Identify the initial amount a
and the rate of decay r
(a a percent) of the exponential function h(t)=1250(0. 865)t. Evaluate the function when t=3. Round your anwer to the nearet tenth

For each of the equations;

a) Two solutions

b) Two solutions

c) Two solutions

d) Two solutions

In mathematics, the number of solutions that the equation would have has a lot to do with the kind of equation that we are dealing with. If the equation that we are dealing with is a linear equation then it would have only one solution.

In the same way, if what we have is a quadratic equation of a system of linear equations that have two variables then we are going to have two solutions for the equation.

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The measure of central tendency best suited for the given situation are mode (a), median (b) and mean (c) respectively.

a. The measure of central tendency best suited for this situation is the mode, because it would provide the most representative score of the favorite season. The mode is the most commonly occurring value in a set of data, so it would be useful for determining the most popular season among the sample of 50 adults.

b. The measure of central tendency best suited for this situation is the median, because it would provide the most representative score of the length of stay in the hospital after a routine appendectomy. The median is the middle value in a set of data when the values are arranged in numerical order, and it is not affected by very high or very low values (as the mean is). Therefore, it would be the most useful for determining the average length of stay in the hospital for this particular sample.

c. The measure of central tendency best suited for this situation is the mean, because it would provide the most representative score of the standardized reading test scores. The mean is the average of all the values in a data set, so it would be useful for determining the average score of the sample of children from the middle-class, suburban elementary school.

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The amount of silk used in one minute by the factory was 126

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

A factory makes 3.5 silk flowers every second.

60 second = 1 minute

Amount of silk made in one minute = 3.5 silk flowers every second * 60 seconds = 210 silk flowers

Each flower uses 60.3 cm of silk.

Hence, for 210 silk flowers:

Amount of silk used = 210 silk flowers * 60 cm of silk = 12600 cm of silk

100 cm = 1 m

12600 cm =  12600 cm * 1 m per 100 cm = 126 m

The amount of silk used was 126

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The system of equations is:

-2x + 3y = 15

x + y = 10

We can use elimination to solve this system. One way to eliminate x is to multiply the first equation by -2 and add it to the second equation:

(-2) * (-2x + 3y = 15) + (x + y = 10)

4x - 6y + x + y = 15 + 10

5x - 6y = 25

5x = 25 + 6y

x = 5 + (6/5)y

Substituting x back into the second equation, we get:

x + y = 10

5 + (6/5)y + y = 10

Combining like terms:

y = 10 - 5 - (6/5)y

(11/5)y = 15 - 5

(11/5)y = 10

y = 10 * (5/11)

y = 10/11

Finally, substituting x = 5 + (6/5)y back into the equation we found earlier:

x = 5 + (6/5)y

x = 5 + (6/5) * (10/11)

x = 5 + (60/55)

x = 55/11 + 60/55

Combining like terms:

x = (55 + 60) / 55

x = 115/55

The solution to the system of equations is (x, y) = (115/55, 10/11).

So the answer is (d) (9, 11).

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The other two factors of given polynomial are (x+2) and (2x-1).

A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction Using the sum of powers in one or more variables multiplied by coefficients, a polynomial is a type of mathematical expression.

Given that x+3 is a factor of polynomial 2x³ + 9x² + 7x - 6. So that

2x³ + 9x² + 7x - 6

⇒ 2x³ + 6x² + + 3x² + 7x - 6

⇒ 2x²(x+3) + 3x² + 7x - 6

⇒ 2x²(x+3) + 3x² + 9x - 2x - 6

⇒ 2x²(x+3) + 3x(x+3) - 2(x+3)

⇒ (x+3)(2x² + 3x - 2)

⇒ (x+3)(2x² + 4x - x - 2)

⇒ (x+3)[2x(x+2) -1(x+2)]

⇒ (x+3)(x+2)(2x-1)

Hence, Factors of given expression are (x+3)(x+2)(2x-1)

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Answer:

0.625 miles

Step-by-step explanation:

1/2 of a mile is 880 yards and 1/8 of a mile is 220. 880+220=1100. 1100 yards is 0.625 miles.

Answer:

Parallelogram, Rhombus or a regular trapezium.

Step-by-step explanation:

Since all the units add up to 10 units, which is a factor of 180 degrees, all quadrilaterials work in this case as all quadrilaterals must have angles summing up to 180 degrees.

I might be wrong though. :(

The cross-sectional area of a sphere that passes through its center is a circle with a diameter equal to the diameter of the sphere. In this case, the diameter of the sphere is 6.69 meters * 2 = 13.38 meters.

The formula for the area of a circle is: A = π * r^2, where r is the radius.

Therefore, the cross-sectional area of the sphere that passes through its center is: A = π * (13.38/2)^2 = π * (6.69)^2 = 136.57 square meters.

A sphere is a three-dimensional shape that has a uniform, rounded surface that is symmetrical in all directions. When you cut a sphere through its center, you get a cross-sectional area that is a circle.

This is because a sphere can be thought of as a set of circular cross-sections that are concentric with each other and with the center of the sphere.

The cross-sectional area of the sphere that passes through its center is called the central cross-section of the sphere. It has the same diameter as the sphere itself and its area can be calculated using the formula for the area of a circle: A = π * r^2, where r is the radius of the circle.

In this case, the sphere has a radius of 6.69 meters, which means that its diameter is 6.69 * 2 = 13.38 meters.

The radius of the central cross-section of the sphere is half of the diameter, which is 6.69 meters. Therefore, the area of the central cross-section of the sphere is: A = π * (6.69)^2 = 136.57 square meters.

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Answer: Domain Is always the x-input, while range will be the y-output.

Step-by-step explanation:

domain- -10,-1,2,6,8

Range- -5,1,2,6

Answer:

You want to multiply the 6 to the numbers inside the parythesis:

6 * x = 6x

6 * 5 = 30

6x + 30

Step-by-step explanation:

Hope it helps! =D

Answer:

6x + 30

Step-by-step explanation:

1. 6(x + 5)

2. 6x+30

Accordingly, 1 ml (milliliter) is just 1/1,000 of a liter. Consequently, 1 ml is less than 1 l.

Small quantities of liquid are measured in milliliters. Liters can be used to measure bigger amounts of liquid. 1 ml is equal to 0.001 liter, or 1000 milliliters. The symbol for a milliliter is either ml or mL.

The metric prefix "m" stands for "milli," which denotes "1/1,000 of" in English. Accordingly, 1 ml (milliliter) is just 1/1,000 of a liter. Consequently, 1 ml is less than 1 l.

The smallest metric unit, the milliliter, measures the tiniest amount of liquid and is a thousandth of a litre. So, 1 liter is equal to 1000 milliliters.

Therefore, the correct answer is option b. 4 liters 300 milliliters < 4,000 milliliters.

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The patient will receive 4875mg

Some drugs, particularly those for children, may be administered based on the individual’s body weight (kg) or body surface area (m2). Simply multiply the dose by the weight to get the needed dose, which can then be used in other formulas. A single dosage of medication containing 2mg/kg is necessary.

The force of gravity pressing down on an item is measured by its weight. It is determined by the mass of the item and the acceleration due to gravity, which is 9.8 m/s2 on Earth. Weight is calculated using the formula F = m 9.8 m/s2, where F is the object’s weight in Newtons (N) and m is the object’s mass in kilograms. Assume the active substance’s optimal dose is 2 mg/kg of body weight.

Given:

the weight of the patient is: 65kg

he is asked to receive 75 mg/kg of her medicine

therefore, she will have to consume 65*75mg

Finally, the patient will get 4875 mg

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There are the newspaper has 750 readers.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.

If the number of letters to the editor is 60, and it represents 8% of all of the newspaper's readers, we can find the total number of readers by dividing the number of letters by the percentage as a decimal:

60 / 0.08 = 750

So the newspaper has 750 readers.

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The total number of readers the newspaper have is 750.

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

Given, The local newspaper has letters to the editor from 60 people and it is 8% of the total readers.

let, The total number of readers be 'x'.

Therefore, 60 is 8% of 'x' which can be numerically expressed as,

(8/100)×x = 60.

0.08x = 60.

x = 60/0.08.

x = 750.

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Given a quadratic function y = 36 - x² , the intervals over which the function is increasing is: (-∞ , 0) and the intervals over which the function is decreasing is:  (0, ∞).

The standard form of a quadratic function is given by:

f(x) = ax² + bx + c

If a > 0, the graph of the function opens upward and the extreme point is the minimum one.

If a < 0, the graph of the function opens downward and the extreme point is the maximum one.

In this case, the function is: y = 36 - x²

Since the coefficient of the quadratic term is negative, or a < 0, then the graph opens downward and has a maximum point.

y = 36 - x²  is already in the form of perfect square, hence, we can immediately compute:

x-intercepts : (-6,0) and (6,0)

y-(intercept = maximum point = (0, 36)

Before the maximum point, the function is increasing, while after the maximum point, the function is decreasing.

Hence,

increasing interval = (-∞ , 0)

decreasing interval = (0, ∞)

Your question is incomplete, most likely, it was:

Find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.

y = 36 - x²

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The sales price is $36.

We have been told that the discount on the pair of rollerblades is 25%. It has also been told that the discounted price is $12.0. Now, first, we need to find the original price of the rollerblades. Let the original price of the rollerblades be = $x.

Now - x/100 * 25 = $12

- x/100 = 12/25

- 25x = 1200

- x = $48

Now, in order to find the sale price, we need to -

= Original price - Discounted price

= $48 - $12

= $36

Hence, the price of the rollerblades after putting in a 25% discount is $36.

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In the study conducted by John Darley and Bibb Latané, the number of people present in the room with the participant served as an independent variable, as it was manipulated by the researchers to observe its effects on helping behavior.

Specifically, the researchers examined how the presence of other people in the room would affect whether or not the participant would choose to help in a given situation. By changing the number of people present in the room, the researchers were able to measure the effects of diffusion of responsibility on helping behavior.

Diffusion of responsibility is a phenomenon in which individuals are less likely to help a victim when they are in the presence of other people, as they assume that someone else will take responsibility. Therefore, the number of people present in the room was an important variable in the study, as it allowed the researchers to measure how the presence of others affected helping behavior.

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Rabia is currently classified as unemployed, option .D since she has no job and has declined a job offer.

She falls into the category of frictionally unemployed, which means she is unemployed due to the time it takes to find a job that meets her qualifications and salary needs.

This is different from someone who is cyclically unemployed, which means they are out of work due to economic conditions, or someone who is structurally unemployed, which means they are out of work due to changes in technology or other factors that eliminated their job.

Rabia is still employed in the sense that she is actively seeking employment, but she is not employed in the sense that she has no job.

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Answer:

4.21

Step-by-step explanation:

The hundredths place is the second number after the decimal. when rounding, you want to look at the number after. In this case the number after 1 is 0 which is lower than 5. Since it's lower than 5 we will keep the number the same.

Say the number after 1 was 7. Then we would round up and make the 1 into a 2. Any number above 5 you round up and add one to the number. If the number after is below 5, the number doesn't change.

Hope that made sense! :)

Answer:

4.21

Step-by-step explanation:

In this case, the hundredths place is 1 (4.2101, bold number is the hundredths place.) To round it you need to look at the number to the right of it which is 0, and if the number to the right of it is between 0-4 you keep the hundredths place the same and remove any numbers to the right of the hundredths place. Leaving you with 4.21. I hope this makes sense!

Answer:

If you have 3 bags of fertilizer that cover 150 square feet and 2 bags of fertilizer that cover 175 square feet, the total number of square feet that can be covered is:

3 bags x 150 square feet/bag = 450 square feet

2 bags x 175 square feet/bag = 350 square feet

450 square feet + 350 square feet = 800 square feet

So with these total bags of fertilizer, it can cover 800 square feet.

Step-by-step explanation:

Answer:

[tex](-1, -2)[/tex]

Step-by-step explanation:

In this problem, we are asked to solve a system of equations given two equations each containing two variables: x and y. We can solve it using the substitution method.

First, we need to solve for a variable in terms of the other using one of the equations. I will solve for x in the first equation.

[tex]4x-7y=10[/tex]

↓ add [tex]7y[/tex] to both sides

[tex]4x=7y+10[/tex]

↓ divide both sides by 4

[tex]x=\dfrac{7y+10}{4}[/tex]

Now that we have solved for x in terms of y, we can substitute the solved x-value into the bottom equation.

[tex]3x + 2y = -7[/tex]

↓ substitute in solved x-value

[tex]3\left(\dfrac{7y+10}{4}\right) + 2y = -7[/tex]

↓ distribute 3

[tex]\dfrac{21y+30}{4}\right) + 2y\left(\dfrac{4}{4}\right) = -7\left(\dfrac{4}{4}\right)[/tex]

↓ rewrite all terms as fractions over 4

[tex]\dfrac{21y+30 + 8y}{4}\right)= -\dfrac{28}{4}[/tex]

↓ cancel denominators

[tex]29y+30= -28[/tex]

↓ isolate y's

[tex]29y = -28 - 30[/tex]

↓ simplify

[tex]29y= -58[/tex]

↓ divide both sides by 29

[tex]y = -2[/tex]

Now that we have solved exactly for y, we can solve for x using the substitution value we solved for earlier.

[tex]x=\dfrac{7y+10}{4}[/tex]

↓ substitute in y-value

[tex]x=\dfrac{7(-2)+10}{4}[/tex]

↓ simplify numerator

[tex]x=\dfrac{-14+10}{4}[/tex]

[tex]x=\dfrac{-4}{4}[/tex]

[tex]x = -1[/tex]

Finally, we can put the solved x and y values into a Cartesian coordinate in the form (x, y).

[tex](-1, -2)[/tex]

The statement is false because the limit of the denominator is equal to zero.

In this case, the limit of the denominator (lim x→1 x2 3x − 4) is equal to zero, so this statement is false.

The limit of the quotient of two functions is equal to the quotient of their limits only when the limit of the denominator is not equal to zero.

In this case, the limit of the denominator (lim x→1 x2 3x − 4) is equal to zero, so this statement is false.

The statement is false because the limit of the denominator is equal to zero.

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Answer:

the answer is 77

Step-by-step explanation:

suppose the answer is z and the width is x
the perimeter would be 4x+8 = 36
4x = 28
x=7
7+4=11
7*11=77

The set of solutions are [-6,-3,3,8,10] for the inequality

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequalities are 4(x + 3) ≤ 0 or x+1>3

we know that, In this system of inequalities, for a value to be the solution of the system, it is enough that it satisfies at least one of the two inequalities.

x=-6

Substitute the value of x=-6 in the inequality 1

4(-6+3)≤ 0

-12≤ 0

The value of x=-6 is a solution of the compound inequality-----> It is not necessary to check the second inequality, because the first one satisfies

Substitute the value of x=-3 in the inequality 1

0≤ 0

The value of x=-3 is a solution of the compound inequality

Substitute the value of x=3 in the inequality 1

The value of x=3 is a solution of the compound inequality

The value of x=8 is a solution of the compound inequality

The value of x=10 is a solution of the compound inequality

Hence, the set of solutions are [-6,-3,3,8,10] for the inequality

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Answer:

293.1596091

Step-by-step explanation:

Average speed= speed/time

average speed= 1500/4.67

The required number of miles Clara jogs each day during training is 4..5 miles.

You can anticipate that it will take between 1 and 2.5 minutes to travel one mile because the majority of roads have speed limits between 25 and 60 mph. Do not allow algebra cause you to lose focus on the road! Also keep in mind how crucial it is to properly insure your vehicle.

Let miles does Clara jog each day during training be x.

During a 5-day training period, she jogs and rides a total of 50 miles.

5x + 5(5.5) = 50

5x + 27.5 = 50

5x = 50 - 27.5

5x = 22.5

x = 4.5 miles.

Thus, Clara jogs 4.5 miles each day.

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The answer is 3.0 x 10^13

Answer: [tex]3x10^1^3[/tex]

Explanation: When writing a number in scientific notation, the decimal point should be placed or moved until the coefficient is higher than 1 and less than 10.

Answer: [tex]\{y|y=-9, -3, 0, 5, 7\}[/tex]

Step-by-step explanation:

The range is the set of [tex]y[/tex]-values.

The limit value is equal to 2 .

Given,

2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² +  2

According to sandwich theorem,

g(x)≤ f(x) ≤ h(x)

[tex]\lim_{x \to \ a} g(x) = \lim_{x \to \ a} h(x) = L[/tex]

Then,

L= [tex]\lim_{x \to \ a} f(x) = L[/tex]

Here we have,

2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² +  2

And so if we take the limit as x→1; then

[tex]\lim_{x \to \ 1} 2x = 2\\\\ \lim_{x \to \ 1} x^{4} - x^{2} + 2 = 2\\[/tex]

Thus we can apply the sandwich theorem,

[tex]\lim_{x \to \ 1} g(x) = 2[/tex]

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Correct expression:

2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² +  2