what is the probability that a five-digit integer chosen at random is divisible by 5? (enter your probability as a percent.) %

Answer:

A and C similar

Step-by-step explanation:

A: 80/100 = 0.8

B: 100/120 = 0.833...

C: 72/90 = 0.8

Since the ratio of the lengths of the sides of rectangle A and C are equal, the only similar rectangles are A and C.

Answer: A and C similar

Using Pythagoras' theorem, we know that the exact values of x and y are (A) 2√3 and  4√3 respectively.

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relationship in Euclidean geometry between the three sides of a right triangle.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, the trigonometric ratio formula:

Tanθ = opp. sides of θ/adj. sides of θ

Tan60° = 6/x

We know  60° = √3:

√3 = 6/x

Multiply both LHS and RHS by x as follows:

√3 *  x = 6/x * x

√3 *  x = 6

Divide both LHS and RHS by √3 as follows:

√3 *  x/√3 = 6/√3

x = 2√3

Use of Pythagoras' theorem:

y² = 6² + (2√3)²

y² = 36 + 12

y² = 48

y = 4√3

Therefore, using Pythagoras' theorem, we know that the exact values of x and y are  (A) 2√3 and  4√3 respectively.

Know more about Pythagoras' theorem here:

https://brainly.com/question/28921824

#SPJ4

The value of AC is 22.5

The property of three parallel lines and their transversals is used to solve this sum. The property explains that if the ratio of the corresponding intercepts made on any other transversal by the same parallel lines is the same as the ratio of the intercepts made on a transversal formed by three parallel lines.

XY ║seg AC

2AX = 3BX

XY = 9

Since, 2AX =3BX

∴ AX÷ BX = 3÷2

AX + BX÷ BX = 3+2÷2

AB ÷ BX = 5÷2

Δ BCA ~  ΔBYX (SAS test of similarity)

( The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.)

∴ BA ÷ BX = AC ÷ XY ( Corresponding sides)

∴ 5÷ 2 = AC ÷ 9

∴ AC = 22.5

Read more regarding triangles here https://brainly.com/question/27996834

https://brainly.com/question/22313622

In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. Progressive Overload.

Progressive overload is the gradual increase of stress placed on the body during physical activity. By requiring the novice golfer to sink four consecutive putts before moving on to the next step, the study is increasing the difficulty of the task and placing additional stress on the body.

Progressive overload is an effective and essential technique for improving physical performance. It involves gradually increasing the intensity of the activity or exercise, which places additional stress on the body and forces it to adapt and become stronger. In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. This increased the difficulty of the task and allowed the golfer to gradually improve their performance. By gradually increasing the difficulty of the task, the study was able to effectively use progressive overload to improve the golfer's performance.

Learn more about consecutive here

https://brainly.com/question/29775116

#SPJ4

If the dimensions of the cardboard sheet is 16 inches by 10 inches , then the maximum volume of the box is  144 in³ .

In the question ,

it is given that the length of the sheet is = 16 inch

and width of the sheet is = 10 inch

let width of box be ⇒ "w" ,

let length of box be ⇒ "l"

let the length of the corner cut out be = "x"

let volume of box be ⇒ "V" ;

we need to find the point of dV/dx that is maximum ,

given width = 16 ; and length = 10 ,

we have : width = x + w + x ⇒ w = 2(8 - x)

length = x + l + x = 10 ⇒ l = 2(5 - x)

the Volume of rectangular box is written as ; V = w*l*x ;

substituting the values of w , l and x ,

we get ;

V = 2(8 - x)2(5 - x)x

V = 4x³ - 52x² + 160x

differentiating with respect to "x" , and for critical point equating it to 0 ,

we have ;

12x² - 104x + 160 = 0

solving the above quadratic, we get ;

x = 2 & x = 20/3 .

On substituting the values , in d²V/dx² = 24x - 104 < 0 for x = 2 ,

that is maximum ;

Substituting x = 2 , in the V = 4x³ - 52x² + 160x ,

we get ;

Volume of the box as 144 in³ .

Therefore , the maximum volume of the box is = 144 in³ .

Learn more about Volume here

https://brainly.com/question/7992757

#SPJ4

Answer:

d

Step-by-step explanation:

d

Answer:

a) [tex]\frac{5}{6}[/tex]

b) 18

Step-by-step explanation:

The unit rate is [tex]\frac{5}{18}[/tex].

This means that in 1 hour, you will travel [tex]\frac{5}{18}[/tex] of a mile.

distance = rate x time

d = [tex]\frac{5}{18}[/tex] x 3

d = [tex]\frac{5}{18}[/tex] [tex](\frac{3}{1})[/tex]

d = [tex]\frac{15}{18}[/tex]           Divide the numerator and denominator by 3 to simplify.

d = [tex]\frac{15}{18}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{5}{6}[/tex]

d = rate x time

5 = [tex]\frac{5}{18}[/tex]t  Multiply both sides by [tex]\frac{18}{5}[/tex]

[tex]\frac{18}{5}[/tex] [tex](\frac{5}{1})[/tex] = [tex]\frac{18}{5}[/tex][tex](\frac{18}{5})[/tex]t

18 = t

The statement that will help prove angle FGH is also a right angle is opposite angles in a parallelogram are congruent.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

Given:

EFGH is a parallelogram and ∠HEF is a right angle.

Then ∠FGH is also right angle.

Since opposite angles in a parallelogram are congruent.

Hence, the statement that will help prove angle FGH is also a right angle is opposite angles in a parallelogram are congruent.

To know more about parallelogram, click on the link

https://brainly.com/question/970600

#SPJ1

With 99% certainty, the population proportion of adults who say they have started paying bills online in the last year is between the given confidence interval's endpoints.

We have the following confidence interval of proportions in a sample of n people surveyed with a success probability of π and a confidence level of 1 - α.

Confidence interval = [tex]\pi[/tex] ± z [tex]\sqrt{\(\pi (1 - \pi ))/n}[/tex]

z = 1 - α/2

Here given, According to a survey of 3102adults, 1443 have begun paying bills online in the last year.

That is, n = 3102 and x = 1443

p = x / n

  = 1443 / 3102

  = 0.465

significance level = α

= 1 - confidence

= 1 - 0.99

= 0.01

zα/2 = z0.01 / 2 = 2.58

By substituting in confidence interval formula,

The lower limit is :

0.465 - 2.58[tex]\sqrt{(0.465 * 0.535) / 3102}[/tex]

= -0.01894056008

The upper limit is:

0.465 + 2.58[tex]\sqrt{(0.465 * 0.535) / 3102}[/tex]  

= 0.02722425658

To learn more about confidence interval refer to :

https://brainly.com/question/20309162

#SPJ4

The lower limit is 0.456 and upper limit is 0.474

What is confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

As confidence interval (C) = π ± z√[π(1-π)/n]

In the above expression, z = 1 - α/2, where α is the significance level.

Given in the question, n=3102 as the survey was conducted on 3102 adults. Also, x=1443, as 1443 people have started paying bills online in last year.

π = x/n

Substituting the values, we get,

π = 1443/3102

⇒ π = 0.465

Confidence level(α) = 1 - confidence

= 1 - 0.99

= 0.01

Since, z = 1 - α/2

⇒ z = 1 - 0.01/2

⇒ z = 1 - 0.005

⇒ z = 0.995

By substituting in confidence interval formula,

The lower limit is = 0.465 - 0.995√[(0.465*0.535)/3102]

= 0.456

The upper limit is = 0.465 + 0.995√[(0.465*0.535)/3102]

= 0.474

To learn more about confidence interval refer to :

brainly.com/question/20309162

#SPJ4

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &\\ P=\textit{initial amount}\dotfill &2.5\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &13 \end{cases} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}} \end{array}} ~\hfill[/tex]

well, let's instead find when will there be 1 gram first off, then after that it's all downhill, so A = 1

[tex]\stackrel{A}{1}=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \cfrac{1}{2.5}=\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \log\left( \cfrac{1}{2.5} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{t}{13}} \right][/tex]

[tex]\log\left( \cfrac{1}{2.5} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]\implies \cfrac{\log\left( \frac{1}{2.5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]}=t\stackrel{\textit{after about 17 days and 5 hours}}{\implies 17.19\approx t ~\hfill }[/tex]

The probability that we are lucky and find both of the defective fuses in the first two tests with replacement is 1/13 and without replacement is 12/169.

In the given question, 9 good fuses and 4 defective ones have been mixed up.

To find the defective fuses, we test them one-by-one, at random.

We have to find the probability that we are lucky and find both of the defective fuses in the first two tests.

1). with replacement

2). without replacement

There are 9 good fuses and 4 defective ones.

So the total number of defective fuses = 9+4 = 13

Now the probability first test will find a defective is 4/13

Without replacement, 2nd will find another defective with probability = 3/12.  

Probability of finding 2 defectives on 1st two tests is

P(R) = 4/13 x 3/12

P(R) = 12/156

P(R) = 1/13

Now the with replacement the probability is

P(E) = 4/13 x 3/13

P(E) = 12/169

The probability that we are lucky and find both of the defective fuses in the first two tests with replacement is 1/13 and without replacement is 12/169.

To learn more about probability link is here

brainly.com/question/11034287

#SPJ4

Answer:

the equations listed are inconsistent because the do not intersect or overlap.

Step-by-step explanation:

use the desmos graphing calculator website to graph the two equations. if they are parallel then they are inconsistent. if the cross or overlap then they are consistent

The length of AB will be 32

Given that,

AC=32

AD=8

∠ABC=90 degree

From the diagram, we can see that it is a right-angle triangle so we can use that trigonometry to find the value of AB.

We know that,

                     sinФ=[tex]\frac{perpendicular}{hypotenuse }[/tex]

Now using this formula we can find the value of AB. And we know that the value of sin90= is 1.

sin90=AB/AC

⇒1=AB/32

⇒32=AB

⇒AB=32

So the length of AB mean x is 32

To know more about trigonometry:

https://brainly.com/question/28025415

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie is 3/23.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

A box of cookies contains 12 chocolate-chip cookies, 6 peanut-butter cookies, and 6 sugar cookies.

Total number of cookies = 12 + 6 + 6 = 12 + 12 = 24

Now,

The probability of randomly selecting a chocolate-chip cookie.

= 12/24

= 1/2

The remaining chocolate.

= 24 - 1

= 23

Now,

The probability of randomly selecting a sugar cookie.

= 6/23

Now,

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie

= 1/2 X 6/23

= 3/23

Thus,

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie is 3/23.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Answer:it is 24 ∪w∪

Step-by-step explanation: 100% is 24

The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

The gradient vector field of a function

Suppose that  a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.

In which:

fx(x,y) is the partial derivative of f relative to variable x.

fy(x,y) is the partial derivative of f relative to variable y.

The function in this problem is defined as follows:

f(x,y) = xe^(9xy).

The partial derivative relative to x  as follows:

fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).

The partial derivative relative to y  as follows:

fy(x,y) = 9x²e^(9xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

To learn more about Gradient Function visit:

brainly.com/question/13646769

#SPJ4

Answer:

-13

Step-by-step explanation:

combine the numbers and just add the - sign

hope this helps

The product of 1/100 is 0.01.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

Given that the expression 1/100.

To find the product of 1/100,

means the decimal value of 1/100

And the decimal value of 1/100 is part of 1 in hundredth

= 1/100

= 0.01

Hence, product of 1/100 is 0.01.

To learn more about the decimal;

https://brainly.com/question/109147

#SPJ1

Answer:

Step-by-step explanation:300 mStep-by-step explanation:20 meters per minute. 15 minutes it dives. 20x15 is 300

Answer: a=9 b=11

Step-by-step explanation:

This is a parallelogram; we know by the definition of the shape that the opposites sides are congruent.

That means a, the opposite of the 9, is 9.

That means b, the opposite of the 11, is 11.

When 13% VAT is levied on Rs 5000, the total price becomes Rs. 5650. This amount is Rs. 150 more than Rs. 5500.

VAT refers to value-added tax, a flat consumption tax levied on goods and services. It is most commonly charged in the countries of the EU. VAT is calculated by multiplying the percentage given by the original price.

VAT amount = percentage × original price

= 13% × 5000

=  Rs. 650

We must add the VAT amount to the original amount to get the total price.

= 5000 + 650

= Rs. 5650

The difference in Rs. 5000, including 13% VAT from Rs. 5500, can be found by subtracting the lower amount from the larger amount.

= 5650-5500

= Rs. 150

For more information on VAT, please refer to the question given below:

https://brainly.com/question/20628016

The quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.

        f(x)=a(x - h)² + k

For the stated question-

Whether you're going to increase by 2, you must also add 2.

The horizontal movement is determined by the h. It goes left or right depending on what you enter in h.

Finding the value that will cause the parenthesis to equal 0 when x equals -2 is necessary to make the necessary adjustments because shifting the vertex point to a left implies subtraction and negatives

x - h = 0

-2 - h = 0

-h = 2

h = -2

As a result, the function appears as follows:

f(x)=a(x - (-2))² + 2

A negative is subtracted to eliminate the signs and create a positive:

f(x)=a(x + 2)² + 2

Thus, the quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.

To know more about the vertex form of quadratic function, here

https://brainly.com/question/16970575

#SPJ4

The graph of Stewart's assignment added as an attachment

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

This means that the equation of the scenario is

Number of assignments remaining = Initial number of assignments - Rate of assignment per day * Number of days

Represent the number of assignments remaining with y and the number of days with x

So, we have the following representation

y = Initial number of assignments - Rate of assignment per day * x

Substitute the known values in the above equation, so, we have the following representation

y = 36 - 4 * x

Evaluate the products

y = 36 - 4x

So, the equation is y = 36 - 4x and the graph is added as an attachment

Read more about linear graphs at

brainly.com/question/4025726

#SPJ1

The function of the area of the square is A(t) = 49t².

A function is a relation between the input abd output values.

The length of a square's side starts from 0 cm and increases at a constant rate of 7 cm per second.

Let us assume that the function 'f' determines the area of the square (in cm²)

Also Lets  the length of side of square is x

rate of change of length with respect to time can be denoted as (dx/dt) = 7 cm/sec

⇒ x = 7*t

Area of square = ( length of side )²

{as the length of side is 7t} {varies by time}

Area of square A(t) = ( 7*t )²

Therefore, The function of the area of the square is A(t) = 49t².

To know more about function,

https://brainly.com/question/28447855

#SPJ4

Answer:

y = (-256)/5

Step-by-step explanation:

Solve for y:

y/32 + 8/5 = 0

Put each term in y/32 + 8/5 over the common denominator 160: y/32 + 8/5 = (5 y)/160 + 256/160:

((5 y)/160 + 256/160) = 0

(5 y)/160 + 256/160 = (5 y + 256)/160:

(1/160 (5 y + 256)) = 0

Multiply both sides of (5 y + 256)/160 = 0 by 160:

(160 (5 y + 256))/160 = 160×0

(160 (5 y + 256))/160 = 160/160×(5 y + 256) = 5 y + 256:

(5 y + 256) = 160×0

0×160 = 0:

5 y + 256 = 0

Subtract 256 from both sides:

5 y + (256 - 256) = -256

256 - 256 = 0:

5 y = -256

Divide both sides of 5 y = -256 by 5:

(5 y)/5 = (-256)/5

5/5 = 1:

Answer: y = (-256)/5

Answer:

GOOD MORNING

Step-by-step explanation:

I AM SINGLE

Answer:

Monthly income of a Man is ₹53000

Total salary earned in an year = 53000 × 12

= 636000

20% in civil investment fund.

So, 636000 × 20 ÷ 100 = 127200.

10% in charity.

So, 636000 × 10 ÷ 100

= 63600.

1% is social security tax on first 300000 = 3000.

300000 × 15 ÷ 100 = 45000.

Total tax he should pay = Amount remained is 390840

Step-by-step explanation:

Cost of one sandwich is $7 and cost of milkshake $5.

What is an equation?

In arithmetic, associate equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

According to question:

let cost of one sandwich be x and cost of milkshake be y .

7x + 5y = $79           -------(1)

2x + 5y = $44          -------(2)

subtracting equation 2 from 1 , we get

5x = 35

x = $7

so cost of one sandwich is $7.

now substituting value of x in equation 1 , we get

7(7) + 5y = 79

49 +5y = 79

5 y = 20

y = 4

so cost of one milkshake is $5.

Hence cost of one sandwich is $7 and cost of milkshake $5.

To know more about equation , visit:

https://brainly.com/question/22688504

#SPJ1

A correlational research design investigates relationship between variables without the researches controlling or manipulation any of them.

Correlational analysis is statistical method that is used to discover if there is a relationship between two variables/dataset, and how strong that relationship may be.

A correlation reflects the strength and direction of the relationship between two variables. The direction of a correlation can be either positive or negative.

Correlational research is ideal gathering data quickly from natural settings. They helps you generalize your findings to real-life situations in an externally valid way.

Correlation is also used to establish the reliability and validity of measurements. A positive correlation is a relationship between two variable s in which bothe variables move in the same direction. A negative correlation is a relationship between two variables in which as increase in one variable is associated with a decrease in the other. A zero correlation exist when there is no relationship between two variables.

To know more about correlation here

https://brainly.com/question/28325468

#SPJ4