If you know the volume of the solid and the length of two of the three sides, b and c the length of the remaining side, a can be calculated by putting this values in the formula of volume(height*breadth*length).
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.
Volume = a× b× c
a = V / b×c
Cubic units are used to quantify a solid's volume. For instance, the volume will be given in cubic metres if the dimensions are given in metres. The International System of Units uses this as the reference unit for volume (SI). Cubic metres, cubic feet, cubic inches, etc. are additional volume units.
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In a survey of 135 adults, 85 were employed full time and the remainder were employed part time. Of those employed full time, 70 had been to a doctor in the last year. Of those employed part time, 25 had been to a doctor in the last year.
From the question, we can conclude that the survey produced the following results.
Employed Full Time, Yes doctor = 70
Employed Full Time, No doctor = 15
Employed Part Time, Yes doctor = 25
Employed Part-Time, No doctor = 25
The question states that there are:-
135 adults
85 fully employed, which also means that there are
135 - 85 = 50 part employed
Full employed, 70 = yes doctor
Part employed, 25 = yes doctor
From the above, we can subtract that
Full employed = 85
Yes doctor = 70
No doctor = 85 - 70 = 15
Part employed = 50
Yes doctor = 25
No doctor = 50 - 25 = 25
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Consider the following quadratic function: f(x) = 3x^2 - 8x + 2. Find the x-intercept
For the quadratic function f(x) = 3x² - 8x + 2, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is - f(x) = 3x² - 8x + 2.
The quadratic function is in the standard form ax² + bx + c = 0.
Here, a = 3, b = -8 and c = 2.
The x-intercepts can be found using the formula -
x1 = (-b + √Δ) / (2a)
x2 = (- b - √Δ) / (2a)
Here, Δ = b² - 4ac.
Substitute the values in the above equation -
Δ = b² - 4ac
Δ = (-8)² - 4(3)(2)
Δ = 64 - 24
Δ = 40
Now, substitute the value of Δ in the x-intercepts formula -
x1 = [-(-8) + √40) / [2(3)] x2 = [-(-8) - √40) / [2(3)]
Open the brackets and use arithmetic operation of multiplication -
x1 = (8 + √40) / 6 x2 = (8 - √40) / 6
Take out the common value -
x1 = (8 + 4√10) / 6 x2 = (8 - 4√10) / 6
Use arithmetic operation of division -
x1 = (4 + √10) / 3 x2 = (4 - √10) / 3
Therefore, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.
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Water comes out of a garden hose at a constant rate to fill a pool. After 3 minutes, the pool is filled with 30 gallons of water. After 6.5 minutes, the pool is filled with 65 gallons of water.
a. Write an equation that represents the number of gallons of water y in the pool after x minutes.
b. How long will it take to fill a pool that needs 10,000 gallons of water?
Answer:
a. y = 10x
b. 1000 minutes of 16 2/3 hours
Step-by-step explanation:
a.
30 gal / 3 min = 10 gal/min
65 gal / 6.5 min = 10 gal/min
The relation is a direct proportion.
y = kx
The filling rate is the slope which is also the constant of proportionality.
The equation is
y = 10x
b.
y = 10x
10,000 = 10x
x = 10,000/10
x = 1000
The time is 1000 minutes, or 16 2/3 hours.
classifying polynomials by degree and number of terms
Answer:
Step-by-step explanation:
Polynomials are mathematical expressions that consist of variables raised to a power and combined with coefficients. The degree of a polynomial is the highest power of the variable in the expression. The number of terms in a polynomial is the number of separate terms that are added together to form the polynomial.
Here are some common examples of polynomials classified by degree and number of terms:
Degree 1, one term: a linear polynomial, such as 3x + 4
Degree 2, one term: a constant polynomial, such as 25
Degree 2, two terms: a quadratic polynomial, such as 3x^2 + 4x + 5
Degree 3, three terms: a cubic polynomial, such as 2x^3 + x^2 + 4x + 7
Degree 4, four terms: a quartic polynomial, such as x^4 + 3x^3 + 4x^2 + 2x + 6
Note that a polynomial with only one term is always a constant polynomial, regardless of its degree
I know 6x + 64 = 90 but i doesn’t know what the value of x
Answer:
x = 4 1/3
Step-by-step explanation:
To solve the equation 6x + 64 = 90, we must isolate the variable.
6x + 64 = 90
- 64 - 64
6x = 26
/ 6 / 6
x = 4 1/3
Answer:
4.3333333 on going so a stop will be 4.3
Step-by-step explanation:
the total 90, minus 64 will give you 26, the divide 26 by 6 which will give you 4.33333
A wheel on a tractor has a 28-inch diameter. How many full revolutions does the wheel make if the tractor travels 5 miles?
4706 revolutions are made by the wheel over the course of 7 miles.
How many complete wheel revolutions does the wheel make?The wheel is a circular, therefore one revolution covers its entire circumference.
So, circumference C = d, where d is the wheel's diameter in inches, which is 30.
So, C = πd
= π × 30 in
= 30π in
= 94.25 in
Now that the tractor has traveled D = 7 miles, we need to determine how many revolutions the wheel completes.
As 1 mile equals 63360 inches,
D = 7 miles when converting miles to inches
= 7 × 1 mile
= 7 × 63360 in
= 443520 in
N = D/C is the number of revolutions the wheel completes in 7 kilometers.
= 443520 in/94.25
= 4705.89
To the nearest whole number, enter 4706.
Therefore, 4706 revolutions are made by the wheel over the course of 7 miles.
The Complete Question.
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Define the following terms.(a) Experimental unit (d) Factor(b) Treatment (e) Placebo(c) Response variable (f) Confounding(a) Define experimental unit.A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variableB. A person, object, or some other well-defined item upon which a treatment is appliedC. Any combination of the values of the factors (explanatory variables)D. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication(b) Define treatment.A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variableB. The number of individuals in the experimentC. Any combination of the values of the factors (explanatory variables)Your answer is correct.D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
Define the terms mentioned above:
Experimental unit, a person, object, or some other well-defined item upon which a treatment is applied. Correct answer: letter B.Treatment, Any combination of the values of the factors (explanatory variables). Correct answer: C Response variable, the quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable. Correct answer: letter D.Factor, a variable whose effect on the response variable is to be assessed by the experimenter. Correct answer: letter A.Placebo, An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication. Correct answer: letter C.Confounding, The effect of two factors (explanatory variables on the response variable) cannot be distinguished. Correct answer: letter A.Experimental terms refer to the set of procedures used to conduct a scientific investigation. These terms include experimental design, data collection, interpretation of results, discussion of theoretical models, and formulation of hypotheses.
These terms are used to describe the research process, from the selection of the topic to the publication of the results. Experimental terms are also used to describe the methods of analysis of the data collected, such as linear regression and analysis of variance.
Define the following terms: (a) Experimental unit (d) Factor (b) Treatment (e) Placebo (c) Response variable (f) Confounding
(a) Define experimental unit:
A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
B. A person, object, or some other well-defined item upon which a treatment is applied
C. Any combination of the values of the factors (explanatory variables)
D. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
(b) Define treatment:
A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
B. The number of individuals in the experiment
C. Any combination of the values of the factors (explanatory variables)
Your answer is correct.
D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
(c) Define response variable:
A. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
B. The variable whose effect on the response variable is to be assessed by the experimenter
C. The effect of two factors (explanatory variables on the response variable) cannot be distinguished.
D. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
(d) Define factor:
A. A variable whose effect on the response variable is to be assessed by the experimenter
Your answer is correct.
B. Grouping together similar experimental units
C. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
(e) Define placebo:
A. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
B. Grouping together similar experimental units
C. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
D. Using treatments on many experimental units
(f) Define confounding:
A. The effect of two factors (explanatory variables on the response variable) cannot be distinguished.
B. Using treatments on many experimental units
C. Grouping together similar experimental units
D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable
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PLEASE ANSWER ITS EXIT TICKET!!, Elizabeth wrote the following clues. What is the relationship between the shapes?
You did not include enough information to figure out the answer!!
a jar contains 2 red marbles numbered 1 to 2 and 8 blue marbles numbered 1 to 8. a marble is drawn at random from the jar. find the probability of the given event. enter your answers as either decimals or fractions, not as percents.(a) the marble is redyour answer is :
The probability of drawing a red marble is 2/10 or 1/5.
To determine this:
The probability of drawing a red marble is 2/10 or 1/5. This means that if we randomly select one marble from the jar, there is a 1 in 5 chance that it will be red.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
Probability is an important concept in statistics and mathematics, and it is widely used in many areas such as insurance, finance, and scientific research.
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The probability of drawing a red marble is 2/10 or 1/5.
To determine this:
The probability of drawing a red marble is 2/10 or 1/5. This means that if we randomly select one marble from the jar, there is a 1 in 5 chance that it will be red.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
Probability is an important concept in statistics and mathematics, and it is widely used in many areas such as insurance, finance, and scientific research.
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Philip's granola direstions call for 3 oz. of nuts to every 4 oz. of raisins. He uses 2 oz. of nuts to every 3 oz. of raisins. Is Philip using the correct ratio of nuts to raisins.
Answer:
Step-by-step explanation:
yes
Solve the system of linear equations using substitution. X= 7y-6 x+7y=2
Answer:
(-2, 4/7)
Step-by-step explanation:
Ahh the wonderful world of substitution:
x = 7y - 6
x + 7y = 2
So, we need to find what x and y are. Since we know what x is equal to because of the first equation, we can plug that into the second equation:
7y - 6 + 7y = 2
Now let's solve this
14y - 6 = 2
+6 +6
14y = 8
/14 /14
y = 4/7
Now that we know what y is equal to, we can plug this into the equation. I'll choose the first one, since it is much easier:
x = 7(4/7) - 6
x = 4 - 6
x = -2
Therefore, x is equal to -2 and y is equal to 4/7, final answer.
Hope this helps :D
Please help I'm so confused!!!
Answer:
its not possible
Step-by-step explanation:
6=14
10 = 22
if ten is 22
how can 20 be 42
a survey of a number of large corporations gave the following probability table for events related to the offering of a promotion involving a transfer two career marriage one career marriage unmarried total rejected promotion 0.184 0.0555 0.0170 0.2565 accepted promotion 0.276 0.3145 0.1530 0.7435 total 0.46 0.37 0.17 what is the probability that a professional (selected at random) would accept the promotion? report your answer as a decimal with no more than two places.
The probability that a professional would accept the promotion is 0.7435.
The total row represents the sum of the probabilities of each event for all the categories, and in this case, the probability of accepting the promotion is the sum of the probabilities of accepting the promotion for each category, which is 0.276 + 0.3145 + 0.1530 = 0.7435.
This means that if we randomly select a professional, there is a 0.7435, or 74.35%, chance that they would accept the promotion. The probability is calculated by taking the sum of the probabilities for each category that corresponds to accepting the promotion and dividing it by the total number of professionals surveyed.
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Which is a correct similarity statement for the figures below?
A- ABC~EDF
B- ABC~DFE
C- ABC~DEF
D- ABC~EFD
Answer:
C!
Step-by-step explanation:
the sides all have the same ratio
8/12 = 10/15 = 14/21 = 2/3
two containers, A and B begin with equal volumes of liquid.
120 ml is then poured from A to B.
Container B now contains 4 times as much liquid as A.
Find the volume of liquid left in container A at the end.
Volume left in container A= ml
the mainor school district a. the district estimates that the equipment has a useful it is considering four alternaives
The Expenditure incurred by the mainor school district is $60,000 & inter-period equity is not achieved.
Interperiod equity refers to a government's obligation to disclose whether current-year revenues are sufficient to pay for the services provided that year and whether or not future taxpayers will be required to shoulder the burdens for services previously provided. It also refers to whether current-year revenues are sufficient to pay for the benefits provided that year or whether current citizens deferred payments to future taxpayers.
Thus, The Expenditure incurred by the mainor school district is $60,000 & inter-period equity is not achieved.
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an environmental engineer tracking replacements of pump rotors has noticed that of the newest batch of rotors purchased by her company, 12% of the rotors have failed after 235 hours of operation. assuming a constant failure rate, what is the mean time to failure (mttf) of the new rotors?
Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
What is rate ?
Rate is a measure of the change of a quantity per unit of time or per unit of another quantity. It can refer to various physical or abstract quantities, such as speed, velocity, frequency, interest rate, growth rate, etc. It is often expressed as a ratio or a fraction and has units specific to the quantity being measured.
The mean time to failure (MTTF) can be calculated as the reciprocal of the failure rate. The failure rate can be calculated as the number of failures per unit of operating time.
In this case, the failure rate is 12% per 235 hours, or 0.12 / 235 = 0.00051 failures per hour.
So, the MTTF would be:
MTTF = 1 / failure rate = 1 / 0.00051 = 1952 hours.
Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
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Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
Rate is a measure of the change of a quantity per unit of time or per unit of another quantity. It can refer to various physical or abstract quantities, such as speed, velocity, frequency, interest rate, growth rate, etc. It is often expressed as a ratio or a fraction and has units specific to the quantity being measured.
The mean time to failure (MTTF) can be calculated as the reciprocal of the failure rate. The failure rate can be calculated as the number of failures per unit of operating time.
In this case, the failure rate is 12% per 235 hours, or 0.12 / 235 = 0.00051 failures per hour.
So, the MTTF would be:
MTTF = 1 / failure rate = 1 / 0.00051 = 1952 hours.
Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
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!100 POINTS!!!
I need help with these geometry problems unit 1.14 circles
Answer:
Convert from degrees to radians using the ratio
π
180.001989675
radians
Mason is going to invest in an account paying an interest rate of 5. 3% compounded
quarterly. How much would Mason need to invest, to the nearest hundred dollars,
for the value of the account to reach $205,000 in 14 years?
Rounding to the nearest hundred dollars, the amount Mason needs to invest is $144,000.
Compound Interest Investment CalculationTo determine the amount Mason needs to invest, you can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = initial investment (principal)
r = annual interest rate (5.3%)
n = number of times interest is compounded per year (quarterly = 4 times)
t = number of years
Setting A = 205,000 and solving for P:
205,000 = P * (1 + 0.053/4)^(4 * 14)
P = 205,000 / (1 + 0.053/4)^(4 * 14)
Rounding to the nearest hundred dollars, the amount Mason needs to invest is $144,000.
The information provided is about calculating the initial investment (or principal) that Mason needs to make in an account paying an interest rate of 5.3% compounded quarterly, in order to reach a target amount of $205,000 in 14 years. The calculation uses the formula for compound interest, which takes into account the initial investment, the interest rate, the number of times the interest is compounded in a year, and the number of years the investment will grow.
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In a blueprint, each square has a side of lenght of 1/4inch.
The cost of the tiles and carpet will be $1,600 and $640, respectively.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The area of the bedroom is given as,
A = (5 x 1/4 x 16) x (4 x 1/4 x 16)
A = 20 x 16
A = 320 square feet
A = 320 / 9
A = 35.56 square yards
Ceramic tile costs $5 per square foot. Then the cost of tiles is given as,
⇒ 320 x 5
⇒ $1,600
The carpet costs $18 per square yard. Then the cost of the carpet is given as,
⇒ 35.56 x 18
⇒ $640
The cost of the tiles and carpet will be $1,600 and $640, respectively.
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14+2(3x-1) dived by 2
Answer:
14+2(3x-1) dived by 2 = 16
Step-by-step explanation:
Answer:
3,x+13 all you have to do is simplify
Use the image below to determine what relationship exists between AGC and FGD
A: supplementary angles
B: vertical angles
C: adjacent angles that form EGA
D: complementary angles
Answer: Your mom?
Step-by-step explanation: Your mom?
If A is invertible, then A∼I (A is row equivalent to the identity matrix). Therefore, A has n pivots, one in each column, which means that the columns of A are linearly independent.
The given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.
What is the identity matrix?
The identity matrix is a square matrix with 1's on the main diagonal and 0's everywhere else. It is denoted as I. The identity matrix has the property that for any square matrix A, the product of A and I is equal to A itself, so I serve as a sort of "do-nothing" matrix.
Yes, this is correct. If a matrix A is invertible, then it means that it has a unique inverse. This implies that the columns of A are linearly independent, as they form a basis for the space. A row equivalent matrix to the identity matrix (A∼I) will have one pivot in each column, indicating that the columns are linearly independent.
Hence, the given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.
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how many fruit skewers do they make
Answer:
100
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
sum of 2k - 1 = n^2 proof
The sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.
The formula for the sum of the first n consecutive odd numbers is n^2. This can be proven by induction.
Let n = 2k – 1.
Base case: When k = 1, then n = 2k – 1 = 1. The sum of the first 1 consecutive odd numbers is 1^2 = 1.
Inductive step: Assume that for some k = p, the sum of the first 2p – 1 consecutive odd numbers is (2p – 1)^2.
Now, consider the case when k = p + 1. The sum of the first 2(p + 1) – 1 consecutive odd numbers is:
(2p – 1)^2 + (2p + 1) + (2p + 3) + … + (4p + 1).
This can be written as (2p – 1)^2 + 2(1 + 2 + … + (p + 1)) (2p + 1).
By the sum of an arithmetic sequence, the expression in the parentheses is equal to (p + 1)(2p + 2).
Therefore, the sum of the first 2(p + 1) – 1 consecutive odd numbers is (2p – 1)^2 + 2(p + 1)(2p + 2).
Simplifying, this is equal to (2p + 1)^2.
Therefore, the statement holds for k = p + 1, and by induction, it holds for all positive integers k.
Therefore, the sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.
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The product of a number and -7 is 63 Translate into an equation -7x=63 8 What is the answer? X=-9
The unknown number is -9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the product of a number and -7 is 63.
Let the unknown number be x.
Now, -7×x=63
-7x=63
x= -9
Therefore, the unknown number is -9.
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if z = f (x, y) where x = r cos! and y = rsin! find dz/dr
dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!) By applying the chain rule, we can calculate the derivative dz/dr.
The derivative of z with respect to r is given by the chain rule:
dz/dr = (∂z/∂x) * (∂x/∂r) + (∂z/∂y) * (∂y/∂r)
Where (∂z/∂x) and (∂z/∂y) are the partial derivatives of z with respect to x and y respectively, and (∂x/∂r) and (∂y/∂r) are the partial derivatives of x and y with respect to r.
Since x = r cos! and y = rsin!, we can substitute these values into the above equation to get:
dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!)
Thus, by applying the chain rule, we can calculate the derivative dz/dr if we know the partial derivatives of z with respect to x and y.
dz/dr = (∂z/∂x) * cos(!) + (∂z/∂y) * sin(!) By applying the chain rule, we can calculate the derivative dz/dr if we know the partial derivatives of z with respect to x and y.
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how many positive four-digit integers are there such that no two consecutive digits are multiples of 3?
There are 720 positive four-digit integers that satisfy the condition of having no two consecutive digits being multiples of 3.
how many positive four-digit integers that satisfy the condition of having no two consecutive digits?To find this number, we can consider the first digit and then the next digits, one by one.First digit: The first digit can be any of the digits 1, 2, 4, 5, 7, 8, 9. (The digits 0, 3, 6 are not allowed as they are multiples of 3.)Second digit: After the first digit, the second digit cannot be equal to the first digit plus 3.For example, if the first digit is 1, the second digit cannot be 4. Hence, the second digit can be any of the digits except the ones that are 3 greater than the first digit. So, there are 6 possible digits for the second digit.Third digit: The third digit also cannot be equal to the second digit plus 3. So, there are 6 possible digits for the third digit.Fourth digit: The fourth digit can be any of the digits except the one that is 3 greater than the third digit. So, there are 6 possible digits for the fourth digit.Now, we can multiply the number of possibilities for each digit to find the total number of positive four-digit integers that satisfy the given condition:7 * 6 * 6 * 6 = 720.Hence, there are 720 positive four-digit integers that satisfy the given condition.To learn more about consecutive digit refer:
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Rewrite the expression in the form k•y^n
Answer= 6 and 7/y6 this will be the correct answer
Please Need Help ASAP!!
a) The time for the battery to be 40% charged is given as follows: 48 minutes.
b) The charge in 1 hour and 48 minutes is given as follows: 90%.
What is a proportional relationship?A direct proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The constant for this problem is given as follows:
k = 10/12 = 30/36 = 5/6.
Hence the equation is given as follows:
y = 5x/6.
The battery will be 40% charged when y = 40, hence:
5x/6 = 40
5x = 40 x 6
5x = 240
x = 240/5
x = 48 minutes.
1 hours and 48 minutes is equivalent to 108 minutes, hence the charge is given as follows:
y = 5 x 108/6
y = 90%.
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