after 5 years, sammy has $7500 left on his student loans. with an interest rate of 8%, how much did sammy take out originally to fund his education?

Answer:

I believe thats 8 to the power of 7

Step-by-step explanation:

Answer:

i clicked your link adn it looks like 8^7 or 8 to the 7th power which would be 2,097,152

Step-by-step explanation:

Answer: B

Step-by-step explanation:

7(-2) - 4(1) = -18

-14 - 4 = -18

-18 = -18

TRUE

(-2) + 12(1) = 10

-2 + 12 = 10

10 = 10

TRUE

Answer:

7

Step-by-step explanation:

The following table shows the number of innings pitched by each of the Greenbury Goblin's starting pitchers during the Rockbottom Tournament.

Pitcher Calvin Brody Thom Shawn Kris

Number of innings pitched 111111 555 121212 777 333

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

arranging the numbers in ascending order gives :

3, 5, 7, 11, 12

there are two numbers to the left and right of 7. 7 is the median

Find the median number of innings pitched.

The probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%. We can use the standard normal distribution to find the probability that the next report will weigh less than 45g.

z = (x - mu) / sigma

where z is the standard score, x is the value we want to standardize (45g), mu is the mean (60g), and sigma is the standard deviation (12g).

Substituting the given values, we get:

z = (45 - 60) / 12

z = -1.25

Next, we use a standard normal distribution table (or a calculator) to find the cumulative probability of z being less than -1.25. This gives us:

P(z < -1.25) = 0.1056

Therefore, the probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%.

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Answer:

1.V=288, A=288

2. V=460, A=494

3. V=672

4. A=898

Step-by-step explanation:

1.

V= l×b×h

288

A=2(lb+lh+bh)

=288

2.

V¹= larger cuboid =320

V²=smaller cuboid=140

V=460

A¹=328

A²=166

A=494

3.

V=(Area of cross section)×length

=672

4.

Area of cube=l³

³√294=6.65

add 3

9.65³=898

The 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

What is Confidence interval?

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

As given,

n = 150 = drivers

x = 100 = wear seat belts.

We have to find 95% confidence interval for proportion P that do not wear seat belt.

From 150 we have 100 wear seat belts

Not wear seat belt = 150 - 100

Not wear seat belt = 50

P = 50/150

P = 0.33

95% confidence interval for P is

CI = (P - zα/2√(P(1 - P)/n), P + zα/2√(P(1 - P)/n))

For 95% CI, zα/2 = 1.96

Substitute values,

CI = (0.33 - 1.96√(0.33(1 - 0.33)/150), 0.33 + 1.96√(0.33(1 - 0.33)/150))

CI = (0.33 - 0.075, 0.33 + 0.075)

CI = (0.255, 0.405)

Therefore 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

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Answer:

(5,15)

Step-by-step explanation:

A.

Answer:

(5,15)

Step-by-step explanation:

that's the answer, I hope it helps!

So, -7π/9, -19π/9, and -31π/9 are three negative angles coterminal with 5π/9.

To find angles coterminal with 5π/9, we need to add or subtract a multiple of 2π until we reach another angle with the same terminal side.

To find a positive coterminal angle, we can add 2π (one full revolution) repeatedly until we get an angle between 0 and 2π:

5π/9 + 2π = 19π/9

19π/9 - 2π = 11π/9

11π/9 - 2π = 3π/9 = π/3

So, 19π/9, 11π/9, and π/3 are three positive angles coterminal with 5π/9.

To find a negative coterminal angle, we can subtract 2π (one full revolution) repeatedly until we get an angle between -2π and 0:

5π/9 - 2π = -7π/9

-7π/9 - 2π = -19π/9

-19π/9 - 2π = -31π/9

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Returning to your initial problem, you plug in the value for R, then you solve for C and get C=30.

Assumptions: Each rabbit has one head and four legs, while each chicken has one head and two legs. Then, you may create a few straightforward equations, like C + R = 43 (where C is a chicken, R is a rabbit, and you both have one head).

Then, each C has two legs, and each R has four, making the sum 2C + 4R = 112. A total of 112) people.

Solve it now. C=43 - R

When you solve 2(43-R)+4R=112, you get 86-2R+4R=112, and when you work out the equation, you discover that R=13.

Returning to your initial problem, you plug in the value for R, then you solve for C and get C=30.

To verify, you can test the answer after that.

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The probability that the student will fail, given that he guesses the answers, is 0.227.

Since there are only two possible outcomes for each question (true or false),

the probability of guessing a correct answer is 1/2 = 0.5.

Likewise, the probability of guessing a wrong answer is also 1/2 = 0.5.

To find the probability of failing the exam,

we need to find the probability of answering less than 11 questions correctly.

Using the binomial probability formula,

the probability of getting k successes (correct answers) in n trials (questions) is given by:

P(k) = (n C k) * p^k * q^(n-k)

where p is the probability of success (getting a correct answer),

q is the probability of failure (getting a wrong answer), and (n C k) is the number of combinations of n things taken k at a time.

In this case,

n = 17, p = 0.5, and

q = 0.5.

The number of ways to get less than 11 correct answers is:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)P(X = k) = (n C k) * p^k * q^(n-k)

Substituting the values:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

P(X = 0) = (17 C 0) * (0.5)^0 * (0.5)^17 = 0.0015

P(X = 1) = (17 C 1) * (0.5)^1 * (0.5)^16 = 0.0146

P(X = 2) = (17 C 2) * (0.5)^2 * (0.5)^15 = 0.0586

P(X = 3) = (17 C 3) * (0.5)^3 * (0.5)^14 = 0.1558

P(X = 4) = (17 C 4) * (0.5)^4 * (0.5)^13 = 0.268

P(X = 5) = (17 C 5) * (0.5)^5 * (0.5)^12 = 0.327

P(X = 6) = (17 C 6) * (0.5)^6 * (0.5)^11 = 0.2732

P(X = 7) = (17 C 7) * (0.5)^7 * (0.5)^10 = 0.1537

P(X = 8) = (17 C 8) * (0.5)^8 * (0.5)^9 = 0.0573

P(X = 9) = (17 C 9) * (0.5)^9 * (0.5)^8 = 0.013

P(X = 10) = (17 C 10) * (0.5)^10 * (0.5)^7 = 0.0015

Therefore, P(X < 11) = 0.0015 + 0.0146 + 0.0586 + 0.1558 + 0.268 + 0.327 + 0.2732 + 0.1537 + 0.0573 + 0.013 + 0.0015P(X < 11) = 0.8857

Thus, the probability of failing is: P(fail) = P(X < 11) = 0.8857

The probability that the student will fail, given that he guesses the answers, is 0.227 (rounded to three decimal places).

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Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

8000

Step-by-step explanation:

Jack sold worth $8000 computer sales in the last week.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Jack is selling used computers. He is paid $15/h plus a 5% commission on sales.

He made $1000 in a 40-h week,

∴ He made $(15×40) = $600 for his work hours and $(1000 - 600)

= $400.

So, $400 dollars in 5% of the total sales and assuming he made a sell of $x.

∴ (5/100)×x = 400.

0.05x = 400.

x = 400/0.05.

x = 8000.

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Answer: 12.357312274

Step-by-step explanation:

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh

here 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle

The minimum value of P(x, y) is -22, and the maximum value is 32 within the given Feasible region.

The minimum and maximum values of the objective function P(x, y) = 14 - 2x + y, we need to analyze the feasible region determined by the given constraints.

The constraints are:

1) x + y ≤ 18

2) 8 ≤ y ≤ 2x + 3

To find the feasible region, we need to determine the points of intersection between the two lines represented by the constraints.

First, we consider the line x + y = 18. By setting x = 0, we find that y = 18. By setting y = 0, we find that x = 18. So, the points of intersection are (0, 18) and (18, 0).

Next, we consider the line y = 2x + 3. By setting x = 0, we find that y = 3. By setting y = 0, we find that x = -1.5. So, the points of intersection are (0, 3) and (-1.5, 0).

Now, we have four vertices that define the feasible region (0, 18), (18, 0), (0, 3), and (-1.5, 0).

We substitute these vertex coordinates into the objective function P(x, y) to determine the corresponding values:

P(0, 18) = 14 - 2(0) + 18 = 32

P(18, 0) = 14 - 2(18) + 0 = -22

P(0, 3) = 14 - 2(0) + 3 = 17

P(-1.5, 0) = 14 - 2(-1.5) + 0 = 18

From these calculations, we can see that the minimum value of the objective function P(x, y) occurs at (18, 0), with a value of -22. The maximum value occurs at (0, 18), with a value of 32.

Therefore, the minimum value of P(x, y) is -22, and the maximum value is 32 within the given feasible region.

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Answer:

The value of tan F = 8/15  or  0.533333

Step-by-step explanation:

To find the value of tan F, we will follow the steps below;

We will use trigonometric ratio. that is;

SOH CAH TOA

sin Ф = opposite / hypotenuse

cosФ = adjacent/hypotenuse

tan Ф = opposite/adjacent

if Ф = F

then opposite = DE = 8

adjacent = EF = 15

web can now proceed to insert the values into the formula

tan F = opposite/ adjacent

tan F = 8/15

tan F = 0.5333

tanF = oppos

Step-by-step explanation:

I don't know the options to pick from.

the 2 main possibilities coming to my mind are

y = f(x)

or

(x, f(x)) or (x, y)

there is no specific function coming to mind. the functional values bounce around above and below the x-axis (positive and negative y-values) with not detectable pattern related to the x values.

the other 2 questions can be found directly in the table :

f(3) means f(x) with x=3, and that is -2

and f(x) = -5 is true, when x = 4

Answer:

m% of n is (m/100)(n)

Step-by-step explanation:

When removing a %, you just move the period two places to the left (ex. 50% = 0.50), or just divide the number by a 100 (ex. 50% = 50/100). So then, m% of n is just the product of m/100 and n.

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.

To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example

If x = 0, then y = 0/2 = 0, so the first point is (0,0).

If x = 2, then y = 2/2 = 1, so the second point is (2,1).

If x = 4, then y = 4/2 = 2, so the third point is (4,2).

If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).

We can plot these points on a coordinate plane

As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.

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The following are the solution to the given inequalities;

-13 < 4x + 7 ; -5 < x

-2x + 7 < 19 ; x > -6

-45 < 5(p - 2) ; -7 < p

21 < -7(x - 2) ; -1 > x

-9x + 10 > -8 ; x < 2

2 - 6 < 3 ; -4 < 3

-13 < 4x + 7

combine like terms

-13 - 7 < 4x

-20 < 4x

divide both sides by 4

-5 < x

-2x + 7 < 19

combine like terms

-2x < 19 - 7

-2x < 12

x < 12/-2

x > -6

When dividing inequality with negative, the inequality sign will flip.

-45 < 5(p - 2)

open parenthesis

-45 < 5p - 10

-45 + 10 < 5p

-35 < 5p

-7 < p

21 < -7(x - 2)

21 < -7x + 14

21 - 14 < -7x

7 < -7x

divide both sides by -7.

-1 > x

-9x + 10 > -8

-9x > -8 - 10

-9x > -18

x > -18/-9

x < 2

2 - 6 < 3

-4 < 3

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Answer:

I believe the correct answer is B! Hope this helped.

Answer:

b

Step-by-step explanation:

The current passing through the capacitor in terms of Zc, Zr1, Zr2, Zl, and Vin is given by -[(Zr1 * Zr2 * Zl) / (jωC * (Zr1 + Zr2 + Zl))] or alternatively -(Zr1 * Zr2 * Zl) / (jωC * (Zr1 + Zr2 + Zl)).

To determine the current passing through the capacitor in terms of the impedances Zc, Zr1, Zr2, Zl, and Vin, we need to analyze the specific circuit configuration.

Assuming we have a circuit where the capacitor is connected in parallel with other components, we can use the concept of complex impedance to express the current passing through the capacitor.

The complex impedance of a capacitor is given by Zc = 1/(jωC), where j is the imaginary unit, ω is the angular frequency, and C is the capacitance.

Now, if we have a circuit with multiple components such as resistors (Zr1 and Zr2) and inductors (Zl), and a voltage source Vin, we can use Kirchhoff's current law (KCL) to analyze the current passing through the capacitor.

According to KCL, the sum of currents entering and leaving a node in a circuit must be zero. Therefore, we can write the following equation for the circuit:

Vin / Zr1 + Vin / Zc + Vin / Zr2 + Vin / Zl = 0

To isolate the current passing through the capacitor, we rearrange the equation:

Vin / Zc = -[Vin / Zr1 + Vin / Zr2 + Vin / Zl]

Dividing both sides by Vin:

1 / Zc = -[1 / Zr1 + 1 / Zr2 + 1 / Zl]

Substituting the complex impedance of the capacitor:

1 / (1 / (jωC)) = -[1 / Zr1 + 1 / Zr2 + 1 / Zl]

Simplifying:

jωC = -[1 / Zr1 + 1 / Zr2 + 1 / Zl]

Finally, solving for the current passing through the capacitor (Ic), we divide both sides by jωC:

Ic = -[1 / (jωC) / (1 / Zr1 + 1 / Zr2 + 1 / Zl)]

Ic = -[(Zr1 * Zr2 * Zl) / (jωC * (Zr1 + Zr2 + Zl))]

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Given:

prtion D is the correct answer.

The measure of angle ADB is equal to the square root of (\(AB \times BA\)).

In triangle ABC, let the angle bisectors drawn from vertices A and B intersect at point D. To find the measure of angle ADB, we can use the angle bisector theorem. According to this theorem, the angle bisector divides the opposite side in the ratio of the adjacent sides.

Let AD and BD intersect side BC at points E and F, respectively. Now, we have triangle ADE and triangle BDF.

Using the angle bisector theorem in triangle ADE, we can write:

AE/ED = AB/BD

Similarly, in triangle BDF, we have:

BF/FD = BA/AD

Since both angles ADB and ADF share the same side AD, we can combine the above equations to obtain:

(AE/ED) * (FD/BF) = (AB/BD) * (BA/AD)

By substituting the given angle bisector ratios and rearranging, we get:

(AD/BD) * (AD/BD) = (AB/BD) * (BA/AD)

AD^2 = AB * BA

Note: The solution provided assumes that points A, B, and C are non-collinear and that the triangle is non-degenerate.

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if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

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