The sum of a digit and a 2digit number is 7,when the digit is interchanged. The later is 9 greater than the former, find the digit

Answer:

2.83 seconds

Step-by-step explanation:

In the given equation, h represents the height (in feet) of the rock above the river at time t seconds after it is dropped, and the equation is h = -16t^2 + 128.

When the rock reaches the river, its height above the river will be zero. So, we can set h = 0 in the equation and solve for t:

0 = -16t^2 + 128

Dividing both sides by -16, we get:

t^2 = 128/16

t^2 = 8

Taking the square root of both sides, we get:

t = ±√8

Since time cannot be negative, we take the positive square root:

t = √8 ≈ 2.83 seconds

Therefore, it will take the rock approximately 2.83 seconds to reach the river.

The group which completes the given work in 13 days is Group A with members of P, Q, and R.

Total number of men = 4

P, Q, R, S.

Let us consider that S takes 1 unit of time to complete the work.

Then, the time taken by each of the other men to complete the work as follows,

R takes 3 units of time to complete the work.

Q takes 9 units of time to complete the work.

P takes 27 units of time to complete the work.

Let the group that completes the work in 13 days be called Group A.

and the group that completes the work in 31 days be called Group B.

Let us assume that Group A consists of P, Q, and R,

Group B consists of S, Q, and R.

Group C consists of P, Q, S.

The total work done by the two groups is the same.

Let us consider that the total work is 1 unit.

Then, the amount of work done by Group A in 1 day is,

=   1/((1/27)+(1/9)+(1/3))

= 1/((1 + 3 + 9 )/ 27)

= 27/13

The amount of work done by Group B in 1 day is,

= 1/((1/1)+(1/9)+(1/3))

= 1/((9+3+1)/9)

= 9/13

The amount of work done by Group C in 1 day is,

=  1/((1/27)+(1/9)+(1/1))

= 1/((1 + 3 + 27 )/ 27)

= 27/31

Group A completes 27/13 units of work in 1 day.

Group B completes 9/13  is equivalent to 27 / 39 units of work in 1 day.

and Group C complete 27/31 units of work in 1 day.

If we consider 27 as one unit.

Then Group A completes the work in 13 days.

And Group C completes the work in 31 days.

Therefore, the group that completes the work in 13 days is Group A, which consists of P, Q, and R.

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The discounted price of the hat at store A is $4.50 less than the discounted price of the hat at store B.

Given information:

Two stores each advertise a discount on the same type of hat at both stores.

The original price of the hat was $45 store A discounted the price of the hat by 25% store B discounted the price of the hat by 15%.

The discount at store A is 25% off $45, which is $11.25. So the discounted price at store A is $33.75 ($45 - $11.25).

The discount at store B is 15% of $45, which is $6.75. So the discounted price at store B is $38.25 ($45 - $6.75).

The difference between the discounted price at store A and store B is $38.25 - $33.75 = $4.50.

Therefore, the discounted price of the hat at store A is $4.50 less than the discounted price of the hat at store B.

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The value of the function (f - g)(x) is given as -

(f - g)(x) =  4x³ + 7x² - 6x + 1.

The given functions are -

f(x) = 4x³ +7x² - 2x - 1

g(x) = 4x - 2

We can write the function (f - g)(x) as -

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 4x³ + 7x² - 2x - 1 - (4x - 2)

(f - g)(x) = 4x³ + 7x² - 2x - 1 - 4x + 2

(f - g)(x) =  4x³ + 7x² - 6x + 1

Therefore, the value of the function (f - g)(x) is given as -

(f - g)(x) =  4x³ + 7x² - 6x + 1.

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The interval for which the ball's height is increasing is from 0 to 1.5 seconds

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

The graph

The interval for which the ball's height is increasing is when the graph values increase as the x-values increase

In this case, the interval is [0, 1.5]

Also, the seconds is represented by the x-axis

Hence, the interval for which the ball's height is increasing is from 0 to 1.5 seconds

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Answer: The given expression can be factorized as (2k - 3)(k² - 1) using the difference between squares.

Step-by-step explanation: To factorize the given expression using the difference between squares, we need to identify terms that can be written as the square of some other term.

We can rewrite the expression as:

(2k³ - 3k²) - (2k - 3)

Now, we can factor out the common terms from each bracket:

k²(2k - 3) - 1(2k - 3)

We can see that both brackets have a common factor of (2k - 3), which we can factor out:

(2k - 3)(k² - 1)

Therefore, the given expression can be factorized as (2k - 3)(k² - 1) using the difference between squares.

The quadratic equation of the graph is y = - 16 · x² + 12 · x + 1. (Correct choice: C)

In this question we know the graph of a quadratic equation, whose expression is described below:

y = a · x² + b · x + c, where a, b, c are real coefficients.

According to algebra, we can find the values of the real coefficients by knowing three distinct points of the graph. If we know that (x₁, y₁) = (0, 1), (x₂, y₂) = (0.4, 3.25) and (x₃, y₃) = (0.826, 0), then the coefficients of the quadratic equations are, respectively:

1 = c

3.25 = 0.16 · a  + 0.4 · b + c

0 = 0.683 · a + 0.826 · b + c

(a, b, c) = (- 16, 12, 1)

The quadratic equation is y = - 16 · x² + 12 · x + 1

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After set s1.addAll(s2), set s2 remains unchanged as [2, 3, 6]. Only set s1 is modified and becomes [1, 2, 5, 2, 3, 6].

After executing the operation s1.addAll(s2) on the sets s1 and s2, where s1 is [1, 2, 5] and s2 is [2, 3, 6], the set s2 remains unchanged. So, after s1.addAll(s2), s2 is still [2, 3, 6] and only set s1 is modified and becomes [1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

The addAll() method only affects the set it is called on, which is s1 in this case, by adding all elements from the specified set (s2) that are not already present in the original set (s1).

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A system of linear inequalities represented by the graph include the following:

Inequality 1: y ≥ -3x + 2

Inequality 2: y ≥ 2x/3 - 2

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

0 2 1 -1

First, we would determine the slope of line 1;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 - 2)/(1 - 0)

Slope (m) = -3/1

Slope (m) = -3.

At data point (0, 2) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -3(x - 0)

y = -3x + 2

y ≥ -3x + 2 (since the solid line is shaded above)

For line 2, we have:

Slope (m) = (0 + 2)/(3 - 0)

Slope (m) = 2/3

y - 0 = 2/3(x - 3)

y = 2x/3 - 2

y ≥ 2x/3 - 2 (since the solid line is shaded above)

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21

Step-by-step explanation:

4×5=20

Means greater than 20

5×5=25 and less than 25

So you can check it by dividing all the 4 numbers 21,22,23,and 24 with 5 the correct answer will be which has 1 as reminder.

Factors contributing to gauge variability in a measurement systems experiment include the gauge, operator, and parts being measured, and can be quantified and controlled through methods such as ANOVA, gauge R&R studies, operator training and procedures.

There are several factors that can contribute to gauge variability in a measurement systems experiment, including the gauge itself, the operator using the gauge, and the parts being measured.

These factors can be quantified and controlled for through methods such as analyzing variance components using ANOVA, conducting gauge R&R studies to estimate repeatability and reproducibility, and implementing training and standard operating procedures for operators.

Additionally, proper maintenance and calibration of the gauge can help reduce variability.

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The complete question is :

What are the factors that contribute to gauge variability in a measurement systems experiment, and how can they be quantified and controlled for?

The correct answer is: option (A) . Since the data is categorical and discrete, a bar graph is the most appropriate way to display the data

What is bar graph ?

A bar graph, also known as a bar chart, is a graphical representation of data in which the data is presented using rectangular bars. The length or height of each bar is proportional to the value that it represents.

The correct answer is: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44.

Since the data is categorical and discrete, a bar graph is the most appropriate way to display the data. The bars should be labeled with the sports and their corresponding heights should be the number of students who chose that sport.

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Answer:

Step-by-step explanation:

The equation of the parabola is:y = -13/36(x + 2)^2 + 5.

What is equation?

Equation is a mathematical statement that two expressions are equal. It is written as an expression that shows the equality of two values using mathematical symbols. Equations are used to solve problems by finding the unknown value. They are used in almost all branches of mathematics, and help to explain the behavior of physical and chemical systems.

The equation of a parabola with vertex (x_0,y_0) and that passes through (x_1,y_1) can be expressed as

y = a(x - x_0)^2 + y_0

where a is a constant.

In this case, the vertex of the parabola is (-2, 5) and it passes through (4, -8). We can substitute these values for x_0, y_0 and x_1, y_1 into the equation to get:

y = a(x - (-2))^2 + 5

We can solve for a by substituting the coordinates of the given point (4, -8) into the equation:

-8 = a(4 - (-2))^2 + 5

-8 = a(6)^2 + 5

-8 = 36a + 5

-13 = 36a

a = -13/36

Therefore, the equation of the parabola is:

y = -13/36(x + 2)^2 + 5

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Solutions of the  system of equations are x = -5 and y = -35

The substitution method is a technique used to solve systems of linear equations. It involves solving one of the equations for one variable in terms of the other and then substituting that expression into the other equation.

This results in a single equation in one variable, which can then be solved to find the value of that variable.

Here we have

y =  −7x and y = −5x+10  

The given equations can be solved using the Substitution method as follows

=>  − 5x+10 = −7x

=> 7x − 5x = − 10    [ Adding 7x on both sides ]

=> 2x = − 10

=> x = − 5               [ Dividing by 2 into both sides ]

Hence,  y =  −7x = −7 (− 5) =  − 35

Therefore,

Solutions of the  system of equations are x = -5 and y = -35

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Complete Question:

Solve the system by substitution.  y =  −7x and y = −5x+10  

At the end of the additional 20-minute period, there are approximately 18.71 pounds of salt in the tank.

Let's denote the amount of salt in the tank at any time t by Q(t), measured in pounds.

Initially, the tank contains 0 pounds of salt. Then, water containing 0.8 lb of salt per gallon is poured into the tank at a rate of 8 gal/min for 20 min, so the total amount of salt added to the tank during this time is

Q₁ = (0.8 lb/gal) × (8 gal/min) × (20 min) = 128 lb

The total volume of water in the tank after 20 minutes is

V₁ = 100 gal + (8 gal/min) × (20 min) = 260 gal

So the concentration of salt in the tank at this point is

C1 = Q₁ / V₁ = 128 lb / 260 gal = 0.4923 lb/gal

During the next 20 minutes, fresh water is poured into the tank at a rate of 8 gal/min, and the mixture is allowed to leave at the same rate. Since the tank initially contains 260 gallons of water, and 8 gallons are leaving every minute, we can see that the total volume of water in the tank during this time is

V₂ = 260 gal - (8 gal/min) × (20 min) = 100 gal

This means that the tank is back to its initial volume of 100 gallons, and all the water in it is fresh. However, there is still some salt left in the tank. We need to find the amount of salt Q₂ in the tank at the end of this period.

During the second 20-minute period, no salt is added to the tank, so the amount of salt in the tank is decreasing only due to the outflow of the mixture. We can use the formula

Q(t) = Q₀ × [tex]e^{-kt}[/tex]

where Q0 is the initial amount of salt (in our case, Q₁), k is the rate constant (which we need to find), and t is the time. We know that Q(20) = Q1 × [tex]e^{-k20}[/tex] is the amount of salt in the tank at the end of the first 20 minutes, and we want to find Q(40), the amount of salt in the tank at the end of the second 20-minute period.

To find k, we can use the fact that the concentration of salt in the tank is decreasing at a rate of 0.8 lb/gal × 8 gal/min = 6.4 lb/min, which means that

dQ/dt = -C₁ × 8 gal/min = -3.14 lb/min

We can write this as

dQ/dt = -k × Q(t)

Substituting Q(t) = Q₁ × [tex]e^{-kt}[/tex] and C₁ = Q₁ / V₁, we get:

-k × Q₁ ×  [tex]e^{-kt}[/tex]  = -Q₁ × C₁ × 8 gal/min

Simplifying:

k = 0.0300

Now we can find Q(40) as

Q(40) = Q₁ × [tex]e^{-k40}[/tex] = 18.71 lb

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Answer:

First, we need to convert 11-11/1 months into a decimal number of months.

11-11/1 months = 11 - 1/1 = 10

Now we can calculate Tran’s dessert making rate:

152 desserts / 10 months = 15.2 desserts per month

So Tran’s dessert making rate is 15.2 desserts per month.

Step-by-step explanation:

Answer: the answer is /

Step-by-step explanation: due to the placement of the dots and how many there are there is 40 dots in total. which is the equivalent pixels to a backspace, therefore the answer is /

The correct equation for the area of the triangle is A= 1/2st sin(R).

We know that the Area of the triangle is (1/2) × Base × Height

The correct calculation for the area of the triangle.

Step 1: Use a formula to calculate the area.

Area = (1/2) × Base × Height

Here Base is s and the height is h

A = 1/2 hs     ...(1)

Step 2: Use the sine function to get the value of height h.

We know that Sin(R) = Perpendicular/Hypotenuses

Here perpendicular is h and the hypotenuse is t

sin(R) = h/t

h = t sin(R)

Step 3: Substitute the value of h in equation (1)

A = 1/2(t)(s)sin(R)

Therefore, the correct area of the triangle is A = 1/2 t s sin(R).

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The Answer is D

When you divide a negative by a positive the answer will be negative

When you divide negative by negative the answer will be positive

The number of weeks it will take Emma to afford the £4,104 cruise holiday, found using the ratio of the amount she earns is 12 weeks

A ratio is a relationship between two quantities indicating the number of times one item is contained in the other item, or contains the other item.

The amount of money Emma earns per hour = £9.50

The number of days Emma works per week = 6 days

Number of hours worked per day = 8 hours

The ratio in which Emma shares her wages with Joy = 3 : 1

The cost of the cruise holiday = £4,104

The number of weeks it will take Emma to afford the cruise holiday therefore can be found as follows;

The amount Emma saves per week = (3/4) × 8 × 6 × 9.50 = 342

The number of weeks needed to save = 4,104/342 = 12

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Without contention, mutations are modifications to the DNA sequence of an organism.

These alterations can alter the form or purpose of proteins which are mandatory for a range of biological activities. After a mutation takes places, its influence on a creature's phenotype -and consequently their fitness- can vary.

Beneficial mutations will augment the fitness of an organism, thus boosting its ability to conform to its habitat, not like with harmful mutations which diminish fitness and can result in incapability to survive and propagate. Inseparably, there exist neutral mutations which have no evident consequence on the organism's fitness.

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The different ways can he line the textbooks up on his bookshelf is 6

The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation.

Given that, Adam is organizing textbooks on his bookshelf. He has a Spanish textbook, a biology textbook, and a history textbook.

The number of ways to arrange n things = n!

Number of different books = 3

Number of different ways to arrange 3 different books = 3!

Number of different ways to arrange 3 different books = 3 x 2 x 1

Number of different ways to arrange 3 different books = 6

Hence, the different ways can he line the textbooks up on his bookshelf = 6

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Comparing the z-scores, a score of 94 on a test with a mean of 72 and a standard deviation of 11 is relatively better than a score of 687 on a test with a mean of 447 and a standard deviation of 150, as the z-score of the first test (2) is higher than the z-score of the second test (1.6).

To determine which score is relatively better, we will calculate the z-scores for both test results using the given mean and standard deviation values. A z-score represents how many standard deviations a data point is away from the mean. The higher the z-score, the better the performance relative to the mean.

For the first test:
1. Subtract the mean (72) from the score (94): 94 - 72 = 22
2. Divide the difference (22) by the standard deviation (11): 22 / 11 = 2

The z-score for the first test is 2.

For the second test:
1. Subtract the mean (447) from the score (687): 687 - 447 = 240
2. Divide the difference (240) by the standard deviation (150): 240 / 150 = 1.6

The z-score for the second test is 1.6.

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The speed or velocity of the tsunami is determined as 0.027 m/s.

The velocity or speed of the wave is calculated from the ratio of the wavelength and time of motion.

Mathematically, the formula for the velocity of a wave is given as;

V = λ/t

where;

If the amplitude is 12 m, and low depth is another 12 m, then the wavelength = 24 m

V = 24 m / (15 min x 60 s)

V = 0.027 m/s

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Find the velocity of the tsunami

As per the mentioned informations, the probability that x has a value of at least 95 is calculated to be 0.2 or 20%.

Since x is uniformly distributed between 75 and 100, the probability density function (PDF) of x is given by:

f(x) = 1/(100-75) = 1/25 for 75 ≤ x ≤ 100

To find the probability that x has a value between 80 and 90, we need to calculate the area under the curve between x = 80 and x = 90:

P(80 ≤ x ≤ 90) = ∫[from 80 to 90] f(x) dx

= ∫[from 80 to 90] 1/25 dx

= [1/25 × x] [from 80 to 90]

= (90-80)/25

= 0.4

Therefore, the probability that x has a value between 80 and 90 is 0.4 or 40%.

To find the probability that x has a value of at least 95, we need to calculate the area under the curve to the right of x = 95:

P(x ≥ 95) = ∫[from 95 to 100] f(x) dx

= ∫[from 95 to 100] 1/25 dx

= [1/25 × x] [from 95 to 100]

= (100-95)/25

= 0.2

Therefore, the probability that x has a value of at least 95 is 0.2 or 20%.

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The probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game is 0.0196. 

We know that the normal time between pulled hamstring muscles is 342 minutes. Subsequently, the rate parameter λ for the exponential dissemination is:

λ = 1/342

(a) To discover the likelihood that the group will drag a hamstring muscle within the next amusement, we got to discover the likelihood that a pulled hamstring muscle happens within 90 minutes.

Let X be the time (in minutes) until the following pulled hamstring muscle. At that point, X takes after an exponential dispersion with rate parameter λ = 1/342.

P(X < 90) = 1 - [tex]e^[/tex](-λ * 90) = 1 - [tex]e^[/tex](-90/342) ≈ 0.2638

Subsequently, the likelihood that the group will drag a hamstring muscle within another amusement is roughly 0.2638.

(b) To discover the likelihood that the team will involve a pulled hamstring muscle between the 15th and 25th miniature of the diversion, we got to discover the likelihood that a pulled hamstring muscle happens between 15 and 25 minutes.

Let Y be the time (in minutes) until the another pulled hamstring muscle.

P(15 < Y < 25) = [tex]e^[/tex](-λ * 15) - [tex]e^[/tex](-λ * 25) =[tex]e^[/tex](-15/342) - [tex]e^[/tex](-25/342) ≈ 0.0196

In this manner, the likelihood that the group will involve a pulled hamstring muscle between the 15th and 25th diminutive of the amusement is roughly 0.0196. 

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The slope of the line is equal to 1.

The formula for the point-slope form of the equation is y + 2 = (x + 2).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 + 2)/(2 + 2)

Slope (m) = 4/4

Slope (m) = 1.

At data point (-2, -2) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 1(x - (-2))  

y + 2 = (x + 2)

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The probability of getting a diamond or a king from a standard 52-card deck is 4/13.

In mathematics, probability is a measure of the likelihood that an event will occur. It is a way to quantify the chances of different outcomes or events in a random experiment or process. Probability is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event

In a standard deck of 52 cards, there are 13 diamonds and 4 kings. However, the king of diamonds is also a diamond, so we must subtract one from the total count to avoid double-counting.

So there are 13 + 4 - 1 = 16 cards that are either diamonds or kings.

The probability of picking a diamond or a king is therefore 16/52.

Simplifying the fraction, we get:

16/52 = 4/13

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The new amount for Jim's hourly rate is A = $ 15.40

Given data ,

To find Jim's new hourly rate after a 10% raise, we need to add 10% of his current hourly rate to his current hourly rate.

Let's call Jim's current hourly rate "x".

10% of x is 0.10x, so the new hourly rate would be:

x + 0.10x = 1.10x

Therefore, Jim's new hourly rate would be:

On simplifying the equation , we get

$14 x 1.10 = $15.40

Hence , Jim's new hourly rate would be $15.40

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The paired t-test this test is appropriate for comparing the means of two interval variables drawn from related populations, where related means that the same subjects or matched subjects were used in each group.

The paired t-test compares the means of the two variables by calculating the difference between the pairs of scores and then calculating the mean difference.

It then determines whether the mean difference is significantly different from zero using a t-test.

Hence, the appropriate test for comparing the scores of two interval variables drawn from related populations is the paired t-test. It compares the means of the two variables by calculating the difference between the pairs of scores and then determining whether the mean difference is significantly different from zero using a t-test.

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