determine whether each function is an example of growth or decay Mark the appropriate box and please show how you know

Answer:

y=2x-2

Step-by-step explanation:

When looking at the line, you can see the y-intercept is at the point (0,2) so it meets the y-axis at that point.  Then, when you look at the pattern between the points on the line, you can see the line has a slope of 2, making the answer y=2x-2

Answer:

4

Step-by-step explanation:

The first value (10) is the x value. 10 is positive so the point is on your right. The second value (-1) goes down below the x axis. because it is minus. right and down means you are in the 4th quadrant.

Answer:

IV

Step-by-step explanation:

In the picture below, it shows the model of all quadrants. Since the point (10, -1) has a positive as the x, you can eliminate quadrant II and III. The ones left are I and IV. Since y is a negative, you eliminate I because it is only positives while IV has a negative as it's y.

Hope this helps.

a z-test for the proportional difference is the proper hypothesis test.

A hypothesis test can be used to find whether the deviation in proportions impacts the medication's effectivity. We may compare the secondary hypothesis—that the proportions are different—to the null hypothesis.

which states that the dimension of patients who show cut down blood pressure is the same for the two doses of the drug (50 mg and 100 mg).

Popular test statistics like the z-test can be applied to this hypothesis test and other statistical analyses.

\(z = (p1 - p2) / SE\)

where p1 and p2, for the 50 mg and 100 mg doses, respectively, are the sample proportions of patients who show fallen blood pressure, and SE is the standard error of the difference between the proportions.

the samples are assumed to be independent or dependent, impacts the SE formula. The samples in this instance are presumed to be independent because they came from various patients. Consequently, the equation for SE is:

\(SE = \sqrt(p1 \times (1 - p1)/n1 + p2 *\times(1 - p2)/n2)\)

here, the sample sizes for two doses is n1 and n2.

We can compute the z-test statistic based on the sample sizes and proportions and compare the result to a critical value or p-value to decide whether to accept or reject the null hypothesis.

Therefore, a z-test for the proportional difference is the proper hypothesis test.

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The rate at which the spherical balloon's radius is increasing is

3/16π ft/min when the volume is increasing at the rate of 3 ft³/min.

Given, a spherical balloon is inflated so that its volume is increasing at the rate of 3 cubic feet per minute.

we have to find that how fast is the radius of the balloon increasing when the radius is 2 feet.

as, we know the volume of the balloon be,

V = 4/3πr³

now we have to find the rate of change of radius,

On differentiating both the sides with respect to time, we get

V' = 4/3π(3r²)dr/dt

V' = 4πr²dr/dt

as, the rate of change of volume of the balloon be, 3 ft³/min

V' = 3

3 = 4πr²dr/dt

dr/dt = 3/4πr²

Now, on putting r = 2, we get

dr/dt = 3/4π(2)²

dr/dt = 3/16π

so, the radius of the balloon increase at the rate of 3/16π.

Hence, the radius of the balloon increase at the rate of 3/16π.

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162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

Answer:

There are 4 students okay

After the transactions amount of money left in account is -$29. Therefore, option B is the correct answer.

A savings account is a bank account at a retail bank. Common features include a limited number of withdrawals, a lack of cheque and linked debit card facilities, limited transfer options and the inability to be overdrawn.

Given that, On this day, you have $10 in your account and go out and use your debit card to buy lunch for $12, a movie ticket for $12 and dinner for $15.

Here, amount drawn using debit card is

12+12+15=$39

Money left in the account = 10-39

= -$29

After the transactions amount of money left in account is -$29. Therefore, option B is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

When signing up for a new checking account, you answer "Yes" to receive overdraft protection. On this day, you have $10 in your account and go out and use your debit card to buy lunch for $12, a movie ticket for $12 and dinner for $15. What is likely to be the outcome resulting from these transactions?

Answer:

Step-by-step explanation:

R=21

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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Answer:

Let \(u=3x^2-3x\)

Solution: \(\frac{1}{6} \sqrt{3x^2-3x}+C\)

Step-by-step explanation:

See attached for step-by-step

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

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Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

Answer: B. The area of the square pizza is larger.

Step by step solution:

With the information given, we can calculate the area of the circular pizza and the square pizza, to determine which statement is true.

The area of a circle can be calculated using the formula:

We know the circular pizza has a 10-inch diameter, replace D on the above formula:

The area of a square can be calculated using the formula:

We know the sides of the square pizza are 9-inches, replace on the above formula:

The statement about the linear equation 3a + 1/3(6a −9) = 1/2(10a − 6) that is true is: "The equation has an infinite number of solutions." (Option B)

A linear equation is defined as an equation with a maximum of one degree. A nonlinear equation is one with a degree greater than or equal to two.

On the graph, a linear equation looks like a straight line. On the graph, a nonlinear equation creates a curve.

To justify the above answer, we state the linear equation above:


3a + 1/3(6a −9) = 1/2(10a − 6) ; Simplified by opening the brackets, we have

3a + 2a − 3 = 5a − 3; collecting like terms on the left side, we have

5a -3 = 5a -3

Because 5a -3 = 5a -3, the expression holds true regardless of what integer or value a represents. Hence, it has an infinite number of solutions.

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Answer:

$63.75

Step-by-step explanation: I think

Answer:

46.75

Step-by-step explanation:

first, separate the floor into 3 different rectangles to calculate the area and then add them together.

area of rec=L*B

rec 1: 5.5*4=22

rec 2: (6.5-3)*(8.5-3-4)=5.25

rec 3:3*6.5=19.5

Then:

22+5.25+19.5=46.75

Answer:

3.43×10^5

343000

Step-by-step explanation:

i hope this will help you :)

The Standard form is 34100.

The Standard form is

\(3.43\times10^5\\=3.43\times10\times10\times10\times10\times10\\=3.41\times100000\\=341000\)

Hence, the Standard form is 34100.

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Answer:

(4 (x^4 - 20 x^2 - 12))/(3 x^2 (9 x^2 - 32 x - 144))

Step-by-step explanation:

Simplify the following:

(x^2 + x - x - 20 - 12/x^2)/((15 x^2)/4 + 3 x^2 - 24 x - 60 - 48)

Hint: | Put the fractions in x^2 + x - x - 20 - 12/x^2 over a common denominator.

Put each term in x^2 + x - x - 20 - 12/x^2 over the common denominator x^2: x^2 + x - x - 20 - 12/x^2 = x^4/x^2 + x^3/x^2 - x^3/x^2 - (20 x^2)/x^2 - 12/x^2:

(x^4/x^2 + x^3/x^2 - x^3/x^2 - (20 x^2)/x^2 - 12/x^2)/((45 x^2)/12 + 3 x^2 - 24 x - 60 - 48)

Hint: | Combine x^4/x^2 + x^3/x^2 - x^3/x^2 - (20 x^2)/x^2 - 12/x^2 into a single fraction.

x^4/x^2 + x^3/x^2 - x^3/x^2 - (20 x^2)/x^2 - 12/x^2 = (x^4 + x^3 - x^3 - 20 x^2 - 12)/x^2:

((x^4 + x^3 - x^3 - 20 x^2 - 12)/x^2)/((45 x^2)/12 + 3 x^2 - 24 x - 60 - 48)

Hint: | Group like terms in x^4 + x^3 - x^3 - 20 x^2 - 12.

Grouping like terms, x^4 + x^3 - x^3 - 20 x^2 - 12 = x^4 - 20 x^2 - 12 + (x^3 - x^3):

(x^4 - 20 x^2 - 12 + (x^3 - x^3))/(x^2 ((45 x^2)/12 + 3 x^2 - 24 x - 60 - 48))

Hint: | Look for the difference of two identical terms.

x^3 - x^3 = 0:

((x^4 - 20 x^2 - 12)/x^2)/((45 x^2)/12 + 3 x^2 - 24 x - 60 - 48)

Hint: | In (45 x^2)/12, the numbers 45 in the numerator and 12 in the denominator have gcd greater than one.

The gcd of 45 and 12 is 3, so (45 x^2)/12 = ((3×15) x^2)/(3×4) = 3/3×(15 x^2)/4 = (15 x^2)/4:

(x^4 - 20 x^2 - 12)/(x^2 (15 x^2/4 + 3 x^2 - 24 x - 60 - 48))

Hint: | Put the fractions in (15 x^2)/4 + 3 x^2 - 24 x - 60 - 48 over a common denominator.

Put each term in (15 x^2)/4 + 3 x^2 - 24 x - 60 - 48 over the common denominator 4: (15 x^2)/4 + 3 x^2 - 24 x - 60 - 48 = (15 x^2)/4 + (12 x^2)/4 - (96 x)/4 - 240/4 - 192/4:

(x^4 - 20 x^2 - 12)/(x^2 (15 x^2)/4 + (12 x^2)/4 - (96 x)/4 - 240/4 - 192/4)

Hint: | Combine (15 x^2)/4 + (12 x^2)/4 - (96 x)/4 - 240/4 - 192/4 into a single fraction.

(15 x^2)/4 + (12 x^2)/4 - (96 x)/4 - 240/4 - 192/4 = (15 x^2 + 12 x^2 - 96 x - 240 - 192)/4:

(x^4 - 20 x^2 - 12)/(x^2 (15 x^2 + 12 x^2 - 96 x - 240 - 192)/4)

Hint: | Group like terms in 15 x^2 + 12 x^2 - 96 x - 240 - 192.

Grouping like terms, 15 x^2 + 12 x^2 - 96 x - 240 - 192 = (12 x^2 + 15 x^2) - 96 x + (-192 - 240):

(x^4 - 20 x^2 - 12)/(x^2 ((12 x^2 + 15 x^2) - 96 x + (-192 - 240))/4)

Hint: | Add like terms in 12 x^2 + 15 x^2.

12 x^2 + 15 x^2 = 27 x^2:

(x^4 - 20 x^2 - 12)/(x^2 (27 x^2 - 96 x + (-192 - 240))/4)

Hint: | Evaluate -192 - 240.

-192 - 240 = -432:

(x^4 - 20 x^2 - 12)/(x^2 (27 x^2 - 96 x + -432)/4)

Hint: | Factor out the greatest common divisor of the coefficients of 27 x^2 - 96 x - 432.

Factor 3 out of 27 x^2 - 96 x - 432:

(x^4 - 20 x^2 - 12)/(x^2 (3 (9 x^2 - 32 x - 144))/4)

Hint: | Write ((x^4 - 20 x^2 - 12)/x^2)/((3 (9 x^2 - 32 x - 144))/4) as a single fraction.

Multiply the numerator by the reciprocal of the denominator, ((x^4 - 20 x^2 - 12)/x^2)/((3 (9 x^2 - 32 x - 144))/4) = (x^4 - 20 x^2 - 12)/x^2×4/(3 (9 x^2 - 32 x - 144)):

Answer: (4 (x^4 - 20 x^2 - 12))/(3 x^2 (9 x^2 - 32 x - 144))

Answer:

1. 81

2. 4 (square root of) 25^3

3. 30 (square root of) 10

To prove: Area of triangle MAP = 1/2 area of trapezium MNOP

Given: MN//OP and A is the midpoint of NO

Proof:

Let h be the height of trapezium MNOP.

The area of trapezium MNOP is given by:

Area of trapezium MNOP = (1/2) × (MN + OP) × h

Since MN//OP, we have MN = OP.

Therefore, Area of trapezium MNOP = (1/2) × 2MN × h = MN × h

Now, consider triangle MAP.

The base of triangle MAP is MA, which is half of NO.

Therefore, the base of triangle MAP is (1/2) × NO.

The height of triangle MAP is h, which is the same as the height of trapezium MNOP.

Therefore, the area of triangle MAP is given by:

Area of triangle MAP = (1/2) × (base) × (height) = (1/2) × (1/2NO) × h

Substituting NO = 2OA, we get:

Area of triangle MAP = (1/2) × (1/2 × 2OA) × h = (1/2) × OA × h

Since A is the midpoint of NO, we have OA = 1/2NO.

Therefore, Area of triangle MAP = (1/2) × (1/2NO) × h = (1/2) × (base of trapezium MNOP) × h

Hence, Area of triangle MAP = 1/2 Area of trapezium MNOP.

Therefore, the given statement is proved.

Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.

To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:

Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.

Proof:

Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:

css

Copy code

      M _______N

       |\      |

       |  \    |

       |    \  |

       |      \|

      O--------P

            A

We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.

Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.

Since MNOP is a trapezium, the area of trapezium is given by:

Area of trapezium MNOP = (1/2)(MN+OP) × height

Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.

Therefore, the area of trapezium MNOP can be written as:

Area of trapezium MNOP = (1/2)(MN+OP) × height

= (1/2)(MA+AP+OP) × height

= (1/2)(MA+MP) × height (Since AP = NO/2 = height)

So, we have proved that:

Area of trapezium MNOP = (1/2)(MA+MP) × height

Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,

Area of triangle MAP = (1/2) × Area of triangle MAP

Substituting the above in the expression for the area of trapezium, we get:

Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP

= (3/2) × Area of triangle MAP

Therefore, we have:

Area of triangle MAP = (1/2) × Area of trapezium MNOP

Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.

Step-by-step explanation:

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

\(\Huge \boxed{\bold{\text{12 Boys}}}\)

\(\Huge \boxed{\bold{\text{30 Girls}}}\)

Step-by-step explanation:

Let the number of girls be \(g\) and the number of boys be \(b\).

According to the problem: \(b = \frac{2}{5} \times g\)

We also know that the total number of students is 42, so \(b + g = 42\).

Now, we have two equations with two variables:

We can solve these equations to find the values of \(b\) and \(g\).

Step 1: Solve for \(\bold{b}\) in terms of \(\bold{g}\)

From the first equation, we have\(b = \frac{2}{5} \times g\)

Step 2: Substitute the expression for \(\bold{b}\) into the second equation

Replace \(b\) in the second equation with the expression we found in step 1.

\(\frac{2}{5} \times g + g = 42\)

Step 3: Solve for \(\bold{g}\)

Now, we have an equation with only one variable, \(g\):

\(\frac{2}{5} \times g + g = 42\)

To solve for \(g\), first find a common denominator for the fractions:

\(\frac{2}{5} \times g + \frac{5}{5} \times g = 42\)

Combine the fractions:

\(\frac{7}{5} \times g = 42\)

Now, multiply both sides of the equation by \(\frac{5}{7}\) to isolate \(g\):

Step 4: Find the value of \(\bold{b}\)

Now that we have the value of \(g\), we can find the value of \(b\) using the first equation:

So, there are 12 boys and 30 girls in the class.

----------------------------------------------------------------------------------------------------------

Given the points:

(x1, y1) ==> (1, 1)

(x2, y2) ==> (3, 7)

To find an equation of the line that goes through the points, first find the slope using the slope formula below:

Substitue values into the formula and solve for the slope, m:

The slope of the line, m is = 3.

Now, use the point slope form:

(y - y1) = m(x - x1)

Substitute 1 for y1, 1 for x1, and 3 for m:

(y - 1) = 3(x - 1)

Let's rewrite the equation to slope intercept form: y = mx + b

Where m is the slope and b is the y-intercept

y - 1 = 3(x) + 3(-1)

y - 1 = 3x - 3

Add 1 to both sides:

y - 1 + 1 = 3x - 3 + 1

y + 0 = 3x - 2

y = 3x - 2

Therefore, the equation of the line in slope intercept form is:

y = 3x - 2

ANSWER:

y = 3x - 2

Step 1. The expression that we have is:

and we need to find the equivalent expression.

Step 2. The trigonometric identity we will use to solve this problem is:

In this case:

Step 3. Applying the trigonometric identity to our expression, substituting 5x in the place of A:

This is shown in option d).

Answer:

Answer:

A. Normal

B. Between 2.078 and 2.722 visits.

C. About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

Question A:

By the Central Limit Theorem, normal.

Question B:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.9}{2} = 0.05\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.645\frac{2.9}{\sqrt{219}} = 0.322\)

The lower end of the interval is the sample mean subtracted by M. So it is 2.4 - 0.322 = 2.078 visits

The upper end of the interval is the sample mean added to M. So it is 2.4 + 0.322 = 2.722 visits.

Between 2.078 and 2.722 visits.

Question c:

90% confidence level, so 90% will contain the true population mean, 100 - 90 = 10% wont.

About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.

Step-by-step explanation:

If the price is below the equilibrium level, then the quantity demanded will exceed the quantity supplied. Excess demand or a shortage will exist. If the price is above the equilibrium level, then the quantity supplied will exceed the quantity demanded. Excess supply or a surplus will exist.Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium. A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.

\(\dfrac{2+6i}{2-4i}\\\\\\=\dfrac{2(1+3i)}{2(1-2i)}\\\\\\=\dfrac{1+3i}{1-2i}\\\\\\=\dfrac{(1+3i)(1+2i)}{(1-2i)(1+2i)}\\\\\\=\dfrac{1+2i+3i+6i^2}{1-(2i)^2}\\\\\\=\dfrac{1+5i-6}{1+4}~~~~;[i^2=-1]\\\\\\=\dfrac{5i-5}{5}\\\\\\=\dfrac{5(i-1)}5\\\\=i-1\\\\=-1+i\\\\\text{It is in a form of a +bi so,}~ a = -1~ \text{and}~ b = 1\)

Step-by-step explanation:

Step 1:  List out all of the formulas for the trigonometric functions

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

tan(x) = opposite/adjacent

Step 2:  Find the value of RS

cos(31) = RS/24.8 NOT 24.8/RS

sin(31) = QS/24.8 NOT RS/24.8

sin(31) = QS/24.8 NOT 24.8/RS

cos(31) = RS/24.8 WHICH IS SAME AS RS/24.8

Answer: The correct length would be given from Option D, cos(31) = RS/24.8

Answer:the  answer  is  a

Step-by-step explanation:

Given:

To find:

The value of r.

Explanation:

Using function (1) in (2),

Therefore, the value of r is,

Final answer:

The value of r is,