the diagram shows triangle PQR. PSR is a straight line. Size of angle SQR 3:1. Work out the size of angle PSQ

The expression 81x⁴y⁸ rewritten as a power of a product is (3xy²)⁴.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

1) 3³·3⁶ =3⁹

3³⁺⁶ =3⁹

[tex]3^{(6\times3)}=3^{18}[/tex]

3⁶·3³=3⁹

2) 5⁻¹/(-9)⁰

= 5⁻¹/1

= 1/5

3) 3x⁻⁵y⁰/5⁻³z⁻¹⁰

= 3×5³/x⁵z¹⁰

= 375/x⁵z¹⁰

4) (4s⁵t⁻⁷/-2s⁻²t⁴)³

= (4s⁵s²/-2t⁴t⁷)³

= (-2s⁷/t¹¹)³

= -8s²¹/t³³

5) 81x⁴y⁸

= 3⁴x⁴y⁸

= (3xy²)⁴

Hence, the expression 81x⁴y⁸ rewritten as a power of a product is (3xy²)⁴.

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Step-by-step explanation:

Step 1.) Plug in the numbers to each variable

(2(-25) -13) ÷ (-8.25)15

Step 2.) Solve in Parenthesis

(-50-13) ÷ -123.75

= -63÷-123.75

Step 3: Reduce/Solve

=28/55 (Fraction)

or

=0.51 (Decimal Rounded to nearest 10th)

The width of the parallelogram can be any value greater than or equal to 14 feet.

What is parallelogram ?

A parallelogram is a four-sided polygon with opposite sides that are parallel. It has opposite angles that are equal and opposite sides that are equal in length. A special cases of parallelograms are rectangles, which have four right angles, and squares, which have four right angles and all sides are equal in length.

P = 2l + 2w >= 40

where P is the perimeter, l is the length and w is the width.

Substituting the given value for the length, we get ,

2(6) + 2w >= 40

Simplifying and solving for w ,

12 + 2w >= 40

2w >= 28

w >= 14

Therefore, the width of the parallelogram can be any value greater than or equal to 14 feet.

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The four types of roots are: square roots, cube roots, fourth roots and nth roots, where n is any positive integer greater than 1.

The four types of roots are square roots, cube roots, fourth roots and nth roots. Square roots are the inverse of a number multiplied by itself. For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25. Cube roots are the inverse of a number multiplied by itself twice. For example, the cube root of 27 is 3, because 3 multiplied by 3 multiplied by 3 equals 27. Fourth roots are the inverse of a number multiplied by itself three times. For example, the fourth root of 256 is 4, because 4 multiplied by 4 multiplied by 4 multiplied by 4 equals 256. Nth roots are the inverse of a number multiplied by itself n times. N is any positive integer greater than 1. For example, the fifth root of 243 is 3, because 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 equals 243.

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So, on solving the provided question we can say that by probability we have [tex]256.014[/tex]= sample mean for 80th percentile

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

[tex]P(x < 240)[/tex]

Transform to z score =  (sample mean - population mean)/(standard deviation(std)[tex]/sample size^0.5)[/tex]

[tex]P(z < (240-250)/(50/49^0.5)[/tex]

[tex]P(z < -1.4) = 0.0808[/tex]

z-score corresponding to 80th percentile is 0.842

0.842 = (sample mean -[tex]250)/(50/49^0.5)[/tex]

[tex]6.014[/tex] = sample mean - [tex]250[/tex]

[tex]256.014[/tex]= sample mean for 80th percentile

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The approximate number of years for which the species is extinct is 7.7 years.

Zeros of an equation is defined as the value of the independent variable where the equation or function gives zero.

Here,
The population of a species is modeled by the equation,
p(t) = -t⁴ + 56t² + 240,

Where t is the number of years.

The approximate number of years until the species is extinct, is given by determining the zero of the equation,
-t⁴ + 56t² + 240 = 0

So, zeros is given as,
t = 2i, -2i, 2√15, -2√15

Now,
We only consider the positive real value of t,
t = 2√15
t = 7.7 years

Thus, the approximate number of years for which the species is extinct is 7.7 years.

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A. Johnny's biweekly gross pay is $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay is $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $37.63.

D. Johnny's new annual salary with a 14.5% raise is $71,179.93.

A. Johnny's biweekly gross pay is $62,285.50 / 24

= $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay, which is $2,595.23 * 6.2% = $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $2,595.23 * 1.45% = $37.63.

D. Johnny's new annual salary with a 14.5% raise is $62,285.50 * 1.145 = $71,179.93.

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$156.78 is the total cost of material for the bunny costumes.

Given a specified quantity of goods produced, a cost function is a mathematical formula that may be used to determine the overall cost of production. 

Given that,

Total required bunny costumes = 6

Total faux fur requirements for each bunny costume =  2.6 square yards

Cost of faux fur = $10.05 per square yard

The costume budget for the bunny costumes = $200

The total cost of material for the bunny costumes = 2.6 *10.05 *6 = $156.78.

Thus, $156.78 is the total cost of material for the bunny costumes.

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Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

When the equals sign (=) is used to denote equality, an algebraic theorem resembles a rule joining two statements. An algebraic equation is a factual assertion that shows the equivalence of multiple numerical variables. The values ob d + 6 and 12 are separated by an equal sign in the calculation data logger + 6 = 12. The number of syllables that correspond to each side of each letter can be expressed numerically. The message of a symbol is frequently its complete opposite.

Here,

Given :

After a few weeks, you create and calculate an equation

so determine how much money is in your bank account.

M equals -36, as you discover.

Thus,

It mean that you owe 36 amount of money to bank.

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

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Answer:

yes, but not less than zero.

Step-by-step explanation:

The absolute value is only greater than or equal to zero.

[tex] | - x| \geqslant 0[/tex]

where x is real number

Answer:

96m2

Step-by-step explanation:

First we have to find the perimeter of parallelogram

Now,

Breadth(b)=10m

Height(h)=6m

Perimeter of paralleogram(p)=b×h

=10×6

=60m

Then,

Breadth(b)=12m

Height(h)=6m

Perimeter of triangle(p)=1×b×h

2

= 1 ×6×12

2

=36m2

Now,

Perimeter of above figure= Perimeter of paralleogram+perimeter of triangle

= 60+36

. =96m2

The statement that when algebraic or numerical fractions are added or subtracted, the result is a single fraction is True.

For addition or subtraction of algebraic or numerical fractions, the denominator has to be the same for all terms in the equation.

For common denominator,

Suppose 2 numerical fractions are being added which have a common denominator: 3/5 + 1/5

The resultant fraction will be 4/5, which is a single fraction

For algebraic fractions, considering the denominators are common, such as 3x/5 + 4x/5 = 7x/5

The result is also a single fraction.

For different denominators,

Suppose 2 numerical fractions are being subtracted which have different denominators such as, 5/9 – 3/7

In this case, the least common multiple for the denominators are calculated: 9*7= 63, and the opposite numerators are multiplied to the opposite denominators

Therefore, (5*7 – 3*9)/63 = (35 – 27)/63 = 8/63, which gives us a single fraction.

The process is same for algebraic fractions, for example,

4x/7 – 3x/5 = (4x*5 – 3x*7)/35 = (20x – 21x)/35 = -x/35, which is also a single fraction.

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The scientist that made histogram of the data of amount of rainfall he collected each day for a year to study rainfall has performed descriptive statistics.

Descriptive statistics involves organizing, summarizing, and presenting data in a way that makes it easy to understand. Histograms are a common tool used in descriptive statistics. They are used to visualize the distribution of a dataset, by showing the frequency of data points within different ranges or bins. In this case, the scientist has organized the data by showing the frequency of days with different amounts of rainfall over the course of a year.

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Answer:

1 foot 6 inches

Step-by-step explanation:

divide the length value by 12. Hope this helps.

The line's x value at the x-axis intersection is referred to as the x intercept, and the line's y value at the y axis junction as the y intercept.

Because they are located on the horizontal and vertical axes, respectively, the x and y-intercepts are also known as the horizontal intercept and vertical intercepts.

The equation is a non-function

solve f(x)=6^x

Here are some points we can plug in. We should try to use full numbers:

(-2,1/36)

(-1,1/6)

(0,1)

(1,6)

This is the graph:

graph{6^x [-10, 10, -2, 40]}

Make sure the line approaches, but never touches, the x-axis. Even though the line sweeps up until it reaches infinity, it will never be vertical because that would render the equation useless.

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The rate of change of the volume at that particular instant is - 62.8 m^3/h.

How to get the rate of change of the volume?

First, we can write the dimensions as:

radius = R = (5m + 1m/h*t)

height = H = (8m - 4 m/h*t)

Where t is the time in hours.

Then the volume of the cylinder will be:

V = pi*R^2*H = 3.14*(5m + 1m/h*t)^2*(8m - 4 m/h*t)

To get the rate of change, we need to differentiate it with respect to t, we will get:

V' = 3.14*(2*(5m + 1m/h*t)*(1m/h)*(8m - 4 m/h*t) + (5m + 1m/h*t)^2*(-4m/h))

V' = 3.14*( (2 m/h)*(5m + 1m/h*t)*(8m - 4 m/h*t) - (4m/h)*(5m + 1m/h*t)^2)

V' = 3.14*(2m/h)*( (5m + 1m/h*t)*(8m - 4 m/h*t) - 2*(5m + 1m/h*t)^2)

As you can see the rate of change depends on t, but we want the rate of change at this instant, then we use t = 0, replacing that on the above equation we get:

V'(0) = 3.14*(2m/h)*( (5m + 1m/h*0)*(8m - 4 m/h*0) - 2*(5m + 1m/h*0)^2)

V'(0) = 3.14*(2m/h)*( (5m)*(8m ) - 2*(5m)^2)=  -62.8 m^3/h

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Answer:

5/8 is greater than 5/7. 5/8 is 0.625, while 5/7 is 0.714.

Step-by-step explanation:

5/8 is greater than 5/7. 5/8 is 0.625, while 5/7 is 0.714.

Answer:

5/7

A fraction is a fragment of a whole number, used to define parts of a whole.  The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

If we think about 5/7, we can relate this to a circle split into 7 parts, with 5 shaded in.

You can do the same for 5/8. Think of a circle with 8 parts, and 5 shaded in.

A way to figure out which is bigger is to find a common denominator between the two.

A common denominator is two fractions with the same denominator (Hence the name). Solving for a common denominator can be done with cross multiplication.

5/7 = 40/56

5/8 = 35/56

We can visibly see, that 40/56 (5/7) is bigger, therefore making 5/7 the greater fraction.

Using the triangle sum theorem, the value of x = 37.

The triangle sum theorem states that the sum of the three angles of a triangle is always 180 degrees.

The sum of the angles in a triangle is always 180 degrees, so we can use the triangle sum theorem to find the value of x.

So we can set up the following equation:

80 + 75 + (x - 12) = 180

80 + 75 + x - 12 = 180

Combine like terms:

x + 143 = 180

x = 180 - 143

x = 37

Solving for x, the value of x = 37

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Answer: Well you have to see on the number that is close to the decimal point

Step-by-step explanation:

0.2438

0.4485

0.8641

3.2527

17.9926

The values of a and b are 1 and 12 respectively.

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.

Different Types of Equations

Linear Equation.

Radical Equation.

Exponential Equation.

Rational Equation

In the given question:-

y = ax² + bx

dy/dx=2ax+b

If x=3 and dy/dx=18

the solution becomes

18=6a+b

If x=5 and dy/dx=22

The solution becomes

22=10a+b

Solving the equation we get a=1 and b=12

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Answer: The one below the top.

Step-by-step explanation: In order to tell if it is a function or not, you need to do the vertical line test. By examining the graph you can see that majority of the graphs has two points in the same x-axis. The only one that pasts the test is the graph below the top one.

Answer: The second one is because there can't be two y's in a straight line of a function and all of the other graphs have two y's in a line.

Step-by-step explanation:

The present ages of the teachers are 25 and 29 years old.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that sum of the present ages of two teachers is 54 years. If the age of one teacher is 4 years more than the other, then;

Let the ages of teachers are x and y

x + y = 54

x = 4 + y

So, 4 + y + y = 54

4 + 2y = 54

y = 25

x = 29

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Paying a bill amount through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

1. Paying a bill amount through the mail without check is a convenient and secure way of making payments.

2. It allows for payment to be made without having to visit a physical location to do so.

3. It also allows for payment to be made without having to use a credit or debit card.

4. Therefore, an advantage of paying a bill through the mail without check is that it is convenient and secure.

Paying a bill through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

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Answer: The Area of Shaded Region is 576  [tex]cm^{2}[/tex] and the perimeter is 24 (2 + [tex]\pi[/tex]) cm

Step-by-step explanation: Given, the length of the line segment BC is 24 cm.

     First, The area of the Semi Circle AD : We know that area of a circle is [tex]\pi[/tex][tex]r^{2}[/tex]  where r=radius of the circle. Since the shape ABCD is a sqaure, BC=AD=24cm. We can see from the figure that AD is the diameter for the semi circle AD. And diameter = 2 x Radius. Therefore radius of the semi circle is 12cm.

Therefore, area of the first Semi circle AD will be :

⇒ [tex]\pi \frac{r}{2}cm ^{2}[/tex]

⇒([tex]\pi[/tex]*12*12)/2

⇒72[tex]\pi[/tex] [tex]cm^{2}[/tex]

Now, perimeter of semi circle AD : We know perimeter of a Semi circle is [tex]\pi[/tex]r + length of the base.

Therefore, perimeter of Semi circle AD is :

⇒[tex]\pi[/tex]*12 + 24 cm

⇒12 (2 + [tex]\pi[/tex])

Now, Area of the Shape ABCD, As we can see from the figure, The area will be Area of square ABCD - Area of the semi circle BC. Therefore,

Area of Square = [tex]side^{2}[/tex]

⇒24 x 24 [tex]cm^{2}[/tex]

Area of semi circle BC :

⇒(12 x 12 x [tex]\pi[/tex])/2 [tex]cm^{2}[/tex]

∴ Area of shape ABCD = [(24 x 24) - (12 x 12 x [tex]\pi[/tex])/2] [tex]cm^{2}[/tex]

⇒576 - 72[tex]\pi cm^{2}[/tex]

Now, Perimeter of Shape ABCD :

We can see from figure, the perimeter will be Sum of 3 sides of the square and the circumference of the semi circle BC.

Therefore,

⇒72 + 12[tex]\pi[/tex] cm

Now, Finally The Area of the shaded region :

⇒ Area of Shape ABCD + Area of Semi circle AD

⇒[576 - 72[tex]\pi cm^{2}[/tex]] + [72[tex]\pi[/tex] [tex]cm^{2}[/tex]]

⇒576 [tex]cm^{2}[/tex]

Perimeter of the shaded region :

⇒ Sum of 2 sides of the square ABCD + 2 Times the Circumference of the semi circle

⇒[24 + 24] + [2 x 12[tex]\pi[/tex]]cm

⇒ 24 (2 + [tex]\pi[/tex]) cm, Final Answer  

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Answer:

none of the statements are true

Step-by-step explanation:

given the final statement in the solution is

5 = 0 ← not possible

this indicates the system has no solution.

then none of the previous statements are true

Using the interactive ruler, we can determine that there are 4 Units between the dilation's center and the image and pre-image.

This digital instrument, which appears on the computer screen and is often referred to as an Interactive Teaching Program ruler, is used to measure the lines and sides of a shape.

In units,

how far is it between points C and A?

With the help of the interactive ruler, we can calculate that the separation between points C and A is 2 units.

Additionally, the distance is 1.5 units between point C and point A'.

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The ratio of the lengths of the parallel sides of the trapezoid CD/AB = 13

A trapezoid is a quadrilateral that has a pair of parallel sides.

The median line of a trapezoid is the line joining the midpoint of the non parallel sides of a trapezoid

The parallel sides of the trapezoid are; AB and CD

The area of trapezoid ABMN = 8

Area of trapezoid NMCD = 20

The ratio of the lengths of the parallel sides, CD/AB is found as follows;

The length of the median, MN = (1/2) × (AB + CD)

Area of a trapezoid = (The sum of the length of the parallel sides) × (The distance between the parallel sides) ÷ 2

Area of the trapezoid ABCD = [ABMN]  + [NMCD]

[ABCD] = 8 + 20 = 28

Area of trapezoid [ABCD] = NM × h = 28

The height of trapezoid ABNM = h/2

Height of trapezoid NMCD = h/2

[ABNM] = ((AB + NM)/2) × (h/2)

[ABNM]  = ((AB × h + NM × h)/4) =  ((AB × h +28)/4) = 8

(AB × h + 28) = 4 × 8 = 32

AB × h = 32 - 28 = 4

AB × h = 4

[NMCD] = (NM + CD)/2 × (h/2)

[NMCD] = (NM × h + CD × h)/4 =  (28 + CD × h)/4 = 20

CD × h = 20 × 4 - 28 = 52

CD × h = 59

(CD × h)/(AB × h) = 52/4 = 13

CD/AB = 13

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According to the algebraic fundamental theorem, a polynomial equation of degree n has exactly n roots, be they real or imaginary.

Any polynomial of degree n has n roots, which is the fundamental theorem of algebra. Any polynomial has at least one solution, according to this statement. The theorem only reveals how many roots there are, not what the roots of a polynomial are. The theorem merely specifies how many roots there are in a polynomial; understanding what the roots are required knowledge of elementary mathematics. Additionally, it helps with the solution of polynomial equations [tex]x^2-9=0[/tex]. Use the definition of the algebraic fundamental theorem to determine the number of roots in the equation [tex]x^2-9=0[/tex].

Now, Solving above equation

[tex]x^2-9=0[/tex]

[tex](x-3)*(x+3)=0\\x=3,-3[/tex]

As here degree of equation is 2 and root of equation are also 2.

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