16. Lena always keeps her bank account
balance above $50, If she spent $11.60 on
lunch, what was her balance before buying
lunch?
PLEASE HELP

The exponential form of xxxxyyyzzzzz is \(x^4 y^3 z^5\).

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

For example, , where a is a constant is an exponential function.

Given that

The function with 3 variables xxxxyyyzzzzz

Now,

xxxx=\(x^4\)

yyy=\(y^3\)

zzzzz= \(z^5\)

Substituting the following values in the function

= \(x^4 y^3 z^5\).

Therefore, the exponential function will be  \(x^4 y^3 z^5\).

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The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

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Answer:

Step-by-step explanation:

d

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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The approximately 99.7% of the students have commute distances between 13.9 miles and 24.1 miles, the area within two standard deviation is 95%

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

a) We have:

mean u = 19.0 miles,

\(\rm \sigma = 5.1 \ miles\)

According to the empirical rule, the area between \(\mu - \sigma\) and \(\mu + \sigma\) is 99.7%

\(\mu - \sigma = 19- 5.1 = 13.9\)

\(\mu + \sigma = 19+5.1 = 24.1\)

b) = P(8.8 < X < 29.2)

\(\rm P(\dfrac{8.8-\mu}{\sigma } < \dfrac{X-\mu}\sigma < \dfrac{29.2-\mu}{\sigma})\)

\(\rm P(\dfrac{8.8-19}{5.1} < Z < \dfrac{29.2-19}{5.1})\)

P(-2 < Z < 2)

Thus, the approximately 99.7% of the students have commute distances between 13.9 miles and 24.1 miles, the area within two standard deviation is 95%

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Answer:

I'd say x=30

cause the angle is 60°

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

8.2cm

Step-by-step explanation:

Using SOH CAH TOA

cos theta = adjacent/hyp

cos 47 = h/12

h = 12cos47

h = 12(0.6819)

h = 8.18

Hence the height h to 1 dp is 8.2cm

Answer:

  yes, they are parallel; the general form equation differs only in the constant.

Step-by-step explanation:

Subtract y from the first equation and multiply by 2.

  y -y = 1/2x -y +3

  0 = x -2y +6

  x -2y +6 = 0 . . . . . put in general form

Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.

This means the lines are parallel.

The value of the function f(a+4) is  \(\frac{7}{a^{2} +8a+11}\)

function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable called the dependent variable.

if f(x) = \(\frac{7}{x^{2} - 5}\), which means this equation is a function of x,

To find another equation whose function is f(a + 4)

We substitute x for a + 4 in the above equation

f(a+4) = \(\frac{7}{(a+4) ^{2} - 5 }\)

expanding \((a + 4)^{2}\), and simplifying the denominator, we have

\(a^{2}\) +8a + 16 - 5 = \(a^{2}\) + 8a + 11

so the simplified form of the new function would be  \(\frac{7}{a^{2} +8a+11}\)

In conclusion, the function f(a +4) =  \(\frac{7}{a^{2} +8a+11}\)

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The amount that Ethan pays for the video game is 47.988.

From the information illustrated, it should be noted that it was stated that Ethan buys video games for 39.99 sale on 20% tax.

In this case, the amount that he will pay will be:

= Original amount + Tax

= 39.99 + (20% × 39.99)

= 39.99 + 7.998

= 47.988

The amount is 47.988.

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Complete question

Ethan buys vidio games for 39.99 sale on 20% tax how much ethan payed

Answer: The probability that the basketball player will miss her next free throw is 60 percent

Step-by-step explanation: So there is a chance they will make their next free throw of 40%, meaning there is still a 60% chance she will miss her free throw also.

Fraction form:

There is 40/100 chance she'll make it, and 60/100 chance she'll miss.

Decimal form:

There is a 0.4 percent chance she'll make it, and 0.6 chance she'll miss.

Step-by-step explanation:

Given: To make smallest 3-digit number of 825.

To find: The smallest 3-digit number of 825.

Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...

Final answer: The smallest 3-digit number of 825 is 258.

hope it helps

Answer:

258

Step-by-step explanation:

We are given 3 numbers:

8 2 5

And we are asked to find the smallest 3 digit number using those 3 digits above.

To make the smallest number, place the numbers in value from least to greatest:

2 5 8

This is your 3 digit number: 258.

Hope this helps! :)

The sum total by the given data is equals to $658,880.

We are given that;

Percent=15%

Amount= $98,880

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:

15% = 0.15

To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:

$98,880 / 0.15 = $98,880 x 1/0.15

To multiply by 100, we can move the decimal point two places to the right. This gives us:

$98,880 x 1/0.15 x 100 = $658,880

Therefore, by the percentage the answer will be $658,880.

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Answer:

$245

Step-by-step explanation:

Step-by-step explanation:

Divide 35 by 1/2 by multiplying 35 by the reciprocal of 1/2.

35*2=x / 3*2+1/2

Multiply 35 and 2 to get 70.

70=x / 3*2+1/2

Divide x by 3*2+1/2 by multiplying x by the reciprocal of 3*2+1/2.

70=x*2/3*2+1

Multiply 3 and 2 to get 6.

70=x*2/6+1

Add 6 and 1 to get 7.

70=x*2/7

Swap sides so that all variable terms are on the left-hand side.

x*2/7=70

Multiply both sides by 7.

x*2=70*7

Multiply 70 and 7 to get 490.

x*2=490

Divide both sides by 2.

x=490/2

Divide 490 by 2 to get 245.

x=245

Answer:

2

Step-by-step explanation:

The equation has 2 terms in it which means 2 is the answer.

To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:

Refer to the attachment below.

There are three pairs of faces on a rectangular prism:

8 cm × 3 cm = 24 cm²

Since there are two of these faces, the total area is:

2 × 24 = 48 cm²

8 cm × 6 cm = 48 cm²

Since there are two of these faces, the total area is:

2 × 48 = 96 cm²

3 cm × 6 cm = 18 cm²

Since there are two of these faces, the total area is:

2 × 18 = 36 cm²

Now, add up the areas of all six faces:

Surface Area = 48 + 96 + 36 = 180 cm²

So, the surface area of the rectangular prism is 180 cm².

________________________________________________________

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The solution of the given inequality is y ≤ -3.

The given inequality is -

3y ≤ −9

We have to solve this given inequality.

Now, we have the inequality as -

3y ≤ −9

=> y ≤ -3

Thus, the solution of the given inequality is y ≤ -3.

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The measure of each exterior angles of rectangle is 90°

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

A rectangle

A rectangle is a polygon with 4 sides

So, the measure of the exterior angle can be calculated using the formula for the exterior angles in a polygon

The exterior angles in a polygon are found by using:

Exterior of a rectangle in a polygon =  360°/Number of sides of the polygon

In this case,

The number of sides of the rectangle = 4

So, we have

Exterior of a rectangle =  360°/4

Evaluate

Exterior of a rectangle =  90°

Hence, the value of the measure of each exterior angles of rectangle is 90°

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Complete question

Find the measure of each exterior angles of rectangle?

Step by step​

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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The equations Ax = b are not compatible.

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

To determine whether the equations Ax = b are compatible and to compute a solution x, you would first form the augmented matrix [A|b]. Then, you would perform row operations on [A|b] to reduce it to an upper triangular matrix [C|d]. Finally, you would use the software package to solve the square system of equations Cx = d.

If the software terminates with an error message, it means that C is singular, and the equations Ax = b are not compatible. If the software finds the unique solution of Cx = d, it means that the equations Ax = b are compatible and that the solution x is unique. However, it is important to note that the uniqueness of the solution depends on the rank of A being equal to n. If the rank of A is less than n, the equations are not compatible, and if the rank of A is greater than n, the equations have infinitely many solutions.

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Answer: View the image attached

Step-by-step explanation:

Due to the x being squared the graph will be a parabola. The line is solid due to it being a less than AND equal to and the shading it below due to the symbol facing right. (<)

Answer:

Jamie is correct. This is because 41 is a combination of 40 and 1. Salena thinks that the 4 is just a 4, however, the 4 is in the tens place, so the 41 without the 1 is 40. The answer to this 41 times 9 is 369. Not 45.

Step-by-step explanation:

Each skirt is $41

Salena needs 9

(9*40) + (9*1)

360   +   9

    $369

Answer:

184320 Cubic Cenimeters

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

x + 2(4x-6) = 42

x + 8x - 12 = 42

9x = 42 + 12

9x = 54

9/9 x = 54/9

x = 6

The statement that the one with a higher coefficient of variation exhibits higher variability is true.

The coefficient of variation expresses the proportionate level of variability present in a random variable and can be determined by dividing the mean by the standard deviation.

If the coefficient of variation is higher, it means that the random variable shows more variation in relation to its mean.

To illustrate, suppose that the average height of a set of males is 6 feet with a standard deviation of 2 inches.

The variance ratio would result in a coefficient of variation of 0. 033 Suppose that a group of females has an average height of 5 feet with a standard deviation of 1 inch.

The women's coefficient of variation is calculated to be 0. 02 The variance of men's height in relation to their average height is indicated by their higher coefficient of variation.

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