Original price: ?

Percent of discount: 25%

Sale price: $45

Answer:

  $12300

Step-by-step explanation:

You want to know the amount loaned at 7% if $19000 loaned at 7% and 17% earns $2000 in one year.

The interest on an investment P at rate r for t years is ...

  I = Prt

The sum of the amounts of interest on a 7% investment of x and a 17% investment of (19000 -x) is given as 2000:

  0.07x +0.17(19000 -x) = 2000

  -0.10x +3230 = 2000 . . . simplify

  1230 = 0.10x . . . . . . . . . . add 0.10x -2000

  12300 = x . . . . . . . . . . . . divide by 0.10

The amount loaned at 7% was $12,300.

The function h(t)=6+3ln(t+1) is a logarithmic function

The height of the tree will exceed 18 feet after 53.6 years

The function is given as:

h(t)=6+3ln(t+1)

When the height is 18 feet, we have:

6+3ln(t+1) = 18

Subtract 6 from both sides

3ln(t+1) = 12

Divide both sides by 3

ln(t+1) = 4

Take the exponent of both sides

t + 1 = e^4

Evaluate the exponent

t + 1 = 54.6

Subtract 1 from both sides

t = 53.6

This means that the height of the tree will exceed 18 feet after 53.6 years

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Answer:

2/7

Step-by-step explanation:

put the total number of boys over the total number of stuedents

10/35 then simplify by dividing top and bottom by 5      2/7

Answer:

2/7

Step-by-step explanation:

10/35

reduce fraction

10÷5=2

35÷5=7

Answer:

Step-by-step explanation:

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

  x + y + z = 21000 . . . . . . total borrowed

  0.10x +0.12y +0.14z = 2580 . . . . . . total interest

  x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

  x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

__

Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

<95141404393>

The sequence x² - 64 is not a geometic sequence

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

x to the second power minus 64

Express properly

So, we have

x² - 64

The above expression is a quadratic expression

This is because it has a degree of 2 and a constant term

So, the sequence is not a geometic sequence

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Answer:

16 minutes

Step-by-step explanation:

First we are going to want to find the area of the window. We then divide that by the amount of area you can wash per minute ( 6 square feet )

So first lets find the area.

We are told that the window is in a shape of a trapezoid.

The area of a trapezoid can be calculated using the formula A = \(\frac{a+b}{2} h\)

Where a and b are the base lengths and h is the height

We are told that the length of the bases are 10 ft and 14ft so a and b = 10 and 14. We are also told that the window has a height of 8 so h = 8 .

We then plug these numbers into the formula to find the area

Recall formula: \(A=\frac{a+b}{2} h\)

a = 10 , b = 14 and h = 8

plug in these values into formula

\(A=\frac{10+14}{2} 8\)

add 10 and 14 to get 24

\(A=\frac{24}{2} 8\)

simplify fraction : 24 / 2 = 12

\(A=(12)(8)\)

multiply 12 and 8 to get 96.

A = 96 square feet.

To find how long it would take to wash the window we divide the total area of the window by the amount of area that can be washed per minute

Total area of window = 96

Area that can be washed per minute = 6

Time it would take to wash the whole window = 96 / 6 = 16 minutes

Answer:

I got but idk if that is right $7897.5.

Step-by-step explanation:

The balance of the loan after one year with 3.8% interest will be $7,792.50.

If the student has not made any payments, the balance of the loan after one year with 3.8% interest can be calculated using the following formula:

Balance after one year = Principal amount x (1 + (Annual interest rate/100))

Where the Principal amount is $7,500, the Annual interest rate is 3.8%, and the time period is one year.

Plugging these values into the formula, we get:

Balance after one year = $7,500 x (1 + (3.8/100))

= $7,500 x 1.038

= $7,792.50

Therefore, the balance of the loan after one year with 3.8% interest will be $7,792.50.

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Answer:

d=h (3+2)

Step-by-step explanation:

1- you cross multiply to bring d to the other side

h/1=d/3+2

2- this step will make this equation look like this

d=h (3+2)

* we kept 3+2 in brakets because h is multiplying the sum of 3+2

h (3+2) is the same as 5h

but they did not tell us to simplyify so we leave it as it is

3- now we have d as the subject

d=h(3+2)

Answer:

$4.50

Step-by-step explanation:

Please give brainliest!!

Answer:

1.4 people out of 10

Step-by-step explanation:

Just divide it by 10

Answer:

only 4 people

The probability that it will take between 30 and 60 minutes to deal with a reported leak is approximately 0.187.

Mean time, μ = 65 minutes

Standard deviation, σ = 60 minutes

Probability that it will take between 30 and 60 minutes to deal with a reported leak.

The probability of dealing with a leak in a particular range can be found using the standard normal distribution.The standard normal distribution has a mean of 0 and a standard deviation of 1.

The formula for converting a normal distribution to a standard normal distribution is:

z = (x - μ)/σ

where x is the observed value

.We need to find the z-scores for the given values.

z1 = (30 - 65)/60 = -0.5833z2 = (60 - 65)/60 = -0.0833

Now we need to find the area between these two z-scores using a standard normal distribution table or calculator.

P(z1 < Z < z2) = P(-0.5833 < Z < -0.0833) = P(Z < -0.0833) - P(Z < -0.5833) = 0.4664 - 0.2794 = 0.187

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Answer:

Option C is the correct answer

C) 150 m

Step-by-step explanation:

Speed = Distance ÷ Time

Distance = Speed × Time

d = 10 × 15

d = 150 m

Thus, The speed of the object is 150 m.

Answer:

d=150m

Step-by-step explanation:

Speed = Distance /Time 

10= d/155

d= 150m

The interquartile range (IQR) of the data is 70 and the third and the first quartile of the data is (90, 20).

The second and third quartiles, or the middle half of your data collection, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data collection.

The given plot shows the number of days on the market for single-family homes in the city.

The figure shows the first quartile = 20 and the third quartile 90

Therefore the interquartile range of the data is equal to the difference between the third quartile and the first quartile i.

The interquartile range = Q3 - Q1

                                       = 90 - 20

                                       = 70

The third and first quartiles of the data are (90, 20).

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The procedure for revising probabilities based on additional information is referred to as Bayesian updating

The procedure for revising probabilities based on additional information is referred to as Bayesian updating. Bayesian updating is a fundamental concept in Bayesian statistics, which allows for the incorporation of new evidence or data to update and refine prior beliefs or probabilities.

In Bayesian updating, the process begins with an initial prior probability, which represents the initial belief or knowledge about an event or hypothesis before any evidence is observed. As new evidence or data becomes available, it is used to update the prior probability and generate a posterior probability. The posterior probability represents the revised belief or probability after incorporating the new information.

Bayesian updating follows the principles of Bayes' theorem, which mathematically describes the relationship between prior probabilities, likelihoods, and posterior probabilities. It involves combining the prior probability with the likelihood of observing the data given the hypothesis and then normalizing the result to obtain the posterior probability.

The beauty of Bayesian updating is that it allows for a flexible and iterative process of continuously updating beliefs and probabilities as new information emerges. It provides a framework for incorporating both subjective prior beliefs and objective data to make more informed decisions and predictions. Bayesian updating has applications in various fields, including machine learning, decision-making, and scientific research.

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The result of the equation 4 x + 2 + x = x – 19 is - 5.25.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables.

Given equation -

4 x + 2 + x = x – 19

Simplify the equation

5x + 2 = x - 19

5x - x = -19 - 2

4x = -21

x = -21 / 4

x = -5.25

Hence, -5.25 is the answer to the equation 4 x + 2 + x = x - 19.

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Answer:

X^2+6x+8

Step-by-step explanation:

S=a*b

S=(x+4)*(x+2)

S=x^2+6x+8

Answer:

It is the setup.

Step-by-step explanation:

Only 6 is negative. The 11 also needs to be negative.

The measure of the angles are as follows:

∠1 = 105°

∠2 = 75°

when a transversal line cut across parallel lines, angle relationships are formed. Examples are corresponding angles, alternate angles etc.

Therefore,

∠2 ≅ 75 degrees(corresponding angles)

Hence,

∠1  = 180 - ∠2 (angles on a straight line is 180 degrees)

∠1 = 180 - 75

∠1 = 105 degrees

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Answer:

It should be -7/10

Answer:  The answer is -7/10 :)

Step-by-step explanation:

-1/2-1/5=-7/10

Answer:

either 449/25 or 11/25 depends on the -14/5 or

Step-by-step explanation:

\( - \frac{14}{25} or \: \frac{ - 14}{25} \)

if it the first one then the answer should be 449/25 but if ut the second one it should be 11/25 .

u just substitute the -14/5 to x then solve

Given:

\(\cos \angle A=\dfrac{342}{1000}\)

To find:

The measure of angle A to the nearest degree.

Solution:

We have,

\(\cos \angle A=\dfrac{342}{1000}\)

It can be written as

\(\angle A=\cos ^{-1}\dfrac{342}{1000}\)

\(\angle A=70.00123^\circ\)

\(\angle A=70^\circ\)

Therefore, the measure of angle A to the nearest degree is 70 degrees.

Answer:

B) Subtraction Property of Equality

Step-by-step explanation:

In step 8, it says 77 degrees + m<C = 90 degrees. Then in step 9, it is simplified to m<C = 13 degrees... but how did we get there? Well, if you subtract 77 from 90, you get 13. So, it would be the subtraction property of equality since we had to subtract 77 on both sides to isolate m<C. Hope that helps, I'm 100% sure on this one :)

Therefore, the equation of the tangent to the curve at the point (4, 6) by eliminating the parameter is y = 2x - 2.

To find the equation of the tangent to the curve at the point (4, 6) both with and without eliminating the parameter, we need to differentiate the parametric equations and evaluate them at the given point.

Without eliminating the parameter:

Differentiate both equations with respect to the parameter t:

dx/dt = 1/t

dy/dt = 2t

Evaluate dx/dt and dy/dt at t = 4:

dx/dt = 1/4

dy/dt = 8

The slope of the tangent line is given by dy/dx, which can be found by dividing dy/dt by dx/dt:

dy/dx = (dy/dt) / (dx/dt) = (8) / (1/4) = 32

Since the tangent line has a slope of 32 and passes through the point (4, 6), we can use the point-slope form of a line to find the equation of the tangent:

y - y₁ = m(x - x₁)

y - 6 = 32(x - 4)

y - 6 = 32x - 128

y = 32x - 122

Therefore, the equation of the tangent to the curve at the point (4, 6) without eliminating the parameter is y = 32x - 122.

Now, let's find the equation of the tangent by eliminating the parameter:

Solve the first equation, x = 4 + ln(t), for t:

t = e^(x - 4)

Substitute the value of t into the second equation, y = t^2 + 5:

y = (e^(x - 4))^2 + 5

y = e^(2x - 8) + 5

Differentiate the equation y = e^(2x - 8) + 5 with respect to x to find the derivative dy/dx:

dy/dx = 2e^(2x - 8)

Evaluate dy/dx at x = 4:

dy/dx = 2e^(2(4) - 8) = 2e^0 = 2

The slope of the tangent line is 2 at x = 4.

Use the point-slope form of a line with the given point (4, 6) and the slope 2:

y - y₁ = m(x - x₁)

y - 6 = 2(x - 4)

y - 6 = 2x - 8

y = 2x - 2

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The total number of students in the sample who visited city bars every weekend is an example of a count or a discrete variable.

In this scenario, the chancellor of Ferris State University wanted to investigate the portion of students who visited city bars every weekend. To gather data, the advisor took a random sample of 250 students from the university. The variable of interest, in this case, is the number of students in the sample who visited city bars every weekend.

Since the variable represents a count of students, it is a discrete variable. Discrete variables take on specific values and cannot be divided into smaller units. In this context, the total number of students who visited city bars every weekend in the sample can only be a whole number, such as 0, 1, 2, and so on.

Count variables are commonly used in statistical analysis to study events or behaviors that can be counted, such as the number of occurrences of an event, the number of individuals in a category, or in this case, the number of students who visited city bars every weekend. By examining the count variable, researchers can gain insights into the prevalence or frequency of a particular behavior or event within a population.

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x = 2, y = 9, and the side length of the square is 6 units.

A square is a quadrilateral that has four equal lengths, that is, all its sides are equal.

Thus:

y - 6 = 2y - 15

y - 2y = 6 - 15

-y = -9

y = 9

Also:

3x - 3 = y - 6

3x - 3 = 9 - 6

3x - 3 = 3

3x = 3 + 3

3x = 6

x = 2

Therefore, the sides would be:

y - 6 = 9 - 6 = 3 units

In summary, x = 2, y = 9, and the side length of the square is 6 units.

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Answer:

The length of this rectangle is 6 units.

Step-by-step explanation:

Let the width of the rectangle be x.

x • (x+2) = 48

x^2+2x=48

x^2+2x-48=0

x^2 - 6x + 8x - 48

x(x-6) 8(x-6)

(x+8)(x-6)

x=-8,6

Answer:

6+2=8 units..............

The probability that fewer than 60 adults will work from home will be 2%.    

we have to use the Normal probability distribution to find the probability

In a normal distribution with mean μ, SD σ, z-score Z of a measure X  is given by

Z = (X-μ)/ σ

here,

15% adults work from home , So  p= 0.15

                                                       n = 500

∴  μ = np = 500(0.15) = 75

σ  = \(\sqrt{np(1-p)}\)

σ = 7.98

Now we have  selected adults(60) less than n (500)

So using the continuity correction , the probability is P(X< 60 - 0.5)

                                                                            = P( X< 59.5)

which is the p-value of Z when X = 59.5

∴ Z = (X-μ)/ σ

Z  =  (59.5 - 75)/7.98

Z =   - 1.98

so the p-value is 0.02

0.02 = 2% probability that fewer than 60 adults will work from home.

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Answer:

X1= 3 pounds

2= 6 pounds

Step-by-step explanation: