The probability that a five-digit integer chosen at random is divisible by 5 is 13.1 %.
Given :
what is the probability that a five-digit integer chosen at random is divisible by 5 .
Probability :
Probability is a branch of mathematics that deals with the occurrence of a random event.
Probability = 9^3 * 8 * 2 / 9 * 10^4
= 729 * 8 * 2 / 9 * 10000
= 5832 * 2 / 9 * 10000
= 11809 / 90000
= 0.131
converting into percentage :
= 0.131 * 100 %
= 13.1 %
Therefore The probability that a five-digit integer chosen at random is divisible by 5 is 13.1 %
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suppose that 9 good fuses and 4 defective ones have been mixed up. to find the defective fuses, we test them one-by-one, at random. what is the probability that we are lucky and find both of the defective fuses in the first two tests? (5 points) 1). with replacement 2). without replacement
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.
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A submarine dives 20 m each minute for 15 minutes. What is the total change in depth after 15 minutes?
Answer:
Step-by-step explanation:300 mStep-by-step explanation:20 meters per minute. 15 minutes it dives. 20x15 is 300
What is the length of AB
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
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SHOW WORK FOR BRAINLIST AND HEARTS
The graph of Stewart's assignment added as an attachment
How to draw the graph of the scenario?From the question, we have the following parameters that can be used in our computation:
Number of assignments = 36Rate of assignment per day = 4This 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
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The half-life of a certain radioactive substance is 13 days. There are 2.5 grand of the substance in totally. Type an expression for the amount of substance as a function of t. When will there be less than 1 g remaining? Please show work
[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]
in triangle ABC , seg XY || sideAC , If 2AX = 3BX and XY = 9 , then find the value of AC
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
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The parent function f(x)=x^2 is translated 2 units left and 3 units up. Write the quadratic function in vertex form.
The quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.
Explain the vertex form of quadratic function?In the linear model, k defines the vertex of the parabola, just as adding or subtracting b would decide where the line crosses.f(x)=a(x - h)² + k
K functions like b with in slope-intercept formula, just like a linear function would.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.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
-13
Step-by-step explanation:
combine the numbers and just add the - sign
hope this helps
what can identifying a correlation do for your research? aid in the calculation of the mean and mode. present possible solutions to be explored. guide the design of grids or decision matrices.
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.
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fine the product of 1/100
The product of 1/100 is 0.01.
What is decimal?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.
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Each birthday from age 12, You receive $500. You
save the money in an account that pays an annual yield of 6%. How much money will you
have by the time you're 18?
Someone please answer this question it is in the picture I will give you brainliest and your getting 50 points no fraud answers.
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.
given a rectangular sheet of cardboard 16 inches by 10 inches youa re asked to cut off identical squares from each of the four corners of the sheet and then bend up the sides of the remaining cardboard to form a rectangular box. what is the maximum volume of the box
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 .
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Answer:
d
Step-by-step explanation:
d
How much more is Rs. 5000 including 13% VAT on it than Rs. 5500.
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
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please help this is a checkpoint and it's due January 4
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
Find the gradient vector field of f. f(x, y) =xe9xy
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.
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the length of the sides of a square are initially 0 cm and increase at a constant rate of 7 cm per second. suppose the function f determines the area of the square (in cm2) given a number of seconds, t , since the square started growing. write a function formula for f .
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.
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The monthly income of a man is Rs. 53000. He deposits 20% of his yearly income in the Civil investment Fund and 10% in Charity. If Rs.300000 is his yearly income exempted and 1% social security charge and 15% tax is imposed yearly, how much tax should he pay?
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:
The cost of 7 sandwiches and 5 milkshakes is $79. The cost of 2 sandwiches and 5 milkshakes is $44. How much does one sandwich cost and one milkshake cost?
HELP
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.
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A box of cookies contains 12 chocolate-chip cookies, 6 peanut-butter cookies, and 6 sugar cookies. What is the probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie?
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.
What is probability?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.
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in the simek and o'brien study, a novice golfer had to sink four consecutive putts before going to the next step. this exemplifies:
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.
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The sides of a triangle are given by
(3x2 − y2);(4x2−7xy+4y)and (−3x+7xy+8y2)
3x2 − y2;4x2−7xy+4yand (−3x+7xy+8y2)
.
Find its perimeter.
The answers u see already answered is not right an I need help with them
Answer:
GOOD MORNING
Step-by-step explanation:
I AM SINGLE
Which pairs of rectangles are similar polygons? Rectangle A: 100cm & 80cm Rectangle B: 120cm & 100cm Rectangle C: 90cm & 72cm. A and B - similar or not similar? B and C similar or not similar? A and C similar or not similar?
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
a. Lin is using the diagram to prove the statement, "If a parallelogram has
one right angle, it is a rectangle." Given that EFGH is a parallelogram
and angle HEF is a right angle, write a statement that will help
prove angle FGH is also a right angle.
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.
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Solve Proportion
y/32+16/10
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
n a survey of 3102 adults, 1443 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results.
A 99% confidence interval for the population proportion is ( ),( ).
(Round to three decimal places as needed.)
Interpret your results. Choose the correct answer below.
A. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
B. The endpoints of the given confidence interval show that adults pay bills online 99% of the time.
C. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
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.
What is confidence interval?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
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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
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find the exact values of x and y. (let r = 10.)
Using Pythagoras' theorem, we know that the exact values of x and y are (A) 2√3 and 4√3 respectively.
What is Pythagoras' theorem?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.
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25% of what number is 6?
Answer:it is 24 ∪w∪
Step-by-step explanation: 100% is 24
Which of the following pair of linear equations are consistent or inconsistent x - y = 8, 3x - 3y = 16?
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
