A line's equation is given in point-slope form. y=(-(3/8)),(x+8)+4 A point on this line that is apparent from the given equation is [ ]

If he agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. The amount of each yearly payment is  K 368.51.

To calculate the amount of each yearly payment, we can use the formula for the present value of an annuity:

PV = A * [(1 - (1 + r)^-n) / r]

where:

PV = present value of the loan

A = annual payment

r = interest rate per year

n = number of years of the annuity

In this case, Mr. Apo Man borrowed K 2 000 from the bank at an interest rate of 14% p.a. compound interest, and agreed to pay back the loan in 8 yearly payments.

So, we have:

r = 14% = 0.14

n = 8

PV = K 2 000

We can solve for A by rearranging the formula:

A = PV * r / [(1 - (1 + r)^-n)]

Substituting the values, we get:

A = K 2 000 * 0.14 / [(1 - (1 + 0.14)^-8)]

A = K 2 000 * 0.14 / 0.7598

A = K 368.51

Therefore, the amount of each yearly payment that Mr. Apo Man needs to make to repay the loan in 8 years at 14% p.a. compound interest is K 368.51.

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Answer:

The right answer is "1.6053".

Step-by-step explanation:

According to the question,

The expected value will be:

= \(-Cost \ of \ ticket+Probability \ of \ winning\times Winning \ amount\)

As we know,

The probability of winning the lottery will be:

= \(\frac{1}{No. \ of \ ways \ of \ choose \ six \ from \ 40}\)

So that, the expected value is:

= \(-1+\frac{10^7}{\binom{40}6}}\)

= \(-1+\frac{10^7}{3838380}\)

= \(1.6053\)

The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

Answer:

1.2 dollars

Step-by-step explanation:

You have to divide the dollar count by the pound count.

So basically:

6/5

This gives you 1.2 dollars.

When you do unit rate, you just have to divide one value by the other value.

The value you divide by, and the value you divde, vary depending on what the question asks.

For instance, if this question asked what the pound count for 1 dollar would be, you would end up divide the 5 pounds by 6 dollars(5/6) instead of divideing the 6  dollars by 5 pounds like we did above(6/5).

Hope this helps!

Answer: 1.20 is your awnser

first divided 6.00 by 5

then you get $1.20 per pound

Step-by-step explanation:

Answer:

1.309

Step-by-step explanation:

75° =the radian of 1.309

hope it's right have a great day!

Answer:

\( \frac{5 {\pi}^{c} }{12} \)

Step-by-step explanation:

Radian measure of 75°

\( = 75 \times \frac{ {\pi}^{c} }{180 \degree} \\ \\ = \frac{5 {\pi}^{c} }{12} \)

Answer: a²-5a+4

Step-by-step explanation:

When brackets are next to each other in algebra it means to multiply.

So,

a×a=a²

a×-1=-a (in algebra, you don't write -1a you would just write -a)

-4×a=-4a

-4×-1=+4

So then you would write it like this:

a²-a-4a+4

Then you would simplify it:

a²-5a+4

Hope this helps :)

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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Answer:

Billy used 28 mins 30 sec to mow the lawn and Bobby used 43 mins 30 sec to now the lawn both within 72 mins

Step-by-step explanation:

let x represent Billy

let x+15 represent Bobby

x + x + 15 = 72

2x = 72 - 15

2x = 57

2x/2 = 57/2

x = 28.5 minutes = 28 minutes 30 seconds

Bobby = x + 15

= 28.5 + 15

= 43.5 minutes= 43 minutes 30 seconds

Answer:

Step 1: Write your hypotheses and plan your research design

Step 2: Collect data from a sample

Step 3: Summarize your data with descriptive statistics

Step 4: Test hypotheses or make estimates with inferential statistics

Step 5: Interpret your results

Step-by-step explanation:

Answer:

-8.

Step-by-step explanation:

Substitute BC with the -4 and 2, as you were given those values to substitute with B and C. Multiply those two values. You get -8.

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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The linear function there after 18 minutes of calls, then the credit was = $29

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Given that,

Slope = -0.16

There linear function is $29.00 in credit remaining on the card after 25 minutes of calls

There after 18 minutes of calls?

Slope m = -0.16

Let us assume,

x = 25 minutes

y = $29.00 in credit

Substitute this values,

So,

We can write,

y = mx + b

$29.00 = (-0.16) (25) + b

$29.00 = -24.84 + b

b = $29.00 + 24.84

b = $53.84

We can substitute b value,

y = mx + b

y = (-0.16) x + $53.84

y = \(-0.16x\) + $53.84

y = (-0.16)(25) + $53.84

y = -24.84 + $53.84

y = $29

Therefore,

The linear function there after 18 minutes of calls, then the credit was = $29

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Answer:

39

Step-by-step explanation:

Because if you want to know how many years until you get there you would need to divide to find how many year until Diego turns 2 times her age because the opposite of multiplication is division since they said 2 times

The triangles given are congruent as shown below.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

1) KL = LN   [Since L is the midpoint of KN]

ML = LP [ Since L is the midpoint of MP]

∠MLK = ∠MLP  [Vertically opposite pair of angles are equal.]

ΔMKL ≅ ΔPNL [Using the SAS Congruence Rule]

2) ∠BAD = ∠BCD [Given]

∠ABD = ∠CBD [Since BD bisects ∠ABC]

BD = BD [Common side]

ΔABD ≅ ΔCBD [Using AAS Congruence rule]

3) QR = ST [Given]

RS = TU [given]

QS = SU [Since S is the midpoint of QU]

ΔQRS ≅ ΔSTU  [By SSS Congruence rule]

Hence the triangles are congruent.

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Answer:

A, C, D

Step-by-step explanation:

For edge

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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Answer:

-2,1,6,13,22

Step-by-step explanation:

cn = n^2 -3

Let n=1

c1 = 1^2 -3 = 1-3 = -2

Let n=2

c2 = 2^2 -3 = 4-3 = 1

Let n=3

c3 = 3^2 -3 = 9-3 = 6

Let n=4

c4 = 4^2 -3 = 16-3 = 13

Let n=5

c5 = 5^2 -3 = 25-3 = 22

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

the diameter is 4 cm which means the radius is 2 cm. Diameter divided by two will give you the radius. The formulae for circumference is 2 π⋅r. So the circumference would be 4 π.

Step-by-step explanation:

The Bernoulli differential equation is a nonlinear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)y^n, where n ≠ 0, 1.

For n = 0 or n = 1, the equation is linear. For other values of n, a common technique to linearize the equation is to make the substitution y = v^(-1/n-1). The resulting equation is:

dv/dx + (P(x) + Q(x)/v^(1/n-1)) * (1/n-1) * v^(1/n-2) * dv/dx = 0.

For the initial value problem given, we have P(x) = -1/x, Q(x) = -5, and n = 2.

We make the substitution y = v^(-1), so v = y^(-1), and dv/dx = -y^(-2)dy/dx. The equation becomes:

-y^(-2)dy/dx + (-1/x - 5y^2) = 0.

We have the initial condition y(1) = 1/5. In terms of v, the initial condition becomes v(1) = 1/(1/5)^2 = 25.

Now, the differential equation is linear, and we can solve it using standard methods, such as separation of variables. To find the solution that satisfies the initial condition, we may use numerical methods such as the Euler method or Runge-Kutta method.

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Answer:

(-3.5, 8)

Step-by-step explanation:

\(\left(\frac{-5-2}{2}, \frac{9+7}{2} \right)=(-3.5, 8)\)

We are given the equations of four lines and we are asked to determine which ones are parallel. To do that we need to remember that two lines are parallel if they have the same slope. To determine the slope the line equations must be written in the form:

Where "m" is the slope.

The first equation is:

Therefore, the slope of the first equation is:

The second equation is:

We need to rewrite the equation to the wished form in order to know the slope, therefore we need to solve for "y". We do that first by applying the distributive property on the right sides:

Now we add 7 to both sides:

Therefore, the slope of this line is:

For the third equation we have:

The slope of this equation is:

For the fourth equation we have:

Now we solve for "y", first we subtract "x" from both sides:

Now we multiply both sides by "3/4":

Therefore, the slope of the fourth line is:

Since we have:

Then lines 1 and 4 are parallel.

Answer:

\(\boxed{\sf k=6}\)

Step-by-step explanation:

\(\sf kx (x-2)+6=0\)

Expand brackets.

\(\sf kx^2 -2kx+6=0\)

This is in quadratic form.

\(\sf ax^2 +bx+c=0\)

Since this is for equal roots:

\(\sf b^2 -4ac=0\)

\(\sf a=k\\b=-2k\\c=6\)

\(\sf (-2k)^2 -4(k)(6)=0\)

\(\sf 4k^2-24k=0\)

\(\sf 4k(k-6)=0\)

\(\sf 4k=0\\k=0\)

\(\sf k-6=0\\k=6\)

Plug k as 0 to check.

\(\sf \sf 0x^2 -2(0)x+6=0\\6=0\)

False.

So that means k must equal 6.

The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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Answer:

-1/2

Step-by-step explanation:

We know

The dilation of K(-2,4) equals K'(1,-2)

To get from -2 to 1, we time -1/2

To get from 4 to -2, we time -1/2

So, the scale factor used for the dilation is -1/2