you earn a salary of $40,000 per year and decide to save 20% of your gross pay. you then set a goal of creating a $16,000 emergency fund. how long will it take for you to achieve your goal?
A. 6 months
B. 1 year
C. 2 years
D. 3 years

Answer:

Step-by-step explanation:

The value of the test statistic that marks the boundary of a specified area in the tail of the sampling distribution under the null hypothesis is called the critical value.

Now let's delve into the explanation. In hypothesis testing, the critical value plays a crucial role in determining the decision-making process. It is used to define the boundary or cutoff point that separates the critical region from the non-critical region in the sampling distribution under the null hypothesis.

The critical value is selected based on the significance level (alpha) chosen by the researcher, which represents the probability of making a Type I error (rejecting the null hypothesis when it is true). The critical value is determined from a probability distribution associated with the test statistic, such as the t-distribution or the standard normal distribution.

By comparing the calculated test statistic with the critical value, researchers can assess whether the obtained result falls within the critical region or the non-critical region. If the test statistic exceeds the critical value, it falls in the critical region, leading to the rejection of the null hypothesis. On the other hand, if the test statistic is less than or equal to the critical value, it falls in the non-critical region, indicating insufficient evidence to reject the null hypothesis.

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Answer:  Elga is 16 years old

Step-by-step explanation: so first you divide 96 by 2 and get 48, 48 divided by 3=16,

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Work Shown:

x = Elga's age

3x = Alvin's age since he is 3 times older

x+3x = 4x = sum of their ages

4x = 96

x = 96/4

x = 24 is Elga's age

3x = 3*24 = 72 is Alvin's age

Check: 24+72 = 96 which confirms the answer.

Answer:

Step-by-step explanation:

Point( -4 , 1)  ; slope = m = 5

Point-slope form:

y - y1 = m(x -x1)

y - 1 = 5(x - [-4])

y - 1 = 5(x + 4)

y - 1 = 5x + 5*4

y - 1 = 5x + 20

    y = 5x + 20 + 1

   y= 5x + 21

Answer:

Option c. 59°

Step-by-step explanation:

<W+<Y=180

121+<Y=180

<Y=180-121

<Y=59

Answered by GAUTHMATH

Answer: No Possible Triangles

Step-by-step explanation: DeltaMath

Just hit the enter button, don’t type anything in the box or else it will mark it wrong.

The critical region(s) on a normal curve distribution would be located in the tail(s) of the curve. In hypothesis testing, the critical region(s) refers to the area(s) of the distribution that corresponds to rejecting the null hypothesis. This region(s) is based on the significance level of the test, which is typically set at 0.05 or 0.01.

In this case, the null hypothesis would be that listening to Vance Joy does not have a significant effect on happiness levels. The alternative hypothesis, which is what the researcher is testing for, would be that there is a significant difference in happiness levels between those who listen to Vance Joy and those who do not.
Assuming a two-tailed test, where the researcher is interested in whether the effect could be positive or negative, the critical region(s) would be located in both tails of the normal curve distribution. The exact location of the critical region(s) would depend on the sample size and the significance level of the test.
If the sample size is large, the critical region(s) would be located farther from the mean, indicating a higher level of confidence in rejecting the null hypothesis. Conversely, if the sample size is small, the critical region(s) would be located closer to the mean, indicating a lower level of confidence in rejecting the null hypothesis.
Overall, the critical region(s) on a normal curve distribution represents the area(s) of the distribution that corresponds to rejecting the null hypothesis, and its location depends on the sample size and the significance level of the test.

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Answer: 30 minutes.

Step-by-step explanation;

The train travels 85km per hour, so the train moves 85km in 60 minutes. You need to find out how many minutes it takes for the train to move 42 km. Use the rule of three to find this out, using x to represent the x amount of minutes it would take for it to travel 42km.

You can place the rule of three like this: \(\frac{85}{60}\) x \(\frac{42}{x}\). Cross multiply to find out the value of x, which is  29.647, this is the amount of time it takes the train to travel 42 km. Round the number to its closest value, 30 minutes.

Answer:

Carlos=1.5041

Mykala=2.6991

William=4.1350

Emily=4.1773

(i) A Venn-diagram of this information is shown below.

(ii) The number of students who like picnic = 34

(iii) The number of students who like hiking only = 51

(iv) The percentage of students who like picnic only. = 45.33%

Let us assume that A represents the set of students who like picnic.

B represents the set of students who like the hiking.

The total number of students in a  class are: n(A U B) = 75

Out of 75 students, 10 like both the activities.

n(A ∩ B) = 10

The ratio of the number of students who like picnic to those who like hiking is 2 : 3

Let number of students like tea n(A) = 2x

and the number of students like coffee n(B) = 3x

n(A U B) = n(A) + n(B) - n(A ∩ B)

75 = 2x + 3x - 10

75 + 10 = 5x

85/5= x

x = 17

The number of students like picnic = 2x

                                                          = 2 × 17

                                                          = 34

The number of students like hiking = 3x

                                                           = 3 × 17

                                                           = 51

This informtaion in Venn diagram is shown below.

The percentage of students who like picnic only would be,

(34/75) × 100 = 45.33%

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Answer:

the answer is C

Step-by-step explanation:

Answer:

2471.81

Step-by-step explanation:

Let I be the interest, r the annual rate and P the principal. Then:

I = P(r)^2 = 5460

I = P(r)^4 = 12060.6

so r^2 = P(r)^4 /  P(r)^2 = 12060.6/5460

r^2 = 2.2089

r = 1.486

So  P(r)^2 = P* 2.2089 = 5460

P = 5460 / 2.2089 = 2471.81.

Answer:5 multiplied by x-2

x-2 multiplied by 5

Step-by-step explanation: I hope this helps!

I'm not sure If flipping the equation counts but that's what I think would be right.

The 75th percentile for the commute time of LA workers is approximately 37.4 minutes.

To find the 75th percentile for the commute time of LA workers, we need to find the value of x such that 75% of the LA workers have a commute time less than or equal to x.

Using the standard normal distribution, we can convert the original distribution to a standard normal distribution with a mean of 0 and a standard deviation of 1 using the formula:

z = (x - mu) / sigma

where z is the corresponding standard score, x is the commute time, mu is the mean, and sigma is the standard deviation.

Substituting the given values, we get:

z = (x - 28) / 14

To find the z-score corresponding to the 75th percentile, we look up the area to the left of this score in the standard normal distribution table, which is 0.750.

Looking up the corresponding z-score in a standard normal distribution table or using a calculator function, we find that the z-score is approximately 0.6745.

Substituting this value into the formula for z, we get:

0.6745 = (x - 28) / 14

Solving for x, we get:

x = 0.6745 * 14 + 28

x = 37.42

Therefore, the 75th percentile for the commute time of LA workers is approximately 37.4 minutes.

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Therefore , the solution of the given problem of expression comes out to be -1/36 is the evaluation of the given expression.

Mathematical operations such as multiplication, division, addition, and deletion are necessary. If you put them together, you get the following: A formula, some data, and a math operator The components of a statement of fact are values, variables, and operations like additions, elisions, multiplications, and divisions. You can contrast and compare different words and phrases.

Here,

Given :

=> -(6⁻⁵)(6³)

=> - (6 ⁻⁵⁺³)

=> - (6⁻²)

=> -6⁻²

=> -1/36

Thus , -1/36 is the evaluation of the given expression.

Therefore , the solution of the given problem of expression comes out to be -1/36 is the evaluation of the given expression.

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Answer:

Step-by-step explanation:

Step 1

Find the area of 1 Triangle

To find this, we will use this formula:

\(A=\frac{1}{2} *B*H\)

Let's use the formula!

\(A=\frac{1}{2} *14*27\\=\frac{1}{2}* 378\\=189\)

The area of 1 triangle is 189 square units

Step 2

Find the area of the whole intire shape by multiplying the area of 1 triangle with the amount of sides.

There are 12 sides, so let's multiply 189 by 12

189x12=2268

The area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

In this question, we have been given the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)

We need to find the perimeter and area of the rectangle.

Using distance formula we find the length and width of the rectangle.

d1 = √(-2 - 7)² + (3 - 3)²

d1 = √(-9)²

d1 = 9

And d2 = √(-2 + 2)² + (-6-3)²

d2 = √(-9)²

d2 = 9

d3 = √(7 + 2)² + (-6 + 6)²

d3 = 9

This means, the length and width of rectangle are equal i.e., 9 units.

So, perimeter would be,

P = 4 * 9

P = 36 units

And the area would be,

A = 9 * 9

A = 81 square units

Therefore, the area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

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Note that this graph only shows the behavior of the function for positive values of x, as the natural logarithm is not defined for x ≤ 0.

What is Function?

Function can be defined in which it relates an input to output.

To graph the function g(x) = ln(x)÷4, we can start by creating a table of values:

x g(x) = ln(x)÷4

1 0

2 0.173

10 0.575

100 0.921

1000 1.146

Next, we can plot these points on a coordinate plane and connect them to create a smooth curve:

Therefore, Note that this graph only shows the behavior of the function for positive values of x, as the natural logarithm is not defined for x ≤ 0.

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Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

The equation of the trajectory which can be described using the equations for projectile motion is; y(t) = x·tan(θ) - g·x²/(2·v₀²·cos²(θ)), which is a quadratic equation with a path of a parabola

Projectile motion is the motion of an object that is projected in the air under the influence of gravitational attraction.

Let θ represent the angle at which the path of the object makes with the horizontal, and let v₀ represent the velocity of the object. The path of the object can be described using the equations of the motion of a projectile, as follows;

Horizontal component of the velocity, v₀ₓ = v₀ × cos(θ)

Vertical component of the velocity, \(v_{0y}\) = v₀ × sin(θ)

The horizontal motion of the object is therefore;

x(t) = v₀ₓ × t = v₀ × cos(θ) × t

The vertical motion which is under the influence of gravity is; y(t) = \(v_{0y}\)  × t - (1/2) × g × t²

v₀ × sin(θ) × t - (1/2) × g × t²

The horizontal component indicates that we get;

t = x/(v₀ × cos(θ))

Plugging in the above expression for t into the equation for y(t), we get;

y(t) = \(v_{0y}\)  × t - (1/2) × g × t² = \(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

\(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = (v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

(v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = x·tan(θ) - g·x²/(2·v₀×cos(θ))²

The equation, y = x·tan(θ) - g·x²/(2·v₀×cos(θ))², is a quadratic equation, which is an equation of a parabola, therefore, the trajectory of an object thrown at an angle to the horizontal is a parabola.

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Answer:

Indirect variation

Step-by-step explanation:

If two variables change in inverse proportion, then it is called indirect variation.

xy = k where k is a constant.

5*2 = 10

10*1 =10

\(15*\dfrac{2}{3}=5*2=10\\\\\\20*\dfrac{1}{2}=10\)

So, this is indirect variation.

Answer:

width=23.205 in.

length=29.085 in.

Step-by-step explanation:

width=x

length =x+5.88

Perimter=x+x+x=5.88+x+5.88=104.58

4x+11.76=104.58

4x=104.58-11.76

4x=92.82

x=23.205

width=x=23.205 In.

length=x+5.88=23.205+5.88=29.085 in.

Answer:

Rational & integer

Step-by-step explanation:

Rational numbers are terminating. -7 is terminating.

All integers are rational numbers. Integers do not have decimals.

This is not whole because it is negative.

This is not irrational because... it's rational!

it is a rational and integer Hopefully you pass this assignment

You will need 5.2 pounds of candy from each candy. The reason is because you have 2 kinds of candy and 10.4 pounds so divide 10.4 by 2 and you get 5.2

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The remainder when  ƒ(x) = 2x³ – 3x – 2 is divided by x - 4 is 114.

To find the remainder when ƒ(x) is divided by (x - 4), we can use the remainder theorem, which states that the remainder when a polynomial ƒ(x) is divided by (x - a) is equal to ƒ(a).

So, we need to evaluate ƒ(4) to find the remainder when ƒ(x) is divided by (x - 4).

ƒ(x) = 2x³ – 3x – 2

ƒ(4) = 2(4)³ – 3(4) – 2

ƒ(4) = 2(64) – 12 – 2

ƒ(4) = 128 – 14

ƒ(4) = 114

Therefore, the remainder when ƒ(x) is divided by (x - 4) is 114.

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Answer:

300g cereal

300g chocolate

150g nuts

Step-by-step explanation:

5x=750

x=150

2x=300

Standard form

Ax+By= c

y= -4/5x -1/2

4/5x+y =-1/2