7x – 5(х + 8) = 5х – 28​
Step-by-step PLEASE!!!!

Answer:

From 11 am until 2 pm

Step-by-step explanation:

The line is straight meaning its constant throughout the time 11pm - 2pm, it is neither rising nor falling like the other two.

Answer:

James = 119 points

Sarah = 357 points

Roberts = 51 points

Step-by-step explanation:

Given that :

James = x points

Sarah = 3x points

Roberts = x - 68 points

Each point = 3 pence

All students have a total of £15.81

1 pound = 100 pence

£15.81 pound = 1581 pence

3x + 3(3x) + 3(x - 68) = 1581

3x + 9x + 3x - 204 = 1581

15x - 204 = 1581

15x = 1581 + 204

15x = 1785

x = 1785 / 15

x = 119

Hence,

James = 119 points

Sarah = 119 * 3 = 357 points

Roberts = 119 - 68 = 51 points

Among the given statements, the following statement "Compared with location A, the miles were driven for location B display more variability and the median is greater" provides the best comparison of the two locations.

Hence, option (C) is the correct choice.

For finding the interquartile range for location, first, find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.

The interquartile range for location B is Q3 - Q1 = almost 140 - 40 = 100, while it is Q3 - Q1 = nearly 60 - 40 = 20 for location A.

Therefore, the miles travelled for position B are more variable than they are for place A.

Greater than Location A's almost 50 medians is Location B's nearly 80 median.

Therefore, location B's median miles driven is higher than it is for location A.

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The average rate of change of the function f(x) on the interval [1, 4] is:

R = 3.

After a small search online, I found that the table for the function f(x) is:

x  f(x)

0   1

1    4

2   7

3   10

4   13

5   16

For any function f(x), we define the average rate of change on an interval [a, b] as:

R = ( f(b) - f(a))/(b - a)

In this case we want to find the average rate of change on the interval  1≤x≤4, then we will get:

R = ( f(4) - f(1))/(4 - 1)

Using the table we can see that:

f(4) = 13

f(1) =  4

Then the average rate of change is:

R = ( f(4) - f(1))/(4 - 1)

R = ( 13 - 4)/(4 - 1) = 9/3 = 3

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Answer:

28 blocks are filled in so I don't know how this a decimal... maybe it's .28

Step-by-step explanation:

Answer:

50, positive

Step-by-step explanation:

(-5) * (-10) = 50

When a negative multiplies by another negative, the answer is positive

So, the answer is 50 and the sign is positive

After 4 years ratio of their ages be 2 : 1

How do you calculate the ratio?

The steps of calculating a ratio are as follows:

Establish the ratio's function. Choosing what you want your ratio to show should be your first step. Every ratio will use a different set of data, so you need to make sure you are using the right data to provide you with the information you need.

Organize your formula. Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.

Make the equation work. To calculate your ratio, divide data A by data B.

Let the present age of pete be P and claire be C.

According to question:

Two years ago pete was three times as old as his cousin claire.

⇒ P - 2 = 3(C - 2)

⇒ P - 2 = 3C - 6

⇒ P = 3C - 6 + 2

⇒ P = 3C - 4 ..................(1)

Also,  2 years before that, pete was four times as old as claire.

⇒ P - 4 = 4(C - 4)

⇒ P - 4 = 4C - 16

⇒ P = 4C - 16 + 4

⇒ P = 4C - 12 ..................(2)

Equating eq(1) and eq(2)

4C - 12 = 3C - 4

4C - 3C = -4 + 12

C = 8

Substitute the value of C in eq(1) we get,

P = 3(C) - 4 = 3(8) - 4 = 24 - 4 = 20

Let x be the number of years until Pete is twice as old as his cousin.

20 + x = 2(8 + x)

20 + x = 16 + 2x

20 - 16 = 2x - x

4 = x

Therefore, after 4 years ratio of their ages be 2 : 1

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The total distance traveled by the particle over the time interval [1, 5] is 12 units.

To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.

To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit

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Answer:

$24.42

Step-by-step explanation:

3.14*r^2= area

3.14*1.2^2=4.52

5.40*4.52=24.42

Answer:

Step-by-step explanation:

Remark

First find the area of the circular piece of fabric. Then deal with cost per square foot.

Area of the fabric

Area =  pi * r^2

Area = 3.14 * 1.2^2

Area = 3.14 * 1.44

Area = 4.5216 square feet

Cost

1 square foot costs 5.40 dollars

4.5216 square feet costs x                   Cross multiply

x = 5.40 * 4.5216

Answerx = 24.42 dollars for the fabric bought.

Answer:

4860

Step-by-step explanation:

Get the product of twenty and three, then multiply that to three again, repeat this for three more times.

The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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Answer:

57.142%

Step-by-step explanation:

28-12=16

16/28*100=57.142%

Step-by-step explanation:

Event A is a certain event because with 14 girls and only 12 months in a year, by the pigeonhole principle, there must be at least two girls who were born in the same month.

Event B is an elementary event because there is only one part labeled with the number 10 out of 75 parts in the box, so the probability of drawing that part is 1/75.

The relative frequency of hits is calculated by dividing the number of hits by the total number of shots. In this case, it is 20/25.

The relative frequency of boys born in that month is calculated by dividing the number of boys born by the total number of births. In this case, it is 43/100.

There are four balls labeled with numbers divisible by 3 (3, 6, 9, and 12) out of twelve balls in total. So the probability of drawing a ball with a number divisible by 3 is 4/12 = 1/3.

The probability that a part is not of good quality is equal to 1 minus the probability that it is of good quality. In this case, it is 1 - 0.75 = 0.25.

The probability that at least one coin lands heads up is equal to 1 minus the probability that both coins land tails up. The probability that both coins land tails up is (1/2) * (1/2) = 1/4. So the probability that at least one coin lands heads up is 1 - 1/4 = 3/4.

A fair die has six equally likely outcomes when rolled. So the probability of rolling a 2 is 1/6.

A deck of cards containing 36 cards has four suits: clubs, diamonds, hearts, and spades. Each suit has nine cards, so there are nine spades in the deck. So the probability of drawing a spade is 9/36 = 1/4.

There are two white marbles and ten marbles in total in the bag. So the probability of randomly selecting a white marble is 2/10 = 1/5.

There are four ways to roll two dice and get a sum of five: (1,4), (2,3), (3,2), or (4,1). Each outcome has a probability of (1/6) * (1/6) = 1/36. So the probability that the sum of the numbers rolled is five is 4 * (1/36) = 1/9.

If Jānis throws a ball into the basket with a probability of 0.68 and he makes 50 throws, we can expect him to throw the ball into the basket about 0.68 * 50 = 34 times.

The probability that at least one die shows four points when two dice are rolled can be calculated as one minus the probability that neither die shows four points: P(at least one die shows four points) = = 1 - P(neither die shows four points) = 1 - P(first die does not show four points) * P(second die does not show four points) = 1 - (5/6) * (5/6) =11/36

If two events are independent, then the probability that both events occur simultaneously can be calculated as the product of their probabilities: P(both machines need to be regulated within an hour) = = P(first machine needs to be regulated within an hour) * P(second machine needs to be regulated within an hour) =0.8 *0.7 =0.56

15.The area of a circle is proportional to the square of its radius so if we consider each ring as a target then their areas will be proportional to R^2 and (4R)^2 respectively. The ratio between these areas will be R^2 : (4R)^2 = R^2 :16R^2 =1:16 So if we consider each unit area as having an equal chance to be hit then we have: P(the shot hit the smaller ring)= Area(smaller ring)/(Area(smaller ring)+Area(larger ring))=1/(16+1)=1/17

16.There are four winning tickets out of twenty tickets in total in a lottery so if Ilze buys one ticket then her chance to get a winning ticket will be: P(Ilze’s ticket is a winning ticket)= Number of winning tickets / Total number of tickets=4/20=1/5

17.The day on which someone was born can be any day from Monday to Sunday with equal chances so if we consider two friends then: P(both friends were born on Saturday)=P(first friend was born on Saturday)P(second friend was born on Saturday)=(1/7)(1/7)=1/49

18.The student knows seven out of eight questions so if two questions are included in a test then his chance to know both questions will be: P(the student knows both questions)= Number of ways to choose two known questions / Number of ways to choose any two questions=(7 choose 2)/(8 choose 2)=21/28=3/4

19.There are four cards labeled with letters A,P,S,E so if three cards are drawn successively without replacement then there will be: Number of ways to draw three cards=Number of ways to draw first cardNumber of ways to draw second cardNumber of ways to draw third card=432=24 The only way for these cards to be drawn in order A,P,E will be if they are drawn successively as A,P,E so: P(the cards are drawn in order A,P,E)=Number of ways for cards to be drawn in order A,P,E / Number of ways for any three cards to be drawn=1/24

20.Two dice have six faces each so when they are rolled simultaneously there will be: Number of possible outcomes=Number of faces on first dieNumber of faces on second die=66=36 None of these outcomes will result in a sum equal to fourteen so: P(the sum of numbers rolled equals fourteen)=0

Answer:

A: y = -4/5x + 3/2 i believe is the correct answer

Step-by-step explanation:

Answer: its associative property Hope I helped

Step-by-step explanation:

The woman at the dinner party consumed 24 fluid ounces of wine containing approximately 4.8 standard drinks assuming the wine had an alcohol content of 12%. She exceeded the recommended limit for moderate drinking on that day.

Assuming each glass of wine contained 8 fluid ounces, the woman consumed a total of 24 fluid ounces of wine throughout the evening.

To determine the number of standard drinks ingested, we need to know the alcohol content of the wine. In the United States, a standard drink is defined as containing 0.6 fluid ounces or 14 grams of pure alcohol.

Assuming the wine had an alcohol content of 12% (which is a typical percentage for table wine), we can calculate the number of standard drinks ingested by using the following formula:

Number of standard drinks = (Volume of alcohol consumed in ounces x % alcohol by volume) / (0.6 ounces of alcohol per standard drink)

Number of standard drinks = (24 fl oz x 0.12) / 0.6 fl oz

Number of standard drinks = 4.8

Therefore, the woman consumed approximately 4.8 standard drinks.

To determine if she drank alcohol in moderation, we need to consider the recommended limits for moderate drinking. According to the National Institute on Alcohol Abuse and Alcoholism, moderate drinking is defined as up to one drink per day for women.

Since the woman consumed 4.8 standard drinks in one evening, she exceeded the recommended limit for moderate drinking for that day.

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The correct choice for x(t) is: OA X = 3t - (C₁/2)\(e^{4t}\) + (C₂/4)\(e^{8t}\) + K. To solve the given system of differential equations using the elimination method, we'll start by isolating x from the first equation.

x' = 6x - y ...(1)

y' = 6y - 4x ...(2)

From equation (1), we can rearrange it to isolate y:

y = 6x - x' ...(3)

Now, we substitute this expression for y in equation (2):

y' = 6(6x - x') - 4x

y' = 36x - 6x' - 4x

y' = 32x - 6x' ...(4)

Now we have a single differential equation for y, which we can solve.

Differentiating equation (3) with respect to t, we get:

y' = 6x' - x'' ...(5)

Substituting equation (5) into equation (4):

6x' - x'' = 32x - 6x'

x'' - 12x' + 32x = 0 ...(6)

Now we have a second-order linear homogeneous differential equation for x. To solve this, we assume a solution of the form x(t) = e^(rt). Substituting this into equation (6):

r² - 12r + 32 = 0

Factoring the quadratic equation, we have:

(r - 4)(r - 8) = 0

This gives us two roots: r = 4 and r = 8.

Therefore, the general solution for x(t) is:

x(t) = C₁ \(e^{4t}\)+ C₂\(e^{8t}\)  ...(7)

Now, let's find the solution for y(t) using equation (3) and the values of x(t) from equation (7). Substituting x(t) into equation (3):

y = 6x - x'

y = 6(C₁ \(e^{4t}\) + C₂\(e^{8t}\)) - (4C₁ \(e^{4t}\) + 8C₂\(e^{8t}\))

y = 2C₁ \(e^{4t}\) - 2C₂\(e^{8t}\)  ...(8)

Therefore, the general solution for y(t) is:

y(t) = 2C₁ \(e^{4t}\)- 2C₂\(e^{8t}\)

The correct answer for the solution to the system of differential equations is:

OB. y(t) = 2C₁ \(e^{4t}\)       - 2C₂\(e^{8t}\) \(e^{4t}\)

Since we have found the general solutions for both x(t) and y(t), the system is not degenerate.

To find x(t), we can substitute the expression for y(t) from equation (8) into equation (3):

y = 6x - x'

2C₁\(e^{4t}\) - 2C₂\(e^{8t}\) = 6x - x'

Simplifying and rearranging this equation, we get:

x' = 6x - 2C₁\(e^{4t}\) + 2C₂\(e^{8t}\)

Now, we can integrate both sides to find x(t):

∫x' dt = ∫(6x - 2C₁\(e^{4t}\)  + 2C₂\(e^{8t}\) ) dt

x = 3xt - (C₁/2)\(e^{4t}\) + (C₂/4)\(e^{8t}\) + K

Therefore, the general solution for x(t) is:

x(t) = (3t - (C₁/2)\(e^{4t}\) + (C₂/4)\(e^{8t}\) + K)

The correct choice for x(t) is:

OA X = 3t - (C₁/2)\(e^{4t}\) + (C₂/4)\(e^{8t}\) + K.

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The balance increase for card i is $89.24 greater than the balance increase for card h. Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt)

Given, Card h has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually.

Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt),

where A = final amount, P = principal (initial balance), r = annual interest rate (as a decimal), n = number of times compounded per year, t = time (in years)

For card h,

A = 1186.44(1 + 0.1474/1)^(1*3)

A = 1883.99

For card i, A = 1522.16(1 + 0.1205/12)^(12*3)

A = 1973.23

Therefore, the balance for card i will have increased more than that of card h, and the difference in the increase is: 1973.23 - 1883.99 = 89.24

The balance increase for card i is $89.24 greater than the balance increase for card h. Hence, the required answer is card i.

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The technique often used to prove the correctness of a recursive function is **mathematical induction**.

Mathematical induction is a method of proof used to establish that a property holds for all natural numbers (or a well-ordered set). It consists of two steps:

1. **Base Case**: The base case establishes that the property holds for a specific initial value or base case. It typically involves showing that the property is true for the smallest possible input or base case of the recursive function.

2. **Inductive Step**: The inductive step demonstrates that if the property holds for a specific value, it also holds for the next value. This step involves assuming that the property is true for a certain input, and then proving that it holds for the subsequent input using the recursive definition of the function.

By proving that the base case is true and showing that the inductive step holds, mathematical induction establishes the correctness of a recursive function for all valid inputs.

The other options you mentioned, such as commutativity, diagonalization, and matrix multiplication, are not directly related to proving the correctness of recursive functions. Commutativity refers to the order of operations or elements, diagonalization is a technique used in mathematics and logic, and matrix multiplication is a mathematical operation for matrices. While these concepts may have applications in other areas of mathematics and computer science, they are not specifically used for proving the correctness of recursive functions.

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Answer:

1 square and 3 circles

Step-by-step explanation:

that is the circumference of its circular base.

\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=9\\ V=27\pi \end{cases}\implies 27\pi =\cfrac{\pi r^2 (9)}{3}\implies 27\pi =3\pi r^2 \\\\\\ \cfrac{27\pi }{3\pi }=r^2\implies 9=r^2\implies \sqrt{9}=r\implies \underline{3=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \qquad C=2\pi (\underline{3})\implies C=6\pi\)

The circumference of the cone will be;

⇒ 6π

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The volume of a right cone = 27π units³

And, The height = 9 units

Now,

Since, We know that;

The volume of cone = πr²h / 3

⇒ 27π = π × r² × 9 / 3

⇒ 27 = r² × 3

⇒ r² = 27/3

⇒ r² = 9

⇒ r = 3

Since, The circumference of the cone = 2πr

                                                            = 2 × π × 3

                                                            = 6π

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Answer:

60

Step-by-step explanation:

0.2x = 12

x=60

:]

Answer: 16 is the correct answer

Step-by-step explanation:

Answer:

18:25

Step-by-step explanation:

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 90 and 125 is 5

Divide both terms by the GCF, 5:

90 ÷ 5 = 18

125 ÷ 5 = 25

The ratio 90 : 125 can be reduced to lowest terms by dividing both terms by the GCF = 5 :

90 : 125 = 18 : 25

Therefore:

90 : 125 = 18 : 25

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Answer:

379-68=p

Step-by-step explanation:

379 is the total number of tissues. If you take away the single pack tissues then you will have the amount of three pack tissues

The correct equation that shows the number of tissue three-packs, p, Johnson's sold in January is, p = 379 - 68.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that,

At Johnson's Pharmacy, tissue boxes can be purchased as single boxes or in packs of three boxes.

Here, During January, Johnson's sells a total of 379 boxes of tissues, 68 as single boxes, and the rest in three-packs.

Let us assume that, the number of tissue three-packs = p

Hence we get;

p = 379 - 68

p = 311

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In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.

The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:

t = (P - μ) / (s / √n)

Plugging in the given values:

t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2

Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.

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Answer:

Step-by-step explanation:

y= 1x-1

Slope= 1

Y intercept= -1

Answer:

Step-by-step explanation:

Slope m = (5 - 1) / (6 - 2) = 1

y - 1 = 1(x - 2)

y = x - 1 Slope intercept form of linear equation

y-intercept is ( - 1)

x - y = 1 Standard form of linear equation

Hi! I'd be pleased to assist you with your permutations, probability, and position-related query. If a set of 24 children—14 boys and 10 girls—were lined up in a random order, what is the likelihood that the child in the 16th spot is a boy?

Step 1: Compute all possible combinations for the 24 children.

There are 24 children, hence there are 24 possible permutations in all! (Factorial, 24).

Step 2: Determine how many permutations there are with a boy in the sixteenth place.

Consider that there are currently 23 seats available for the remaining 13 boys and 10 girls to do this. The remaining children can be set up in 23! (23 factorial) different ways as a result.

Step 3: Use a to divide the permutations.

Step 4: Calculate the probability.
Probability = (Permutations with a boy in the 16th position) / (Total permutations)
Probability = (14 * 23!) / (24!)

Now, to simplify this expression, we can divide both the numerator and the denominator by 23!:
Probability = (14 * 23!) / (24! * 23! / 23!)
Probability = 14 / 24

Step 5: Simplify the probability.
Probability = 7/12

So, the probability that the person in the 16th position is a boy is 7/12.

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To find the probability that the person in the 16th position is a boy, we need to first calculate the total number of possible permutations in which any person can be in the 16th position. This can be calculated using the formula for permutation, which is n!/(n-r)!, where n is the total number of people and r is the number of positions.

So, the total number of permutations for 24 people in random order is 24!/(24-1)! = 24!

Next, we need to find the number of permutations in which a boy is in the 16th position. Since there are 14 boys and 10 girls, we can choose one of the 14 boys for the 16th position and then arrange the remaining 23 people in any order. This can be calculated using the formula for combination, which is nCr = n!/(r!(n-r)!), where n is the total number of items and r is the number of items chosen.

So, the number of permutations with a boy in the 16th position is 14C1 * 23! = 14 * 23!

Therefore, the probability of a boy being in the 16th position is the number of permutations with a boy in the 16th position divided by the total number of permutations, which is:

(14 * 23!)/24! = 14/24 = 7/12

In conclusion, the probability that the person in the 16th position is a boy is 7/12.

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