Jack has $425 less in savings than Mattias. If the average of the two mens savings is $2,100, how much money does Mattias have in savings?

Answer:

step by step and the dog got 10 fire wood

Answer:

x = 5 - 2y

y = 5 / 2 - y / 2

Step-by-step explanation:

2x+4y=10

x = 5 - 2y

y = 5 / 2 - y / 2

The expected value of each ticket is $0.60. The expected value of each ticket in the lottery can be calculated by summing the products of the probability of winning each prize and the corresponding prize amount, then subtracting the ticket cost.

After performing this calculation, the expected value of each ticket is $0.60.This means that, on average, a player can expect to win $0.60 for every $2.00 ticket they purchase. It is important to note that the expected value is just a statistical average and does not guarantee a win for any particular ticket or player. Additionally, players should always gamble responsibly and within their means.

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The z-score with probability 0.225 to the right is 0.15 and the z-score with probability 0.900 to the left is -1.28. This can be calculated using the Z-score table for a standard normal distribution.

(a) Probability 0.225 to the right is equal to z-score 0.15.

This can be calculated using the Z-score table for a standard normal distribution.

The probability to the right of z-score is equal to the cumulative probability of the z-score.

The cumulative probability of 0.15 is 0.225, which is the probability to the right.

(b) Probability 0.900 to the left is equal to z-score -1.28.

This can be calculated using the Z-score table for a standard normal distribution.

The probability to the left of z-score is equal to the cumulative probability of the z-score.

The cumulative probability of -1.28 is 0.900, which is the probability to the left.

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The nine principles of inference are logical guidelines that let us draw reasonable conclusions from a set of assertions or propositions

So the nine principles of inference are logical guidelines that let us draw reasonable conclusions from a set of assertions or propositions. These guidelines are frequently used in mathematics, philosophy, and computer science to establish the veracity of claims or create new assertions from preexisting ones. These are the nine inference rules:

Modus Ponens (MP) states that if p implies q and p is true, q must also be true.

Modus Tollens (MT) states that if p implies q but q is untrue, then p is untrue.

Hypothetical Syllogism (HS): P implies R if and only if P implies Q and Q implies R.

Disjunctive Syllogism (DS): If p or q and p are both true, then q is true.

When adding (ADD), if p is true, p or q and these guidelines are frequently used in mathematics, philosophy, and computer science to establish the veracity of claims or create new assertions from pre existing ones. These are the nine inference rules.

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Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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Answer:

5*5*5*5

Step-by-step explanation:

5^4 means 5 times itself four times.

Answer:

625

Step-by-step explanation:

5 x 5 x 5 x 5

which is

625

To get System B from System A, you can replace one equation with a multiple of the other equation. Specifically, you can multiply the second equation of System A by 2 and then replace the first equation with the result. So the correct answer is A.

Since we obtained System B by performing a valid operation on System A, the two systems are equivalent and have the same solution. So the correct answer is A. Yes, they have the same solution

The equivalent graph of the function are shown below.

The equation of a line in slope-intercept form is expressed as y = mx + b where:

m is the slope

b is the intercept

Given the equations below
y=-1/3x+1

y=-2x-3

The slope of both equations are -1/3 and -2 respectively showing a negative slope. This means that both lines are oriented downward the plane as shown below;

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We calculated the percentage of yarn that falls outside the range of 80 pounds to 110 pounds. Approximately 22% of the yarn will not meet the design specification.

To determine the percentage of yarn that will not meet the design specification of 95 pounds +/- 15 pounds, we need to calculate the probability that the yarn's strength falls outside the range of 80 pounds to 110 pounds.

Given that the strength of the yarn follows a normal distribution with a mean of 90 pounds and a standard deviation of 11 pounds, we can use the properties of the normal distribution to solve this problem.

First, we need to standardize the values of the lower and upper limits using the z-score formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For the lower limit:

z_lower = (80 - 90) / 11 = -0.909

For the upper limit:

z_upper = (110 - 90) / 11 = 1.818

Next, we need to find the cumulative probabilities corresponding to these z-scores using a standard normal distribution table or a calculator. The cumulative probability gives us the proportion of values that fall below a certain z-score.

P(z < -0.909) = 0.184 (approximately)

P(z < 1.818) = 0.964 (approximately)

To find the probability of yarn that will not meet the design specification, we subtract the cumulative probability for the lower limit from the cumulative probability for the upper limit:

P(yarn outside range) = 1 - P(z_lower < z < z_upper)

= 1 - (P(z < z_upper) - P(z < z_lower))

= 1 - (0.964 - 0.184)

= 1 - 0.78

= 0.22

Therefore, the percentage of yarn that will not meet the design specification is 22%.

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Answer:

80%

Step-by-step explanation:

60/75 = 4/5 = 80%

Answer:

A.  Communative Property of Addition

Step-by-step explanation:

If 6 boys and 4 girls get off the bus at the next bus stop, the ratio of girls to total students will be 14/27.

There are 22 boys and 32 girls on a school bus, 6 boys and 4 girls get off the bus at the next bus stop.

Total boys = 22

Total girls = 32

Total Student = Total boys + Total girls

Total Student = 22 + 32

Total Student = 54

The girls gets off = 4

Now remaining girls in bus = Total girls - The girls gets off

Now remaining girls in bus = 32 - 4

Now remaining girls in bus = 28

The ratio of girls to total students = Now remaining girls in bus/Total Students

The ratio of girls to total students = 28/54

The ratio of girls to total students = 14/27

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Answer:

The GCF of 8 and 36 is 4.

The GCF of 72 and 18 is 18.

The GCF of 14, 28, and 49 is 7.

Step-by-step explanation:

Answer:

-128

Step-by-step explanation:

Given, f(x)=2x

3

−21x

2

+36x−20

∴f

′

(x)=6x

2

−42x+36

When f(x) is a maximum or a minimum, f

′

(x)=0

Hence, 6x

2

−42x+36=0

x

2

−7x+6=0

x

2

−6x−x+6=0

x(x−6)−1(x−6)=0

(x−6)(x−1)=0

x=1,6

Again f

′′

(x)=12x−42

=6(2x−7)

Now, when x=1,f

′′

(x)=−30 ....[negative]

And when x=6,f

′′

(x)=30 ....[positive]

Hence, f(x) is maximum for x=1 and minimum for x=6.

The maximum and minimum values of f(x) are

f(1)=2(1)

3

−21(1)

2

+36(1)−20

=2−21+36−20=−3

f(6)=2(6)

2

−21(6)

2

+36(6)−20

=432−756+216−20=−128

The correct Option (B). Succession may be defined as the change in the ecological community of the species with respect to time. Two main types of succession are primary succession and secondary succession.

The living things that accumulate in the succession is from the simple organism to the complex organism. First lichens will evade in the land. After lichens grass then shrubs and finally the trees will cover the area and convert into the forest.

Primary succession occurs in basically dead areas—regions where the soil is incapable of supporting life due to causes such as lava flows, newly created sand dunes, or glacier-left boulders.

Pioneer microorganisms, plants (lichens and mosses), grassy stage, smaller shrubs, and trees are all stages of primary succession. When there is food available, animals begin to return. The climax community stage is reached when the ecosystem is fully functional.

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Full Question :

After a town is abandoned, the concrete parking lots remain empty and inactive for hundreds of years. What is the most likely order of ecological succession in that area?

A.grass → trees → lichens → moss

B.lichens → grass → shrubs → trees

C.lichens → grass → trees → shrubs

D.shrubs → grass → trees → lichens

Answer:

yₙ₊₁ = yₙ + 15

Step-by-step explanation:

→ Identify the common difference between each term

15

→ Write the nth term

yn + 15

To approximate the sum of the series [infinity] (−1)n 5n/(n!), we can use the alternating series test. To approximate the sum, we can calculate the partial sums and stop when the terms become insignificant.


1. The alternating series test states that if a series (-1)n an is such that the absolute value of the terms decrease and tend to zero as n approaches infinity, then the series converges.
2. In this series, the terms (-1)n 5n/(n!) decrease as n increases because the factorial term in the denominator grows faster than the exponential term in the numerator.
3. Therefore, we can conclude that the series converges.

The sum of the series [infinity] (-1)n 5n/(n!) converges.
To approximate the sum, we can calculate the partial sums and stop when the terms become insignificant.

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The coordinates for a similar triangle DEF by dilating triangle ABC with respect to the origin using a scale factor of √5/2.

In this case, we can choose any point as the center of dilation, but for simplicity, let's choose the origin (0,0). This means that we will stretch or shrink triangle ABC with respect to the origin.

This point has coordinates (2s, s), where s is the scale factor. To see why, consider that the distance from the origin to the point (2s, s) is given by the Pythagorean theorem as:

√((2s)² + s²) = s√5

This distance should be 2 times the scale factor, so we have:

s√5 = 2s

Solving for s, we get:

s = √5/2

Therefore, the corresponding side of triangle DEF is the line passing through (0,0) and (2√5, √5). Similarly, we can find the corresponding sides for the other two sides of triangle ABC to get the complete set of coordinates for triangle DEF.

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final answer:y= - 1/97 - 6

to find slope, just do the opposite reciprocal of the given slope

to find y-intercept just substitute the given point in y=mx+b

hope this helps!

Answer:

Keith; -5, -12

Step-by-step explanation:

Logic ( Subtract 12 from both sides, then factor it out)

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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Answer:

y(t) = 720e^0.3466t

y = 2036.6288

Step-by-step explanation:

The exponential relation :

y = Ae^kt

A = initial value ; y = final value ; r ; k = exponential rate, t = time

At t = 0

y = 720e^0 ; y = 720

At t = 2 ; y = 720e^2k

1440 = 720e^2k

1440/720 = e^2k

2 = e^2k

Take the In of both sides

0.6931471 = 2k

k = 0.6931471 / 2

k = 0.3466

Hence, equation becomes :

y = 720e^0.3466t

After 3 hours ;

t = 3

y = 720e^0.3466*3

y = 720e^1.0398

y = 720 * 2.8286512

y = 2036.6288

a=1

Hope this helps

have a great day!

Step-by-step explanation:

In a multiple regression model, the error term (often denoted as ε or e) is assumed to be a random variable with a mean of zero.

This assumption is a key component of the regression model and is often referred to as the assumption of zero conditional mean or the assumption of homoscedasticity. The assumption of a mean of zero for the error term means that, on average, the errors have no systematic bias or tendency to overestimate or underestimate the predicted values. It implies that the model's predictions are unbiased and that any deviations from the true values are due to random chance or other factors not captured by the model. The other options presented in the answer choices (B) -1, (C) 1, and (D) any value are incorrect. The mean of the error term is specifically assumed to be zero, as it represents the average deviation of the observed values from the predicted values in the model.

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Answer:I think it would be the third one

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Slope: 4/3

Y-intercept: -3

Step-by-step explanation:

The formula is...

y = mx + b

Where m is slope and b is y-intercept so in this case, 4/3 is slope and -3 is the y-intercept.

Hope that helps and have a great day!

Answer: The slope is 43, the y- intercept of y=4/3 x-3 is 0,-3.

Step-by-step explanation:

The kite will be 61.20 feet above the ground when the string from the kite to her hand is 110 feet long.

A right-angled triangle is a triangle with three sides and three angles, one of which is 90°.

Trigonometric ratios are used to demonstrate the connection between the sides and angles of a right-angled triangle.

Let h denote the perpendicular distance between the top of the kite and her hand. The angle of elevation = 34°. Hence:

sin(34) = h/110

h = 58.20 feet

The distance from the kite to the ground = 58.20 + 3 = 61.20 feet

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