4. Tanya Jackson bought a house and during the first year, was able to rent it for only 7 months at $620 a month. Though the house was vacant for 5 months, Tanya had to pay average expenses of $175 a month for the whole year. She also paid $3,600 in mortgage interest. a. For the first year, what was Tanya's gross income? b. What was her net income or net loss?​

The perimeter of a square is the sum of its sides and they are all equal, so to obtain the length of each of them we divide the perimeter of the first fence between 4:

[tex]\text{P1}= \dfrac{\text{64 feet}}{\text{4 sides}}[/tex]

[tex]\text{P1}= 16 \ \text{feet}[/tex]

Then, the length of each side of the second fence will increase 2 feet at each end, as shown in the figure. We have then that the perimeter of the second fence is:

[tex]\text{P2 = 20 feet} \times \text{4 sides}[/tex]

[tex]\text{P2 = 80 feet}[/tex]

The sum of the perimeters of both fences is:

[tex]\text{PT = P1 + P2}[/tex]

[tex]\text{PT = 64 feet + 80 feet}[/tex]

[tex]\text{PT = 144 feet}[/tex]

Total cost = $1.26 x 144 feet

Total cost = $181.44

The total cost of the fences was $181.44

The probability of winning the jackpot with one ticket is approximately 0.000000003724.

There are a total of C(41, 5) ways to choose five numbers from 41 white balls, and there are 35 possible choices for the gold ball.

Therefore, the total number of ways to win the jackpot is:

C(41, 5) * 35

And the total number of possible outcomes (i.e. all the combinations of 5 white balls and 1 gold ball) is:

C(41, 5) * 35 * C(5, 5)

Since there is only one winning combination, the probability of winning the jackpot is:

1 / (C(41, 5) * 35)

Plugging in the values, we get:

1 / (749,398,832 * 35) = 1 / 26,869,866,120

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f(275) represents the average number of days houses stay on the market before being sold for $275,000.

From the question, we have the following parameters that can be used in our computation:

f(p) is the average number of days a house stays on the market before being sold for price p in $1,000s

This means that

In f(275), we have

p = 275

So, the meaning is:

f(275) is the average number of days a house stays on the market before being sold for price $275,000s

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Answer:

D

Step-by-step explanation:

When a number is 5 or more you round up, but when it's 4 or lower you don't round at all. So, when you round the 8, in answer D, you get 6 making the answer 18.96.

Step-by-step explanation:

The number of non square numbers between 12square and 13square are

The length of the guy wire should be option D √(25) ft. that is 25 ft.

Perpendicular means that two lines or objects intersect each other at a 90-degree angle, forming a right angle. This means that if you were to draw a line at the point of intersection, it would split the angles on either side of it into two equal parts. In simpler terms, if you imagine a horizontal line and a vertical line intersecting each other, they would be perpendicular to each other. The concept of perpendicularity is important in geometry and is used in many different applications, such as construction, engineering, and design.

We can use the Pythagorean theorem to find the length of the guy wire c. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore:

c² = a² + b²

Substituting the given values:

c² = (20 ft)² + (15 ft)²

c² = 400 ft² + 225 ft²

c² = 625 ft²

Taking the square root of both sides:

c = √(625) ft

c = 25 ft

Therefore, the length of the guy wire should be 25 feet.

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Answer:

(a) To calculate how much it would cost to hire the coach to travel a distance of 42 miles, we can substitute m = 42 into the formula and solve for C:

C = (42/3) + 40

C = 14 + 40

C = 54

Therefore, it would cost £54 to hire a coach to travel 42 miles.

(b) To find how many miles the coach travels if the cost of the hire is £75, we can set the formula equal to 75 and solve for m:

75 = (m/3) + 40

35 = m/3

m = 105

Therefore, the coach travels 105 miles if the cost of the hire is £75.

The equation is given as y = -x + 8

The purpose of an equation is to find the value of the variable that makes the equation true. Equations are used in various fields of mathematics and science to represent relationships between different quantities and to solve problems.

To create an equation that represents the relationship between x and y in the table, we need to first determine the pattern or trend in the data.

From the given data, we can see that as x increases by 2, y decreases by 2. This suggests that there is a linear relationship between x and y.

Using the two points (-2,10) and (0,8), we can find the slope:

m = (y2 - y1) / (x2 - x1) = (8 - 10) / (0 - (-2)) = -1

Now that we have the slope, we can use any point on the line to find the y-intercept. Let's use the point (0,8):

8 = (-1)(0) + b

b = 8

Therefore, the equation that represents the relationship between x and y in the table is:

y = -x + 8

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The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

[tex]\text{A} = \pi \text{r}^2[/tex]

The circumference of a circle is expressed mathematically as;

[tex]\text{C} = 2\pi \text{r}[/tex]

Given that the area of the circle is 20π cm², we determine the radius of the circle.

[tex]\text{A} = \pi \text{r}^2[/tex]

[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]

[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]

[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]

[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]

[tex]\text{r} = 4.47 \ \text{cm}[/tex]

Now, we determine the circumference of the circle.

[tex]\text{C} = 2\pi \text{r}[/tex]

[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]

[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]

[tex]\text{C} = 8.94\pi[/tex]

Therefore, the circumference of the circle is 8.94π centimeters.

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we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.

How to solve the question?

To determine the average growth rate of each sample over the interval [1, 3], we need to calculate the ratio of the change in bacteria population to the change in time for each sample, and then take the average of these ratios over the given interval.

For Sample A, the change in bacteria population over the interval [1, 3] is 480 - 120 = 360, and the change in time is 3 - 1 = 2. So the average growth rate of Sample A over this interval is 360/2 = 180 bacteria per hour.

For Sample B, the change in bacteria population over the interval [1, 3] is 480 - 240 = 240, and the change in time is 3 - 1 = 2. So the average growth rate of Sample B over this interval is 240/2 = 120 bacteria per hour.

For Sample C, the change in bacteria population over the interval [1, 3] is (1.2600)(1.2*1.2 - 1) = 345.6, and the change in time is 3 - 1 = 2. So the average growth rate of Sample C over this interval is 345.6/2 = 172.8 bacteria per hour.

For Sample A, the growth rate is the highest, followed by Sample C and then Sample B. Therefore, the order of the samples by their average growth rate over the interval [1, 3] from least to greatest is Sample C, Sample A, and Sample B.

It's important to note that the growth rate of Sample C is not constant but increases over time due to the 20% increase in the initial bacteria population. The exponential function f(x) = 200(3/2)in power x represents this growth, and we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.

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Your complete question is :-A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.

Sample A Sample B Sample C

x g(x)

0 60

1 120

2 240

3 480

Answer: C

Step-by-step explanation:

1/2 pound of almonds = 5/6 cup of almond butter

To find out how much almond butter 1 pound of almonds will make, we need to multiply both sides of the equation by 2:

1 pound of almonds = (2 × 1/2) pounds of almonds = 2 × 5/6 cups of almond butter

Simplifying, we get:

1 pound of almonds = 5/3 cups of almond butter

So, a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds is more than 2 cups of almond butter. Therefore, the answer is (c) more than 2 cups of almond butter.

Answer: b) between 1 1/2 and 2 cups of almond butter

Step-by-step explanation:

We can create a proportion to help us solve this question.

         [tex]\displaystyle \frac{\frac{1}{2} lbs\;almonds}{\frac{5}{6}lbs\;butter } =\frac{1lbs\;almonds}{xlbs\;butter}[/tex]

Now we can cross multiply.

         [tex]\displaystyle \frac{1}{2} *x=\frac{5}{6} *1[/tex]

         [tex]\displaystyle \frac{1}{2}x =\frac{5}{6}[/tex]

Next, we will divide both sides of the equation by one-half.

         [tex]\displaystyle x =\frac{5}{6}\div \frac{1}{2}[/tex]

         [tex]\displaystyle x =\frac{5}{6}* \frac{2}{1}[/tex]

         [tex]\displaystyle x =\frac{10}{6}[/tex]

Lastly, we will find which answer option this falls under by creating an improper fraction. This leads us to answer optoin b, b) between 1 1/2 and 2 cups of almond butter.

         [tex]\displaystyle 10-6=4\text{, so } 1\frac{4}{6} =1\frac{2}{3}[/tex]

If the yard is 2000 feet², both companies will charge the same price.

In mathematics, the word "amount" is a broad one that refers to the size or quantity of something, typically given as a numerical value.

It can be used in a number of circumstances where there is a concern with money, measurements, or the quantity of an item.

We must assume both organisations' expenses to be equal and then solve for the yard size to determine the point at which their costs are equal.

Let's assume that x is the yard size at which expenses are equal.

7.5x + 24.5 = 16x + 23.5

When we simplify this equation, we obtain:

0.5x = 1

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We know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.

Arrange in ascending order:

229 234 248 255 263

When, odd terms are there then the middle term is the median:

Median: 248

New Median:

229 234 248 255 263 597

When there are even terms we will add the middle two terms and divide it by 2 as follows:

248+255/2

Median: 251.5

Median change: 251.5 - 248 = 3.5

Therefore, we know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.

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The fundamental core of mathematical activity is problem-solving.

Mathematical problems can be found in many different fields, and the process of solving these problems involves analyzing the problem, identifying relevant information, formulating a strategy or plan, executing the plan, and checking the solution to ensure it is correct and complete.

This process of problem-solving is central to all areas of mathematics, and is a key skill that can be applied to many different contexts both inside and outside of mathematics.

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The point (1, 8) would then represent that the babysitter charges $8 per hour

The point (1, 8) in this situation could mean that the babysitter charges $8 for one hour of work.

In general, when working with a fee-per-hour situation, we can use the slope-intercept form of a linear equation, y = mx + b,

If we assume that the initial fee is $0, then the equation for the babysitter's fee would be y = mx, where m is the hourly rate.

The point (1, 8) would then represent that the babysitter charges $8 per hour, since when x = 1 (one hour of work), y = 8 (the fee for one hour).

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Answer:

  A.  X

Step-by-step explanation:

You want to know which graph is decreasing for x > 3.

A graph is decreasing when it slopes down to the right. The only graph in the group that has any decreasing portion is graph X. The decreasing part of that graph is to the right of x = 3, where x > 3.

Graph X is the one you want.

__

Additional comment

All the other graphs are increasing everywhere, so aren't even worth any consideration.

The proof of the three distributions as required as shown in the explanation part.

For x² distribution:

Let's start with the sample variance, which is defined as:

s^2 = ∑(y_i - y_bar)² / (n-1)

where;

We can rewrite this formula as:

s^2 = (∑y_i² - n*y_bar²) / (n-1)

Multiplying both sides by (n-1)/σ², we get:

s^2 / σ² = (∑y_i² - ny_bar²) / (σ²(n-1))

Now, let's define a new variable:

x² = ∑y_i² / σ²

Substituting x² into the above equation, we get:

s^2 / σ² = (x² - n*y_bar²/σ²) / (n-1)

Notice that n*y_bar²/σ² is just the sample mean squared in units of variance. We can rewrite it as:

n*y_bar²/σ² = (y_bar - μ)² / (σ²/n)

where;

Substituting this into the above equation, we get:

s^2 / σ² = (x² - (y_bar - μ)² / (σ²/n)) / (n-1)

Now, let's define a new variable:

ss = ∑(y_i - y_bar)² / σ²

Substituting ss into the above equation, we get:

s^2 / σ² = (x² - ss/(n-1)) / n

This is the desired result. We have shown that s²/σ² follows a x² distribution with n-1 degrees of freedom.

For t distribution:

Let's start with the sample mean, which is defined as:

y_bar = ∑y_i / n

We can rewrite this formula as:

y_bar - μ = (∑y_i - n*μ) / n

Now, let's define a new variable:

t = (y_bar - μ) / (s/√n)

where;

Substituting y_bar - μ and s into the above equation, we get:

t = (∑y_i - nμ) / (s√n)

This is the desired result. We have shown that t follows a t distribution with n-1 degrees of freedom.

For F distribution:

Let's start with the sample variances, which are defined as:

s₁² = ∑(y_i - y₁)² / (n₁-1)

s₂² = ∑(y_i - y₂)² / (n₂-1)

where;

We can rewrite these formulas as:

s₁² = (ss₁ - n₁*(y₁-μ)²) / (n₁-1)

s₂² = (ss₂ - n₂*(y₂-μ)²) / (n₂-1)

where;

ss₁ = ∑(y_i - y₁)²

ss₂ = ∑(y_i - y₂)²

Dividing these equations, we get:

s₁² / s₂² = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

Now, let's define a new variable:

F = s₁² / s₂

Substituting s₁² / s₂² into the above equation, we get:

F = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

This is the desired result. We have shown that F follows an F distribution with (n₁-1) and (n₂-1) degrees of freedom.

It's worth noting that the F distribution is only defined for positive values. Therefore, if s₁² / s₂² is less than 1, we need to take the reciprocal of the above equation to ensure that F is positive:

F = (ss₂ / (n₂-1)) / (ss₁ / (n₁-1))

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With this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

To solve this problem, we will need to find the time of flight and the horizontal velocity. We can use the following kinematic equations:

Vertical motion:

Maximum height: h = (v^2 * sin^2(angle)) / (2 * g)

Time of flight: t = 2 * v * sin(angle) / g

Horizontal motion:

Range: R = v * t * cos(angle)

Given:

Initial velocity (v) = 20 m/s

Angle = 45 degrees

Acceleration due to gravity (g) = 9.81 m/s²

Calculations:

Convert angle to radians: 45 degrees = 45 * (π/180) = 0.785 radians

Calculate time of flight: t = 2 * 20 * sin(0.785) / 9.81 = 2.04 seconds

Calculate horizontal range: R = 20 * 2.04 * cos(0.785) = 28.98 meters

So, with this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

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A ball is thrown with an initial velocity of 20 meters per second at an angle of 45 degrees with respect to the horizontal. How far does the ball travel horizontally (range) before it hits the ground? Assume no air resistance.

Answer:

27 cubes

Step-by-step explanation:

The volume of Cube A is 1 cubic centimeter. The volume of one Cube C is 1/27 of a cubic centimeter. So 27 Cube C's will fit into Cube A.

Five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).

Given that

f(x) = 4^x.

To find the inverse of the function f(x) = 4^x,

We need to interchange the positions of x and y and solve for y. So, we have:

x = 4^y

Taking the logarithm base 4 of both sides, we get:

y = log₄(x)

Therefore, the inverse of the function f(x) = 4^x is g(x) = log₄(x)

To find five points on the inverse function g(x), we can choose five x-values and find the corresponding y-values:

If x = 1, then g(x) = log₄(1) = 0, so the point is (1, 0).

If x = 4, then g(x) = log₄(4) = 1, so the point is (4, 1).

If x = 16, then g(x) = log₄(16) = 2, so the point is (16, 2).

If x = 1/4, then g(x) = log₄(1/4) = -1/2, so the point is (1/4, -1/2).

If x = 2, then g(x) = log₄(2) ≈ 0.5, so the point is (2, 0.5).

Therefore, five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).

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Answer:

0,-1

Step-by-step explanation:

Hope this helps! =D

Brainliest! =D

Answer:

-1

Remember y=mx+b

m is your slope and b is your y-int
m = -4/3

b = -1

The given information describes a pair of congruent triangles. The corresponding vertices, angles, and sides of the triangles are congruent. The congruent angles are ∠REM ≅ ∠MOC, ∠ERM ≅ ∠MCO, and ∠CMO ≅ EMR. The congruent sides are ER ≅ CO, MO ≅ EM, and CM ≅ RM. The congruent triangles are ΔMER ≅ ΔMOC.

1) the corresponding vertices are

R ~ C and

E ~ 0

2) The corresponding angle are

∠E ~∠O  and

∠ R ~ ∠C

3)

The corresponding sides are;

ER ~ CO;

MO ~ EM

CM ~ RM

4)  the congruent angles are:

∠REM ≅ ∠MOC

∠ERM ≅ ∠MCO

∠CMO ≅ EMR

5) the congruent sides are:

ER ≅ CO;

MO ≅ EM

CM ≅ RM

6) the congruent triangles are;

ΔMER ≅ ΔMOC

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I believe this quadrilateral  is a parallelogram.

There are a few ways to choose within the occasion that a quadrilateral may be a parallelogram: Opposite sides are parallel: Within the occasion that inverse sides of a quadrilateral are parallel, at that point it may be a parallelogram.

Inverse sides are said to be consistent: On the off chance that inverse sides of a quadrilateral are consistent, at that point it may be a parallelogram. From the image attached , you can see the both side red are marked equal hence it is a parallelogram

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Answer:

Step-by-step explanation:

(3n³ + 2n)² = 9n^6 + 12n^4 + 4n^2

(4k² + 2k³) = 2k²(2 + k)

(3y²-y')' = 6y-y''

(4c+30) = 2(2c+15)

(2b² * b)² = 4b^6

(2gh²)* = 2gh^2

(6w³)² = 36w^6

The mean of the data set is 82.77

If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.

The first step is to arrange the data set orderly from smallest to largest;

70, 71,79, 82,88,85,87,91,92

We have nine values in the data set thus the mean is;

70+71+79+82+88+85+87+91+92/9= 745/9= 82.77

Hence the mean of the data set is 82.77

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Answer: direction angle of c is pi/4.

Step-by-step explanation: We can find c by adding the corresponding components of a and b:

c = a + b = ⟨–7, 3⟩ + ⟨–2, –12⟩ = ⟨–9, –9⟩

To find the magnitude of c, we can use the formula:

|c| = sqrt(c1^2 + c2^2)

where c1 and c2 are the x- and y-components of c, respectively. In this case, we have:

|c| = sqrt((-9)^2 + (-9)^2) = sqrt(162) = 9sqrt(2)

To find the direction angle of c, we can use the formula:

theta = atan(c2 / c1)

where theta is the angle between the positive x-axis and the vector c. In this case, we have:

theta = atan((-9) / (-9)) = atan(1) = pi/4

So the direction angle of c is pi/4.

Therefore, the magnitude of c is 9sqrt(2) and the direction angle of c is pi/4.

x = 5.5

we can solve this by using tanø formula i.e p/b

Answer:

a)3.68kg

b)900g

Step-by-step explanation:

a) First off we know that he weighs 4kg now and he weighed 8% less the next week. 8% of 4kg=0.32kg. We then have to subtract 0.32 kilograms from the original weight. 4-0.32=3.68

Your answer for A is 3.68 kg

b) If the baby gains 200g every two weeks, assuming it's a constant rate, he should gain 100g every week. 100*9weeks=900g.

The correct statements regarding the exponential function 3(1/3)^x is given as follows:

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function for this problem is given as follows:

f(x) = 3(1/3)^x.

The parameter b is of 1/3 < 1, hence:

The range is all real values greater than 0, as a = 3 is positive and the function has an horizontal asymptote at y = 0.

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1. The rule states that the product of the lengths of the two segments of one chord equals the product of the lengths of the two segments of the other chord (i.e., (a1 x a2) = (b1 x b2), where a1 and a2 are segments of chord A, and b1 and b2 are segments of chord B).

2. The rule states that the product of the length of the external segment of one secant and the length of the entire secant equals the product of the length of the external segment of the other secant and the length of the entire secant (i.e., (e1 (e1 + i1)) = (e2 (e2 + i2)), where e1 and e2 are the external segments and i1 and i2 are the internal segments).

3.  The rule states that the square of the length of the tangent segment equals the product of the length of the external segment of the secant and the length of the entire secant (i.e., t^2 = e * (e + i), where t is the length of the tangent segment, e is the external segment, and i is the internal segment).

The three rules of segments are:

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