If s varies inversely as t and s = 8 when t = 5, find the equation that connects s and t.

The 50-20-30 savings rule is a simple plan that helps people on managing their money.

It states that over your total after-tax earnings, 50% should be spent on your needs and obligations. 20% should be spent on savings and debt payments, and 30% on whatever else you like.

To determine the center of the circle;

x² + y² - 14x - 10 y - 26 = 0

we have to make the above equation to be in the form;

(x-a)² + (x-b)² = r²

where (a,b) is the center of the circle and r is the radius of the circle

x² + y² - 14x - 10 y - 26 = 0

add 26 to both-side of the equation

x² + y² - 14x - 10 y - 26 + 26 = 0 + 26

x² + y² - 14x - 10 y = 26

x² - 14x +y² - 10y = 26

add square of half of each coefficient

x² - 14x + (-7)² + y² -10y + (-5)² = 26 + (-7)² + (-5)²

(x -7)² + (y-5)² =

(

Answer: 6 a: 1=30 2=44, 3=106 4=30

Step-by-step explanation:

well, 3 is the opposite of 106 so they are equal, 2 is the opposite of 44 so they are equal, then you can just take the straight line and subtract the ones around it from 180 to find the 1 or 4, so 180-106, then 74-44=30. then because 1 and 4 are on opposite sides, they are equal. Sorry for not having enough times for all problems, but to help with 6 and 7, just remember that opposites are equal (you can use in 6b and 7a) and the if they make a straight line they make 180 degrees (use in 7b)

The co-ordinates of the point at which the gradient of the curve y = 3x² is 18 are (3, 27).

Here we are given the equation of a curve as-  y = 3x²

The gradient of a curve can be found out by differentiating it with respect to the independent variable. Thus, the gradient here will be dy/dx.

dy/dx = 6x

Thus the gradient of the curve is 6x.

Further, we are given that the gradient value is 18. thus, the value of x at gradient = 18 will be-

6x = 18

x = 18/6

x = 3

Substituting this in the equation of the curve, we can find the value of y as follows-

y = 3*3²

y = 3*9

y = 27

Thus, the co-ordinates of the point at which the gradient of the curve y = 3x² is 18 are (3, 27).

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We are given the following expression:

We will associate the terms that have common factors, like this:

Now we take the common factor for each of the parenthesis:

Since each parenthesis has a common factor but with inverted signs, we will take -1 as a common factor in the second parenthesis, we get:

Now we can take "y-r" as a common factor for the entire expression:

And thus we have factored the expression.

We want to round up to one decimal place;

The number after the decimal should be rounded up to the nea

1.

9 (3+2)

We have to distribute number 9 in the parenthesis, multiply each term in the parenthesis by 9:

9(3)+9(2)

27+18

45

2.

11(4-1)

11(4)+11(-1)=44-11=33

3.

12(7+7)

12(7)+12(7)

84+84

168

4.

5 (4+8)

5(4)+5(8)

20+40

60

5.

10(9-5)

90-50

40

Explanation

Step 1

Let x represents the cost for the students ticket

Let y represents the cost for the adult ticket

1)A group of 4 students went to the movie theater. They each bought a ticket for $x and spent $10.50 each on snacks

then

2)A group of 3 adults went to the movie theater and paid twice as much for each of their tickets as each student. The group of adults also spent $10.00 each on snacks

First let's draw the square ABCD:

The point is interior to the square, and also is equidistant from the sides AB and BC.

Drawing all the points that follow these rules in green, we have:

So this loci is represented by the diagonal BD of the square. All the points of this diagonal are equidistant to the sides AB and BC.

The most appropriate choice for subject of a formula will be given by -

180° F has been converted to 355.35 K

What is subject of a formula?

Subject of a formula is the variable which is expressed in terms of other variables present in the formula.

Here,

 [tex]F = \frac{9}{5}(K - 273.15) + 32\\F - 32 = \frac{9}{5}(K - 273.15)\\K = \frac{5}{9}(F - 32)+273.15[/tex]

Putting F = 180

[tex]k = \frac{5}{9}(180 - 32) + 273.15\\K=\frac{5}{9}\times 148+273.15\\K=82.2 + 273.15\\K=355.35[/tex]

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Answer:

Explanation:

Given the below;

To simplify the above, we have to 1st find the LCM of 2, 2x - 14, and x^2 - 7x which is 2x(x - 7), so we'll have;

Let's go ahead and simplify;

The correct answer or an inequality is x+6 < 3x + 10.

An inequality in mathematics is said to be a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is said to size-compare two numbers on a number line.

Many straightforward inequalities can be resolved by adding, taking away, multiplying, or dividing both sides until the variable is all that remains.

However, these factors will shift the direction of inequality:

1. By using a negative number to multiply or divide both sides

2. Reversing the left and right sides.

Let the number be x. It is given in the question that the sum of a number and six is less than the sum of three times the number and ten.

According to the question,

x+6 < 3x + 10

Hence, the correct answer is x+6 < 3x + 10.

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Answer: y= -2x -2

Step-by-step explanation:

1) Create an equation going through (1,-4)

Replace 5 with b otherwise, we can't find an equation that goes through it.

y = -2x + b

2) Substitute y and x with the point. Solve.

-4 = -2(1) + b

-4 = -2 + b

-2 = b

3) Reput in the equation

y= -2x -2

Note: It is parallel because they have the same slope!

felicia borrowed $12,000 from her bank at a monthly interest rate of 5%. if she paid back the loan after 3 months, how much interest is she going to pay? how much money will she pay back to her bank?​

we have that

the interest for each month is

0.05*12,000=$600

after 3 months

total interest is 3*$600=$1,800

she going to pay $1,800

Part b

12,000-1,800=$10,200

The velocity of a sound wave as a function of the temperature of the air is given by the equation

Where T is the temperature in degrees celsius.

Using this equation, calculate the velocity of a sound wave at 20 degrees Celsius:

Answer: the velocity is 343 m/s

The value of x is 71.6  degrees

We have a Right angle triangle and a value of an angle 18.4.

That is one angle is 18.4° and other is 90°.

To find third angle just add two angles and subtract that with 180.

The third angle is 71.6°

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In the given right triangle

Applying the Pythagorean Theorem

Solve for b

Answer:

600 miles

Step-by-step explanation:

295$ - 175$ = 120$. 120$ divided by 20 cents equals 600.

The sine of an angle on a right triangle is the ratio of the side opposite to that angle divided by the hypotenuse of the triangle.

The side opposite to alpha, is BC, while the hypotenuse is BA. Then:

Substitute the values of BC and BA to find the sine of alpha:

the compound interest formula is given by

where A is the amount you will have, P is the principal, r is the annual interest rate, n is the amount of times the interest is compounded per time period, and t is the amount of time.

In our case, we need to find the time t. Then, by moving the Principal to the left hand side, we get

By applying natural logarithm on both sides, we get

now, we can isolate t as

Now, we can substitute our given values into this expression. It yields,

which gives

then, the time (in years) is

Now, we must convert this result in months. Since 1 year has 12 months, we have

that is, the answer is 10.56 months

ANSWER and EXPLANATION

We want to graph the given function:

To do that, we have to find two points that lie on the line.

Let us solve for y when x is 0 and 2.

When x = 0:

When x = 2:

Now, we have two points to plot the line: (0, 2) and (2, -3)

Let us plot the graph:

From the graph, we see that the slope of the graph is:

and the y-intercept is:

Given:

A red die is tossed and then a green die is tossed.

Required:

We have to find the probability that the red die shows an even number or the green die shows an even number.

Explanation:

Let A denotes the event that the red die shows an even number and B denote the event that the green die shows an even number.

Here the total number of outcomes is 6(1-6) and the number of favorable outcomes are 3(2, 4, 6).

Then we have

Therefore,

Hence the probability that the red die shows an even number or the green die shows an even number is

Final answer:

----------------------------------------------------------------------------------------------------------------

To evaluate f(4), we take the functional value at x = 4.

Looking at the graph, it is:

At x = 4, y = 2 [counting units]

Thus,

To evaluate f(-3), we take the functional value at x = -3.

Looking at the graph, it is:

At x = -3, y = -5 [counting units]

Thus,

The zeros are the x-intercepts of a graph. Looking at the graph, the x-axis cutting points are:

Zeros

The function f(x) is increasing where the slope of the graph is positive.

Looking at the graph, the increasing part is from x = -3 to x = 5.

That is

- 3 < x < 5

The correct choice is (2).

The relative minimum is the lowest point of the graph shown and the relative maximum is the highest point of the graph.

Looking at the graph,

The lowest point occurs at --- (-3, -5)

The highest point occurs at --- (-7, 5)

So,

Relative Maximum: (-7, 5)

Relative Minimum: (-3, -5)

We want the interval in which f(x) < 0.

This means where the function is less than zero, or below the x-axis.

Looking at the graph,

from x = -5 to x = 2, the graph of f(x) is below the x-axis.

That is -5 < x < 2.

The correct choice is (3).

A new function --

Let's evaluate g(0) by using the formula:

From the graph, f(0) = -2, thus,

g(0) = 2(-2) + 5

g(0) = -4 + 5

g(0) = 1

This means that the functional value of 'g' is 1 at x = 0.

A new function --

We need to find g(h(2)). Let's boil it down to the function f(x).

Thus, the answer is:

(a)  The probability that the mean time spent on academic activities is at least 26 hours per week is 0.317.

(b) If 64 random full-time college students are selected, there is an 85% chance that the sample mean is less than 27.52 hours.

Full-time college students report spending a mean of 27 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 4 hours.

In a set with mean μ, the standard deviation σ and the z score of measure X is given by:

Z = ( X - μ )/σ

The theorem of central limits: According to this, the sample mean with size n can be roughly compared to a normal distribution with mean and standard deviation for a normally distributed random variable, X, with mean and standard deviation:

s = σ/√n

(a) In this we have to find the probability that the mean time spent on academic activities is at least 26 hours per week,

s = σ/√n

s = 4/√16

s = 4/4 = 1

Therefore, 1 is subtracted from the p-value of Z when X = 28.

So,

Z = ( X - μ )/σ

Z = ( 28 - 27)/1 = 1

For Z = 1 the p-value is 0.317.

(b) If 64 full-time college students are selected randomly.

85% chance that the sample mean is less.

s =  σ/√n = 4/√(64) = 4/8 = 1/2 = 0.5

When the p-value is 0.85, Z = 1.04

Z = ( X - μ )/σ

1.04 = ( X - 27)/0.5

X - 27 = 0.52

X = 27.52

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Answer:

At the movie premiere, adult moviegoers enjoyed the movie more because only 25% did not like the movie whereas 68% of the teenager moviegoers did not like the movie. ​

First, let us get the percentage of adults that liked the movie.

It is said that 15 out of 20 adults liked the movie. We can get the percentage by dividing the number of adults who liked the movie by the total number of adults.

We will then find out the percentage of adults and teenagers that did not like the movie by subtracting the percentage that liked the movie from 100%

Adults who did not like the movie:

Teenagers who did not like the movie:

Here, we can conclude that:

At the movie premiere, adult moviegoers enjoyed the movie more because only 25% did not like the movie whereas 68% of the teenager moviegoers did not like the movie. ​

Given:

A regular hexagon inside a circle with a radius of 2 inches.

1)

Two radii are drawn to two consecutive vertices of the regular hexagon to form a central angle whose measure can be found based on the rotational symmetry of the figure.

Yes, Agree, because the rotational symmetry of the hexagon is 6. To find the measure of each central angle, divide 360° by 6. The central angle is 60 degrees.

2)

The hexagon can be decomposed by 6 congruent isosceles triangles.

Agree, because the angles of each of the triangles are 60 degrees.

Each of the 6 triangles is an isosceles because the sides are the radii of the same circle.

3).

The length of the altitude of each of these 6 congruent triangles can be found using trigonometry.

Agree, because an attitude split the triangle into two equals 30-60-90 triangles. The side of the original equilateral triangle is the hypotenuse of the 30-60-90 triangle.

The adjacent side is attitude and the hypotenuse is 2 inches with an angle is 30 degrees.

Use the cosine formula.

The length of the altitude of each of these 6 congruent triangles is a sqaure root of 3 inches.

Answer: b-11

Step-by-step explanation:

b= total number of milk

11= total number of chocolate milk

b - 11 = number of milks that aren't chocolate

GIven a quadratic equation in standard form, we have

c represents the coefficient of the constant in the quadratic equation.

Given the equation 2m² + m +3 = 0

Solution

For this case we have the following:

We can subtract 27 in both sides and we got:

Then we can divide both sides by 3 and we got:

Then the possible to solution are: