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When solving a word problem using a system of equations, how many equations
must you create when there are two unknowns?
a) 1
b) 2
c) 3
d) 4

The formula for z-score is given as

we will have to calculate two values of the z-scores

The given values are

By substitution, we will have

we will then calculate the second z-score

The given values are

By substitution, we will have

P(-0.5833 ≤ z ≤ 0.3333) = 0.3507

Hence the probability that a randomly selected mortgage payment is between $877 and $1,042 is 0.3507

Answer:

The answer is 70

Step-by-step explanation

Add 15 by 15 for each side then add 20 by 20 for each other side

Check the picture below.

The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.

The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.

When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.

To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.

For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.

In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.

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Answer:

a. a, c, d, f : 145

b, e, g: 35

b. Angles: b and 35, a and c, d and f, and e and g

Hope this helps! :)

Answer:

Part a
a = 145°
b = 35°
c = 145°
d = 145°
e = 35°
f = 145°
g = 35°

Part b
a and c
b and 35°
d and f
e and g

Step-by-step explanation:

When parallel lines get crossed by another line (which is called a transversal),eight angles are formed as in the figure you attached.

Some of these angles are equal

Some are supplementary (add up to 180°)

First let's classify and define the angles so that you understand better

Vertical Angles
These are angles that are opposite each other. They are equal to each other

Thus a and c, b and 35°, d and  f, e and g are vertical angles
(Answer to b)

So a = c, b = 35, d = f, e = g

Corresponding Angles
These are angles that  have the same position with regards to the parallel lines and the transversal. Such angles are equal
The corresponding angle pairs are:
a and d, b and g, 35 and e, c and f
So a = d, b = g, e = 35 and c = f

Linear Angles
Linear pair of angles are formed when two lines intersect each other at a single point. The sum of the angle measures will be 180°

Here the pairs of linear angles are

a and 35°
b and c
c and 35°
d and e
g and f
e and f
g and d

There are other properties that apply to two parallel lines and a transversal through them but the above two properties are enough to compute all the angles a -g

Let's write down the two properties relating to vertical angles and corresponding angles:

a = c, b = 35, d = f, e = g  (1)
a = d, b = g, e = 35, c = f  (2)

b =35° and e = 35° and b = g ==> g = 35°

Using the property for linear angle pairs

c + 35 = 180
c = 180 - 35
c = 145°

Since c and a are vertical angles
a = c = 145°
a = 145°

Since a and d are corresponding angles
d = a = 145°

d = 145°

Since d and f are vertical angles
f = d = 145°

f = 145°

So the degree measures of the angles are
a = 145°
b = 35°
c = 145°
d = 145°
e = 35°
f = 145°
g = 35°

You need not necessarily proceed in the same order as I did. Just apply the rules I have provided and you will get the same results

For part b:
The pairs of opposite/vertical angles are
a and c
b and 35°
d and f
e and g

Answer:

Answer: 2pq +7 is the ANS.

Answer:

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

There is a difference between the means

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 5.9pounds/square inch

Given mean of the sample = 6.0pounds/square inch

Given that variance of the Population = 0.36

The standard deviation of the Population = √0.36 =0.6

critical value (Z₀.₀₅)= 1.96

Step(ii):-

Null Hypothesis:H₀: x⁻ = μ

Alternative Hypothesis:H₁:  x⁻ ≠ μ

Test statistic

              \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

               \(Z = \frac{6.0-5.9 }{\frac{0.6}{\sqrt{160} } }\)

              Z  =  2.1097

Final answer:-

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means

Divide 488 by 61 to find the unit rate.

488/61 = 8

You get 8 points for defeating each enemy.

Hope this helps

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Option 2 is the correct graph for the function f(x) = \(4[(1/2)^{x}]\) .

Given ,

f(x) = \(4[(1/2)^{x}]\)

Mathematically the graph will of exponential in nature.

So,

Let us assume few values to understand the nature of graph.

Firstly,

Let x= 1

f(x) = \(4[(1/2)^{1}]\)

f(x) = 2

Let x = 2

f(x) = \(4[(1/2)^{2}]\)

f(x) = 1

Let x = 3

f(x) = \(4[(1/2)^{3}]\)

f(x) = 0.5

Thus from these values of f(x) corresponding to the values of x second graph will be correct .

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Answer:

k = K^2

Step-by-step explanation:

Subtract  K^2 from both sides of the equation.

Answer:

its m=185t

Step-by-step explanation:

because if you divide

An equation which represent the total meters (m) that Sam runs in t minutes is: B. m = 185t.

Mathematically, a proportional relationship can be represented with the following equation or mathematical expression:

m = kt

Where:

Next, we would determine the constant of proportionality (k) for each candy as follows:

From Jacob's running, we have the following:

Constant of proportionality (k) = t/m

Constant of proportionality (k) = 400/2

Constant of proportionality (k) = 200

Since Sam runs 15 meters less each minute than Jacob does, an equation that represent the total meters (m) that he runs in t minutes is given by:

m = (200 - 15)t

m = 185t

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Answer:

(-8, -2)

Step-by-step explanation:

Subtract 2 from -6, so -6 -2 which gives -8.

Subtract 3 from 1 so, 3-1 = -2.

Answer:I just had to do this in Math class and the answer is (-8,-2)

Step-by-step explanation:

Answer: D, 100

Step-by-step explanation:

Answer: 100 (D)

Step-by-step explanation:

cuz

Answer:

Screen B is wider, because 5 and one-third is greater than 5.3..

Step-by-step explanation:

Got it correct on edge

Answer:

first pic answer = first bit

The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is  1,000,016.

To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.

0 hours:

Population = 10^6 + (10^4)0 -(10^3)0^2

Population = 10^6 - 10^3

Population = 10^3 or 1,000

4 hours:

Population = 10^6 + (10^4)4 -(10^3)4^2

Population= 10^6 + 40,000 - 16,000

Population= 1,000,024

8 hours:

Population = 10^6 + (10^4)8 -(10^3)8^2

Population= 10^6 + 80,000 - 64,000

Population= 1,000,016

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Answer:

its 8

Step-by-step explanation:

Answer:

If an equation has no solution, then the solution set is the _empty set_ and

is denoted by _{ } or ∅__.

Answer:

n | 0 | 0 1

| y 2 | 2 y 3 | 3 años

Step-by-step explanation:

Answer:

You can use 48 and 24

Step-by-step explanation:

You can figure out 48 by simply multiplying 6 times 8. You can figure out the 24 by noticing that 24 is divisible by both 6 and 8. 6 x 4 =24, and 8 x 3=24. I hope this helps!

Answer:

The numbers we could use for the denominators is 48  and 24.

As given by the question

There are given that 4<6, so 204<216.

Now,

On the number line, 4 is less tha6 and 204 is also less than 216

Hence, the given reasoning is correct.

Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

By using the power rule for derivatives, we get dy/dx = 3/(2√(3x + 9)).

It is defined as the limit of the ratio of the change in the function to the change in its input, as the change in the input approaches zero.

To find dy/dx, we can use the power rule for derivatives and the chain rule as follows:

y = √(3x + 9)

Inferring the derivative from x, we obtain:

dy/dx = d/dx [√(3x + 9)]

Using the chain rule, we can write:

dy/dx = d/du [√u] * du/dx, where u = 3x + 9

Taking the derivative of √u with respect to u using the power rule, we get:

d/dx [√u] = 1/2 \(u^(-1/2)\)

Substituting back u = 3x + 9 and multiplying by du/dx, we get:

dy/dx = 1/2 \((3x + 9)^(-1/2)\) * d/dx [3x + 9]

Taking the derivative of 3x + 9 with respect to x, we get:

d/dx [3x + 9] = 3

Reentering the preceding equation, we obtain:

dy/dx = 1/2 \((3x + 9)^(-1/2)\) * 3

Simplifying, we get:

dy/dx = 3/(2√(3x + 9))

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Answer:

This actually is false, it doesn't always work.

Step-by-step explanation:

Such as,

256 x 1/2 =

128.

The last digit isn't a 3, it's an 8.

Another Example,

176 x 1/2 =

88.

The last digit is also an 8 here, and not a 3.

It does work for some equations, but not for most of them, hope this helps!

The Investment Income, if any (g) $380 and The Net Income tax payable is $41,516.75

A. The Taxable Income (a) $425,000  

The Prefrentially taxed income (b) $0  

The Income taxed at ordinary rates ( c) $425,000  

The Tax on c above (d)

$124,469.95 = $120,529.75 + [($425,000 - $415,050) x 39.6%]

The Tax on b above ( e) is $0  

Thus, the Total Income tax (f) is $124,469.95 (d + e)

The Investment Income, if any is $0 No Investment Income

The Net Income tax payable is $124,469.95  

B. The Taxable Income (a) $425,000  

The Prefrentially taxed income (b) $2,000  

The Income taxed at ordinary rates ( c) $423,000  

The Tax on c above (d);

$123,677.95 = $120,529.75 + [($423,000 - $415,050) x 39.6%]

The Tax on b above ( e) ;

$400 = $2,000 x 20%, Since marginal rate is 39.6%

The Total Income tax (f) $124,077.95 (d + e)

The Investment Income, if any (g) $76

($2,000 x 3.8% = $76)

The Net Income tax payable is $124,153.95 (f + g)

C. The Taxable Income (a) $425,000  

The Prefrentially taxed income (b) $55,000  

The Income taxed at ordinary rates ( c) $370,000  

The Tax on c above (d);

$105,629.25 = $46,278.75 + [($370,000 - $190,150) x 33%]

The Tax on b above ( e);

$8,747.50 [($45,050 x 15%) + ($9,950 x 20%)]

The Total Income tax (f) $114,376.75 (d + e)

The Investment Income, if any (g) $2,090

($55,000 x 3.8% = $2,090)

The Net Income tax payable $116,466.75 (f + g)

D. The Taxable Income (a) $195,000  

The Prefrentially taxed income (b) $50,000  

The Income taxed at ordinary rates is ( c) $145,000  

The Tax on c above (d);

$33,636.75 = $18,558.75 + [($145,000 - $91,150) x 28%]

The Tax on b above ( e);

$7,500.00 = $50,000 x 15%

The Total Income tax (f) is $41,136.75 (d + e)

The Investment Income, if any (g) $380

The Net Income tax payable is $41,516.75 (f + g)

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Answer:

where is the question tho.....

Step-by-step explanation:

I don't even understand what you talking about

Las cantidades de bolitas para cada una de las tres personas son las siguientes:

Amanda: 19 bolitas

Rodrigo: 15 bolitas

Patricio: 69 bolitas

En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:

Amanda

x = y + 4

Rodrigo

y

Patricio

z = 2 · (x + y) + 1

Total

x + y + z = 103

A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:

x + y + 2 · (x + y) + 1 = 103

3 · x + 3 · y = 102

x + y = 34

y + 4 + y = 34

2 · y = 30

y = 15

Luego, determinamos las cantidades de bolitas de Amanda y Patricio:

x = 15 + 4

x = 19

z = 2 · (19 + 15) + 1

z = 2 · 34 + 1

z = 68 + 1

z = 69

El enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.

The statement is written in Spanish and the language used in the answer is the same of the statement.

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Answer:

The answer is: 1.2 + -0.4y

Answer: -0.4y + 1.2

Step-by-step explanation:

0.4(y) = 0.4y

0.4(3) = 1.2

0.4y + 1.2 - 0.8y

0.4y - 0.8y = -0.4y

-0.4y + 1.2

Answer:

Step-by-step explanation:To find the outer measure of B, denoted as µ*(B), we need to take the infimum of the sums of the lengths of the intervals that cover B.

We start by considering a cover of B by intervals. Since B is a set of four points, we can construct a cover of B with four intervals, each containing one of the points. Specifically, we define:

I1 = (8 - ε, 8 + ε)

I2 = (145 - ε, 145 + ε)

I3 = (287 - ε, 287 + ε)

I4 = (7005 - ε, 7005 + ε)

where ε is a small positive number.

Then, the lengths of these intervals are:

|I1| = 2ε

|I2| = 2ε

|I3| = 2ε

|I4| = 2ε

The sum of the lengths of these intervals is:

|I1| + |I2| + |I3| + |I4| = 8ε

Since ε can be made arbitrarily small, we can take the infimum of the sum of the lengths of the intervals over all covers of B by intervals. Therefore, we have:

µ*(B) = inf{|I1| + |I2| + |I3| + |I4|} = inf{8ε} = 0

Hence, the outer measure of B is 0.