4(x+3)=4x+12
Please help me

Answer:

125

Step-by-step explanation:

58

+67

=125

sum is the same as addition

Answer:

125

Step-by-step explanation:

58 + 67

= (60-2) + (60+7)

= 60 - 2 + 60 + 7

= 2*60 + (7-2)

= 120 + 5

= 125

Answer:

The sum of all the sweets is 54 sweets

Step-by-step explanation:

Here, we want to calculate the number of sweets the three have altogether.

Let the number of sweet Faith has be x

Mathematically;

Faith has 4 sweets fewer than the average number of sweets

The average is the sum of all the sweets divided by 3

The average will be (10 + 30 + x)/3

Thus;

(10 + 30 + x)/3 - 4 = x

(40 + x)/3 = x + 4

40 + x = 3(x + 4)

40 + x = 3x + 12

40-12 = 3x -x

28 = 2x

x = 28/2

x = 14 sweets

So the sum of all the sweets would be 10 + 30 + 14 = 54 sweets

Answer:

14.5 - Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

each student gets 2 bars and a quarter of one (2.25 or 2 1/4)

Step-by-step explanation:

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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Convenience sampling is not a type of statistical sampling.

What is statistical sampling?

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study.

If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

Main body:

Simple random sample:

Each individual and group of individuals have the same chance of being selected for the sample. To obtain a basic random sample, one needs technology, random number generators, or some other type of chance mechanism.

stratified Random sample :

The population is first divided into sections. There are some people from each group in the overall sample. Each group's participants are chosen at random.

Cluster sampling:

Grouping the population first, a cluster random sample is taken. Every member of some of the groups makes up the overall sample. The selection of the groups is random.

Hence Convenience sampling is not a type of statistical sampling.

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Answer:

400

Step-by-step explanation:

The most accurate estimate among the given options is d) 400.

Given that we need to estimate the product of 38 x 9,

To find the product of 38 and 9, you can simply multiply the two numbers together:

38 x 9 = 342

Therefore, the actual product of 38 and 9 is 342.

Now, let's estimate the product using the given options:

a) 30: This is too low of an estimate. 38 is larger than 30, so the product should be greater than 30.

b) 50: This is also too low of an estimate. 38 multiplied by 9 is significantly larger than 50.

c) 120: This estimate is closer to the actual product, but still not accurate. 120 is smaller than the actual product of 342.

d) 400: This is a close estimate. 38 multiplied by 9 is close to 400.

In summary, the most accurate estimate among the given options is d) 400.

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Answer:

Obtuse angle

Step-by-step explanation:

That's the answer

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

The man's BMI is approximately 22.09 based on his weight of 154 pounds and height of 70 inches.

To calculate the Body Mass Index (BMI) of a person, we use the following formula:

BMI = weight (in kilograms) / height^2 (in meters)

First, we need to convert the weight from pounds to kilograms. Since 1 pound is approximately 0.4536 kilograms, the man's weight of 154 pounds is equal to 69.85 kilograms (rounded to two decimal places).

Next, we need to convert the height from inches to meters. Since 1 inch is equal to 0.0254 meters, the man's height of 70 inches is equal to 1.778 meters (rounded to three decimal places).

Now, we can calculate the BMI using the formula:

BMI = 69.85 kg / (1.778 m)^2

Calculating this expression, we find that the man's BMI is approximately 22.09 (rounded to two decimal places).

In summary, the man's BMI is approximately 22.09 based on his weight of 154 pounds and height of 70 inches.

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The  probability that the sample mean would differ from the true mean by greater than 158 dollars if a sample of 226 persons is randomly selected is 0.99

mean per capita income is 19,695 dollars per annum , μ = 19695

a variance of 802,816, σ² = 802816

Standard deviation σ = √802816= 896

Sample size = 226

To find the probability that the sample mean would differ from the true mean by greater than 158 dollars i.e. less than 19537 dollars and more than 19853 dollars.

The formula for z-score :-

\(z = \frac{x - mean}{\frac{\alpha }{\sqrt{n} } } \\\)

For x = 19537 dollars

\(z = \frac{19537 - 19695}{\frac{\ 896 }{\sqrt{226} } } \\\)

z = -2.65

For x = 19853 dollars

\(z = \frac{19853 - 19695}{\frac{\ 896 }{\sqrt{226} } } \\\)

z = 2.65

The P-value=

P(z < -2.65) + P(z > 2.65 = 2P(z > 2.65) = 2x. 0.495975

= 0.99

Therefore, the  probability that the sample mean would differ from the true mean by greater than 158 dollars if a sample of 226 persons is randomly selected is 0.99

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a. Approximately 84% of newborns have a respiratory rate within 1.2 standard deviations of the mean.

b. The probability that a newborn selected at random will have a respiratory rate higher than 55 beats per minute is approximately 15.87%.

c. Thirty percent of all newborns have a respiratory rate lower than approximately 47.38 breaths per minute.

d. Approximately 81.33% of samples of 5 newborns will have an average respiratory rate below 52 breaths per minute.

e. Approximately 10.2% of samples of 10 newborns will have an average respiratory rate above 52 breaths per minute.

f. Approximately 39.76% of samples of 10 newborns will have an average respiratory rate between 50 and 52 breaths per minute.

a. 84% of babies have respiratory rates within 1.2 standard deviations of the mean. The normal distribution can calculate this. Finding the area under the normal curve between 1.2 standard deviations above and below the mean gives us the proportion. The proportion of infants in this range is this area.

b. Calculate the area under the normal curve to the right of 55 to discover the probability that a randomly picked infant will have a respiratory rate higher than 55 beats per minute. The z-score formula (x - mean) / standard deviation helps standardise 55. The z-score is 55 - 50 / 5 = 1. Using a calculator or typical normal distribution table, the likelihood of a z-score larger than 1 is 0.1587. The probability is 15.87%, or 0.1587.

c. The 30th percentile z-score determines the respiratory rate below which 30% of neonates fall. 30th percentile z-score is -0.524. A conventional normal distribution table or calculator can identify the z-score associated with an area of 0.3 to the left of it. Multiplying the z-score by the standard deviation and adding it to the mean returns it to its original units. The respiratory rate is (z-score * standard deviation) + mean = (-0.524 * 5) + 50 = 47.38. 30% of neonates breathe less than 47.38 breaths per minute.

d. The average respiratory rate of 5 newborns will follow a normal distribution with the same mean but a standard deviation equal to the population standard deviation divided by the square root of the sample size, which is 5/sqrt(5) = 2.236. To compute the proportion of samples having an average respiratory rate < 52 breaths per minute, we require the z-score. The z-score is 0.8944. The likelihood of a z-score less than 0.8944 is around 0.8133 using a basic normal distribution table or calculator. Thus, 81.33% of 5 newborn samples will have a respiratory rate below 52 breaths per minute.

e. The average respiratory rate of 10 infants will follow a normal distribution with the same mean but a standard deviation of 5/sqrt(10) = 1.5811. We calculate the z-score using (52 - 50) / 1.5811 = 1.2649. The likelihood of a z-score larger than 1.2649 is 0.102. Thus, 10.2% of 10 babies will have a respiratory rate exceeding 52 breaths per minute.

f. Calculate the z-scores for both values to find the fraction of 10 babies with an average respiratory rate between 50 and 52 breaths per minute. (50 - 50) / 1.5811 = 0. (52 - 50) / 1.5811 = 1.2649. The chance of z-scores between 0 and 1.2649 is approximately 0.3976 using a basic normal distribution table or calculator. Thus, 39.76% of 10 newborn samples will have an average respiratory rate of 50–52 breaths per minute.

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Answer:

its 72, 36, 144

Step-by-step explanation:

yes it is!!!

Answer:

Step-by-step explanation:

Distance=400+200=600km

diplacement=x      200-0km=200km

total distance travelled=400+400=800km

Answer:

x = 27

Step-by-step explanation:

2(7 + 1)7 = (2x + 2)^2

2 (8) 7 = 4x + 4

(16) 7 = 4x + 4

112 = 4x +4

112 - 4 = 4x +4 -4

108 = 4x

108/4 = 4x/4

27 = x

or x = 27

Step-by-step explanation:

let's assume you really meant

2(7 + 1)7 = (2x + 2)²

2×8×7 = (2x + 2)(2x + 2)

112 = 4x² + 4x + 4x + 4 = 4x² + 8x + 4

let's divide everything by 4 to get a simpler equation :

28 = x² + 2x + 1

x² + 2x - 27 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so, in our case

x = (-2 ± sqrt(2² - 4×1×-27))/(2×1) =

= (-2 ± sqrt(4 + 108))/2 = (-2 ± sqrt(112))/2 =

= (-2 ± sqrt(16×7))/2 = (-2 ± 4×sqrt(7))/2 =

= -1 ± 2×sqrt(7)

x1 = -1 + 2×sqrt(7) = 4.291502622...

x2 = -1 - 2×sqrt(7) = -6.291502622...

so, that equation is only an identity for the 2 x-values we found.

for any other x-value it is not.

that is why I suspect you skipped or changed something in the original equation.

could it be it was

(2(x + 1))² = (2x + 2)²

then we would have

4(x + 1)² = 4(x² + 2x + 1) = 4x² + 8x + 4

4x² + 8x + 4 = 4x² + 8x + 4

the equality is given because

2(x + 1) = 2x + 2

please let me know, if it was something else. but given the wording in the question I doubt that your equation really was what you wrote, and what I solved in the first step.

Answer:

D

Step-by-step explanation:

First, we should find the equations of the two lines. The red line is just horizontal, and represents y = 4 while the blue line intersects the y-axis at -4 and every time it goes right one, it goes up 4, so it has a slope of four(also it looks kinda steep, so it cannot have a slope of 1/4). This means the equation is y = 4x - 4.

Notice the red line is dashed, that means the inequality is either less than or greater than. Also, the shaded part is below the vertical line, enclosing all the values of y less than 4, so the first inequality would be y < 4.

The blue line is solid, so it is either greater than or equal to or less than or equal to. To find out which one, we check to se where the point (0, 0) fits in:

y ? 4x - 4

0 ? 0 - 4

0 ? -4

Only a greater than or equal to sign would fit in: 0 ≥ -4

This means the answer is:

y < 4

y ≥ 4x - 4

which is option D

Answer:

Step-by-step explanation:

1)

The equation of a straight line:

y = k·x + b

x = 0

b = y = - 4

k = (y - y₀) / (x - x₀) = ( 4 - (-4)) / (2 - 0) =  8 / 2 = 4

y = 4·x - 4

2)

The equation of a straight line:

y = 4

3)

Shaded area:

y ≤ 4

y ≥ 4x - 4

Right answer:

D.

y ≤ 4

y ≥ 4x - 4

To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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Answer:

We can use trigonometric identities to simplify both sides of the equation and determine whether they are equal.

First, we can use the identity cos(2θ) = cos^2(θ) - sin^2(θ) to rewrite the left-hand side of the equation:

cos(2∅-18°) = cos^2(∅-9°) - sin^2(∅-9°)

Next, we can use the identity tan(θ) = sin(θ) / cos(θ) to rewrite the right-hand side of the equation:

tan 54° = sin 54° / cos 54°

Now we can substitute these expressions into the original equation and simplify:

cos^2(∅-9°) - sin^2(∅-9°) = sin 54° / cos 54°

Using the identity sin^2(θ) + cos^2(θ) = 1, we can rewrite the left-hand side of the equation as:

cos^2(∅-9°) - sin^2(∅-9°) = cos 2(∅-9°)

So the equation becomes:

cos 2(∅-9°) = sin 54° / cos 54°

Using the identity sin(θ - φ) = sin θ cos φ - cos θ sin φ, we can rewrite the right-hand side of the equation as:

sin 54° / cos 54° = sin(60° - 6°) / cos(60° - 6°) = [sin 60° cos 6° - cos 60° sin 6°] / [cos 60° cos 6° + sin 60° sin 6°] = tan 6°

Therefore, the equation simplifies to:

cos 2(∅-9°) = tan 6°

We can solve for ∅ by using the inverse cosine function on both sides:

2(∅-9°) = cos^-1(tan 6°)

∅-9° = 0.3807

∅ = 9.3807°

So the equation cos(2∅-18°) = Tan 54° is true when ∅ is approximately 9.3807 degrees

Answers: The solutions are m = 7/2 and m = -3/2

==================================================

Explanation:

\(\text{If } |x| = k, \text{ then } x = k \text{ or } x = -k, \text{ where } k > 0\)

Use that rule to break up the absolute value into two equations. Then solve each equation for m.

\(|2m-2| = 5\\\\2m-2 = 5 \ \text{ or } \ 2m-2 = -5\\\\2m = 5+2 \ \text{ or } \ 2m = -5+2\\\\2m = 7 \ \text{ or } \ 2m = -3\\\\m = 7/2 \ \text{ or } \ m = -3/2\\\\\)

Notes:

Jenny had 42 stickers at first.

Let's assume that the original number of stickers Melissa had was M, and the original number of stickers Jenny had was J.

According to the first statement, after Jenny gave Melissa 16 stickers, both had the same number of stickers.

This means that Melissa had M + 16 stickers, and Jenny had J - 16 stickers.

After that, Lindy gave 24 stickers to Jenny. Now, Jenny has J - 16 + 24 = J + 8 stickers.

According to the second statement, the ratio of the number of Jenny's stickers to the original number of Melissa's stickers became 5:1.

This can be expressed as:

(J + 8) / M = 5 / 1

Cross-multiplying, we get:

1 × (J + 8) = 5 × M

J + 8 = 5M

Now we have two equations:

J - 16 = M + 16 (Equation 1)

J + 8 = 5M (Equation 2)

We can solve this system of equations to find the values of J and M.

From Equation 1, we can rearrange it to get:

J = M + 32

Substituting this value of J into Equation 2, we have:

M + 32 + 8 = 5M

40 = 4M

M = 10

Now we can substitute the value of M back into Equation 1 to find J:

J = M + 32 = 10 + 32 = 42

Therefore, Jenny had 42 stickers at first.

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The given statement in the form of inequality is given as -

c - 6 > 24.

An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > c

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the statement as -

"Six subtracted from c is greater than 24"

We can write the inequality as -

c - 6 > 24

Therefore, the given statement in the form of inequality is given as -

c - 6 > 24.

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{Question in english -

Six subtracted from c is greater than 24}

Answer:

each book cost $11

Answer:

Step-by-step explanation:

d = c-b / a-n

Make b the subject

d (a - n) = c - b

-b = d (a - n) / c

Divide both sides by - 1

-b / -1 = d (a - n) / c ÷ -1

b = d (a - n) / c × 1/-1

= d(a - n) / - c

= ad - an / - c

The options given doesn't match the final answer

Answer: ....

Step-by-step explanation: ....

9514 1404 393

Explanation:

Make use of the properties of equality.

  a = 2b +6 . . . . . given

  a = 9b -8 . . . . . given

  2b +6 = 9b -8 . . . . . . . substitution property of equality

  6 = 7b -8 . . . . . . . . . . . subtraction property of equality

  14 = 7b . . . . . . . . . . . . . addition property of equality

  2 = b . . . . . . . . . . . . . . . division property of equality

  b = 2 . . . . . . . . . . . . . . symmetric property of equality

The table of values is

n      1    2   3   4   5

T(n) -14 -8 -2   4   10

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

-14,-8,-2,4,.....

In the above pattern, we can see that 6 is added to the current term to get the next term

This means that the fifth term is

T5 = 4 + 6

Evaluate

T5 = 10

So, we have

n      1    2   3   4   5

T(n) -14 -8 -2   4   10

From the above table, we have

T(1) = -14

d = 6

The sequence is represented as

T(n) = T1 + (n - 1) * d

So, we have

T(n) = -14 + (n - 1) * 6

This gives

T(n) = -14 + 6n - 6

Evaluate

T(n) = 6n - 20

This means that

n = 123

So, we have

T(123) = 6(123) - 20

Evaluate

T(123) = 718

This means that

T(n) = 250

So, we have

6n - 20 = 250

So, we have

6n = 270

Divide

n = 45

Hence, the term is 45

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A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

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Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

Answer:

2d+3d-2d+4d= 9d-16

2d is cancelled

3d+4d=9d-16

7d=9d-16

16=9d-7d

16=2

16/2

d=8

The probability that a student is going to be absent given that today is Friday is 3/20.

Here in the given problem, we have been given two conditions, that is -

The probability of the student being absent during professor Pouokam's class is = A = 0.03 (i)

The probability of it being Friday is = F = 0.2 (ii)

We know that in order to solve we need to use Conditional Probability and that the formula for conditional probability is =

= Probability(A/F) = 0.03/0.2

=Probability for the given problem = 3/20 (iii)

Hence, the probability that a student is absent given that today is Friday is 3/20.

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