I need help!!! I don't get it.

The law of exponential change states that when a quantity grows or decays at a rate proportional to its size, then the quantity changes exponentially over time. In other words, it follows an exponential function as opposed to a linear function.

The law of exponential change describes the phenomenon of a quantity changing exponentially over time. This means that the rate of change is proportional to the quantity itself. For example, if a quantity increases by 10% each minute, then the quantity will double every 7.2 minutes. This is because each time the quantity increases by 10%, it is multiplying by 1.1. This process is ongoing and the rate of growth or decay will continue to increase exponentially.

The law of exponential change is used in many areas of science and mathematics, such as population growth and radioactive decay. It is also an important concept in economics, as it can be used to measure the growth of money over time.

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We can write the linear equation:

y = x + 50

And evaluating it on the given values of x, we will get the table:

x        y

10     60

20    70

30    80

40    90

50    100

We know that there are x sparrows in a tree, and there are 50 sparrows on the ground beneath the tree.

y represents the total number of sparrows, then y is equal to the number of sparrows on the tree (x) plus the ones beneath (50) then we will get:

y = x + 50

B) Now we want to make a table. To make that table, we need to evaluate the linear equation in different values of x.

if x = 10

y = 10 + 50 = 60

if x = 20

y = 20 + 50 = 70

if x = 30

y = 30 + 50 = 80

if x = 40

y = 40 + 50 = 90

if x = 50

y = 50 + 50 = 100

Then the table will be:

x        y

10     60

20    70

30    80

40    90

50    100

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Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks. The probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both) is 66%.

60% invest in stocks

50% invest in bonds

44% invest in both bonds and stocks

Percent (only stock) = 60% -44%

Percent (only stock) = 16%

Percent (only bond) = 50% - 44%

Percent (only bond) = 6%

Percent (both) = 44%

Total = 16% + 6% + 44%

Total = 66%

Therefore the probability is 66%.

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Area of a trapezoid is found with the formula, A=(a+b)/2 x h. so the answer is 9(w-3) / (w + 7) (w + 2).

What is meant by trapezoid ?

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The scale factor of a similarity transformation is the ratio of the lengths of the corresponding sides of the two similar figures.

The scale factor is a ratio between two corresponding lengths, areas, or volumes of two similar figures. It is used to compare the size of one figure to another, as well as to enlarge or reduce the size of a figure. The scale factor is expressed as a ratio, such as 1:2, where the first number is the original size and the second is the new size.

It is usually represented as a decimal or fraction, and can be calculated by dividing the length of one of the sides of one figure by the length of the corresponding side of the other figure. For example, if we have two triangles with corresponding sides that measure 3 units and 6 units, then the scale factor of the dilation is 0.5 (3/6). This means that the second triangle is half the size of the first.

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Answer:

-300

just do inverse operation, and multiply both sides of the equation by -15 to cancel out the -15 from the denominator and you get V=20(-15)

solve for 20(-15) and you get -300

The total money earned after working the given number of hours is $18.60.

When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.

Given that to pick green peppers:

15 minutes = $3.20

45 minutes = x

Using cross multiplication solve the above equation:

[tex]x = \frac{(3.20)(45)}{15} \\\\x = 9.60\\[/tex]

For picking carrots:

20 minutes = $3. 00

1 hour = 60 minutes = x

Using cross multiplication solve the above equation:

[tex]x = \frac{(3)(60)}{20}\\ \\x=9[/tex]

The total amount made after all the work is:

A = 9.60 + 9

A = 18.60.

Hence, the total amount of money she earned after all the work is $18.60.

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When a figure is dilated using a scale factor of 1, the resulting figure is the same as the original figure.

This is because a scale factor of 1 means that the dimensions of the original figure are not changed in any way.

Mathematically, this is represented by the equation:

Original Length x Scale Factor = Resulting Length

For a scale factor of 1, the equation simplifies to:

Original Length x 1 = Resulting Length

Therefore, the resulting length is equal to the original length.

For example, if a line had a length of 5 units before dilating, the resulting length would be 5 units after dilating.

5 units x 1 = 5 units

This is because the scale factor of 1 does not change the length of the line in any way.

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The value of y in the right triangle is found to be 3√3 units.

Given data:

So, apply trigonometric ratios:

cos 30 = y / 6

y = cos 30 * 6

y = √3 / 2 * 6

y = 3√3

Thus, the value of y in the triangle is found to be 3√3 units.

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Answer:

BE = 24

Step-by-step explanation:

These triangles are similar because of AA (Angle, Angle)

The given gives us a pair of parallel sides, allowing us to see that angles C and B are congruent due to being alternate interior angles.

Furthermore, we see that <AEB = <CEB due to vertical <'s being =

Next, we must set up a proportion;

If we create a proportion between the triangles, we must divide corresponding sides;

52/26 = 5x -7 / 2x+2 because we divided both triangles by using the same corresponding sides divided by the same corresponding side.

Simplify 52/26 to 2 and we get that 2 = 5x-7 / 2x+2

Multiply both sides by 2x+2 to get 4x+4 = 5x-7

Subtract 4x from both sides and add 7 from the right side to isolate x and get x=11

Finally, substitute the value of 11 for x into BE 2(11) + 2 and get 22 + 2 =24

Part a: Future amount due on a compound interest loan is $12271.78.

Part b: The amount due on the loan would be $12033.64, if the compounding period is increased to monthly.

The formula for compounding is:

A = P(1 + r/100n)∧nt

P = $12,000

r = 0.07

Part a: compounded semiannually.

t = 4 years.

n = 2

A = 12000(1 + 0.07/100*2)∧2*4

A = 12000*1.00280

A = 12271.78

Thus, future amount due on a compound interest loan is $12271.78.

Part  b:

t = 4 years.

n = 12

A = 12000(1 + 0.07/100*12)∧12*4

A = 12000*1.0028038

A = 12033.64

Thus, if the compounding period is increased to monthly, the amount due on the loan would be $12033.64.

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Answer: $15,802

$15,865

Step-by-step explanation:

The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.

With a protractor, you can determine how large an angle is. Alternatively, the congruent angles could be indicated on the figure by an arc. Supplementary angles are two angles whose combined measurements are 180°, such as two right angles since 90° + 90° Equals 180°. the measurement of an angle wherein 1 degree equals 1/360 of a circle.

An angle (created by perpendicular lines) that is exactly 90 degrees is called a right angle. Less than 90 degrees is considered an acute angle. Revolutions, degrees, and radians are the three types of angles that can be measured. Degrees serve as a more widely used measurement unit. In order for a right angle to be 90 degrees, a circle must be divided into 360 equal degrees.

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When two lines are parallel, they do not intersect, so there will be no angle formed between them. Therefore, the number of 90° angles formed by the intersection of EF and the two parallel lines AB and CD is zero.

The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4).

What is an orthocenter of a triangle?

In geometry, an orthocenter is a point in a triangle that is the intersection of the three lines containing the altitudes of the triangle. An altitude of a triangle is a line segment from a vertex of the triangle to the line containing the opposite side, and is perpendicular to that side. The orthocenter of a triangle is the point where all the altitudes of a triangle meet.

To find the orthocenter of a triangle, the first step is to find the equation of the altitudes from each vertex. Then, we can find the point of intersection of these three lines.

Given the triangle ABC with vertices A (2,6), B (8,6), and C(6,2),

The equation of altitude from vertex A is (x-2) = -2(y-6)

The equation of altitude from vertex B is (x-8) = -2(y-6)

The equation of altitude from vertex C is (x-6) = 2(y-2)

By solving the system of these three equations, we can find the coordinates of the orthocenter.

Hence, The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4)

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When t = 3, the exponential function has a value of 809.0.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.

Here,

Given the exponential function h (t) = 1250(0.865)^t

When t = 3

h(3) = 1250(0.865)^3

h(3) = 1250 (0.6472)

h(3) = 809.0

The exponential function when the value of t is 3 is 809.0.

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Answer:

A = 72 units²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

note that the middle section of the lower base = upper base = 6

here h = 8 , b₁ = 3 + 6 + 3 = 12 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 8 × (12 + 6) = 4 × 18 = 72 units²

a. 5 + 7n is the algebraic expression for 7 more than the product of 5 and n

The expression needed to indicate the value of 5 added to the product of 7 and n is "5 greater than the product of 7 and n."

The equation 7n represents the product of 7 and n, and the expression 5 + 7n is obtained by adding 5 to 7n.

This is the proper algebraic expression for the phrase that was given.

It follows that 5 + 7n = 5 + 21 = 26, which is 5 more than the sum of the products of 7 and 3. As an illustration, if we substitute a value of 3 for n, the expression 7n would equal 21.

Because option b is a product of 5 and (7+n), which is not equivalent to 5 greater than the product of 7 and n, the other choices are incorrect.

The product of option c and (5+n) is 7, but it also does not equal 5 greater than the product of 7 and n.

A sum of 5, 7, and n makes up option d, which also does not equal 5 greater than the result of the product of 7 and n.

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In the given word problem the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Gunnar's car travel using per gallon of gas = 22.4 miles.

According to the given question,

Gunnar's car can hold 17.82 gallons of gas. Then number of miles does Gunnar's car can travel is ,

=> 22.4 × Car's total tank has hold

=> 22.4 × 17.82

=> 399.17 miles

Hence the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

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In Q1, The equation k = y² + a is correct,

To make y the subject of the formula, √k = y + a is incorrect, it should be √k = y + √a

√k - √a = y

In Q2, t = v/4 + 1 is correct

t - 1 + v/4 is incorrect, it should be t - 1 = v/4

t - 1/4 = v

so the correct answer is t-1/4=v

The inequality to represent the number of matinee tickets, x, and evening tickets, y, Aiden can buy is,

⇒ 5x + 10y ≤ 50

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Aidan is going to buy movie tickets for his friends. matinee tickets are $5 each and evening tickets are $10 each. Aidan can spend at most $50 dollars.

Now, Let the number of matinee tickets Aiden can buy = x

And, The number of evening tickets Aiden can buy = y

So, We can formulate;

The correct inequality is,

⇒ 5x + 10y ≤ 50

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Profit per kilogram = R1.90

The profit per kilogram is the difference between the selling price and the cost price per kilogram.

a) To find the profit per kilogram, we can use the following formula:

Profit per kilogram = Selling price per kilogram - Cost price per kilogram

Therefore,

Profit per kilogram = R2.80 - R0.90

Profit per kilogram = R1.90

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Answer:

y = 5x - 14

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Given that the line passes through the point (1, -9) and has a slope of 5, we can use the point-slope form of a line, which is y - y1 = m(x - x1)

Substituting the point and slope we have:

y - (-9) = 5(x - 1)

y + 9 = 5x - 5

Now we can solve for y by adding 9 to both sides of the equation:

y = 5x - 14

So the equation in slope-intercept form for the line that passes through the point (1, -9) and has a slope of 5 is:

y = 5x - 14

Answer:

y = 5x - 14

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Given that the line passes through the point (1, -9) and has a slope of 5, we can use point-slope form to write the equation of the line. Point-slope form is written as: y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

We know that the line passes through the point (1, -9) and has a slope of 5, so we can substitute these values into the point-slope form:

y - (-9) = 5(x - 1)

Simplifying, we get:

y + 9 = 5x - 5

Now we can add 9 to both sides to get:

y = 5x - 14

So the equation of the line in slope-intercept form is y = 5x - 14

We can confirm that the point (1,-9) belongs to the line by substitute the values x =1 and y = -9 into the equation y = 5x - 14, if the equation holds true then the point belongs to the line.

The desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.

The discipline of finance is the study of money, money systems, and capital assets. It is associated with economics, which is the study of the production, distribution, and consumption of money, assets, products, and services, but is not the same thing

Let x be the cost of the desktop computer before finance charges.

We know that the laptop cost 150 more than the desktop, so the cost of the laptop is x+150

We also know that the total finance charge for one year is $303 and the interest rate of the desktop is 7% and the interest rate of the laptop is 9.5%

So we can set up the following equations using the information provided:

(x*0.07) + ((x+150)*0.095) = 303

Simplifying and solving for x:

0.07x + 0.095x + 14.25 = 303

0.165x = 288.75

x = $1750

Therefore, the desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.

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On solving the provided question, we can say that - Since the two triangle are similar and each sides are 3 times the others, so x= 3 X 4 = 12 cm

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Since the two triangle are similar

\and each sides are 3 times the other,

so x= 3 X 4 = 12 cm

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Third triangle is congruent to triangle PQR.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

For triangles, there are five primary congruency rules:

Side-Side-Side is an SSS criterion.

The side-angle-side SAS criterion.

Angle, Side, Angle is an ASA criterion.

Angle-Angle-Side is an AAS criterion.

Right Angle Hypotenuse Side (RHS) Criteria

As Height of the triangle PQ is similar to triangle third

Angle 90° ≈ Angle 90° of third triangle

Angle 67° ≈ Angle 67° of third degree

So, By ASA, both the triangles are congruent.

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Answer:

x = 6 / sqrt(2)

Step-by-step explanation:

We are given the diagonal of a square

The side length is x

Using the Pythagorean theorem

x^2 + x^2 = h^2  where h is the length of the hypotenuse which is 6

x^2+x^2 = 6^2

2x^2 = 36

x^2 = 18

Taking the square root of each side

sqrt(x^2) = sqrt(18)

x = 3 sqrt(2)

This can be rewritten as

x = 3 sqrt(2) * sqrt(2)

    ------------------------

             sqrt(2)

x =    3*2  

        -------

          sqrt(2)

x = 6 / sqrt(2)

Answer:

2/3

Step-by-step explanation:

First divide the numerator by the denominator.

You then get the percentage and then you can judge from there.

Answer:

2/3

Step-by-step explanation:

first we have to equalise the denominators

we know 3 × 4 = 12 so we multiply both the denominator and the nominator by 4 which would give us 8/12

so the answer would be 2/3 since 8/12>7/12

Therefore , the solution to the given problem of probability comes out to be P =0.6.

Probability theory, a subfield of mathematics, calculates the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where 1 denotes certainty and around 0 denotes how probable the event is to occur. A likelihood is a numerical representation of the likelihood that a particular event will occur. Probabilities may alternatively be stated as percentages with a range of 0% to 100% or as a number between 0 and 1. the percentage of events over a wide range of comparably likely outcomes that happen in comparison to all other conceivable outcomes.

Here,

Given :

Twelve 16 GB and 18 32 GB pen drives are packaged together in a box.

To find the probability of 16gb pen drive is defective:

Thus,

Total pendrive = 30

Event = 16gb pen drive or defective:

The probability of it is 16gb pendrive = 12/30 = 0.4

The probability of it is defective pendrive = 6/30 = 0.2

thus,

total probability (16gb pen drive or defective) = 0.4 +0.2 =0.6

Therefore , the solution to the given problem of probability comes out to be P =0.6.

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