply the index form, we need to expand the bracket by multiplying the exponential values, we get;

F⁸

Learn more about index forms at: https://brainly.com/question/15361818

#SPJ1

Answer:

-82

Step-by-step explanation:

84/21=4

-25x4=-100

-3x-6=18

-100+18=-82

Answer:

(Triangular pyramid)

Lateral area = 1650\(m^{2}\)

Total surface area = 1860.1\(m^{2}\)

(Triangular prism)

Volume = 660\(cm^{3}\)

Step-by-step explanation:

For the triangular pyramid

Area of triangle = \(\frac{1}{2}\) × base × height

Area of the base = \(\frac{1}{2}\) × 22 × 19.1 = 210.1

Area of the sides = \(\frac{1}{2}\) × 22 × 50 = 550

Number of sides (excluding base) = 3

∴ Total Area = 210.1 + (550 × 3)

= 210.1 + 1650 = 1860.1\(m^{2}\)

Lateral Area = (550 × 3)  = 1650\(m^{2}\)

For the triangular prism

Area of the triangle = \(\frac{1}{2}\) × 12 × 5 = 30

Volume = Area x Height

Volume = 30 ×  22 = 660\(cm^{3}\)

Answer:

Writing formal proofs to prove conjectures about lines, angles and triangles ... parallel to each other or on the same line—and since the altitudes of both ...

By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.Step-by-step explanation:

Hope this helps

Answer:

90 quizzes

Step-by-step explanation:

In 7 weeks, 63 quizzes

In 10 weeks, x quizzes

Making a proportion,

7/10 = 63/x

Cross multiplying,

7x = 630

Dividing by 7 on both sides,

x = 90 quizzes

The solution of the inequality is

-1 > x ≥ -6

The number line is attached

To solve the inequality, we will first solve each part separately and then find the intersection of their solution sets.

First, let's solve the left part of the inequality: 7 < -5x + 2.

7 < -5x + 2

Subtracting 2 from both sides, we get:

-5x > 5.

x < -1.

Next, let's solve the right part of the inequality: -5x + 2 ≤ 32.

-5x + 2 ≤ 32 can be rewritten as -5x ≤ 30.

x ≥ -6.

Now we have the solutions for each part: x < -1 and x ≥ -6. This is also written as -1 > x ≥ -6

Learn more about inequality at

https://brainly.com/question/25275758

#SPJ1