Which equation has exactly one solution?.
A. – 4 + 2x = 6x – 4
B. 3x + 5 = 2x – 6
C. 2(4x + 5) = 8x + 10
D. 4x – 8 = 4(x – 4)

The distribution of the sample mean can be represented as: X ~ N(67.15, 3.084/√30)

The distribution of the sample mean is a normal distribution with a mean equal to the population mean µ and a standard deviation equal to the population standard deviation σ divided by the square root of the sample size n.

Therefore, for this problem, the distribution of the sample mean can be represented as:

X ~ N(67.15, 3.084/√30)

where X is the sample mean, N represents a normal distribution, 67.15 is the population mean, 3.084 is the population standard deviation, and √30 is the square root of the sample size.

This distribution assumes that the sample is randomly selected from the population and the sample size is large enough to satisfy the central limit theorem.

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Answer: Hope you have a good day or night!

Step-by-step explanation:

The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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You can infer causality from a correlational result, but only when the r value is greater than:

C. 1

Causality refers to a situation in which one event causes another. When there is a correlation between two variables, it means that they tend to move in the same direction.

However, this does not necessarily mean that one event causes the other. In order for a correlation to indicate causality, the correlation coefficient (r) must be greater than 1. If the correlation coefficient is below 1, then there is not enough evidence to suggest that one event causes the other.

In addition, there are other factors that need to be considered when assessing causality from a correlational result.

For example, the strength of the relationship between the variables, the direction of the relationship, and the consistency of the results over time. It is also important to consider the context in which the research was conducted, as this may have an effect on the results.

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If the population is known to be exponential, or the sample size is less than 10, the t distribution should not be used.

The t distribution can be used when the population is not normal, as long as certain assumptions are met. Let's examine each of the conditions you mentioned to see whether they meet these assumptions:

"The population distribution is not badly skewed": The t distribution assumes that the population is approximately normally distributed. If the population is not normal, but is not badly skewed, then the t distribution may still be used. However, the more the population deviates from normality, the less reliable the t distribution becomes.

"The sample size is less than 10": If the sample size is less than 10, the t distribution is generally not recommended. Instead, a small sample size can be better analyzed using non-parametric tests or exact tests, which do not assume any particular population distribution.

"The population distribution is known to be exponential": If the population distribution is known to be exponential, then the t distribution should not be used, as it assumes normality. Instead, an appropriate distribution, such as the exponential distribution, should be used to analyze the data.

"The sample size is not too small": The t distribution can be used when the sample size is not too small. Typically, a sample size of at least 30 is recommended for the t distribution to be reliable. However, if the population is not normal or if the sample is highly skewed, a larger sample size may be required.

In summary, using the t distribution requires certain assumptions to be met. If the population is not normal, but is not badly skewed, and the sample size is not too small, the t distribution can be used. However, if the population is known to be exponential, or the sample size is less than 10, the t distribution should not be used.

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The definite integral given is 2e1/x5 x6 dx.

To solve this integral, we need to use integration by parts. We will use u = 2e1/x5 and dv = x6 dx. Using integration by parts, we have:

∫ udv = uv - ∫vdu

Therefore, we have:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) ∫e1/x5 dx

We can solve this last integral by using the substitution x5 = u. Doing so, we have:

∫ e1/x5 dx = (1/5) ∫ eudu

Using integration by parts, we have:

∫ eu du = eu u - ∫ ueu du

Therefore, we have:

∫ e1/x5 dx = (1/5) [eu u - ∫ ueu du] = (1/5) [eu u - u2 eu/2]

Substituting x5 = u, we have:

∫ e1/x5 dx = (1/5) [ex5 x5 - x10 ex5/2]

Finally, we can substitute this result into the original integral and get the answer:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) [(1/5) [ex5 x5 - x10 ex5/2]]

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Answer:

Page 1

1)

a) - 5x^4+3

Degree: 4

Number of terms: 2

b) 5x² + 30x+25

Degree: 2

Number of Terms: 3

c) 16r^4p

Degree: 4

Number of Terms: 1

d) 9m²n + 12mn +4m -6n+19

Degree:2

Number of Terms:5

Note:

Degree: the highest exponent of the variable x)

Number of terms: It is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or - signs, or sometimes by divide

Page 2:

Add or subtract the following polynomials.

a) (3p^3+6p^2+14p)+(-5p^3-2p+8p^2

opening bracket

3p^3+6p^2+14p+(-5p^3-2p+8p^2)

3p^3+6p^2+14p-5p^3-2p+8p^2

Combining like terms

-2p^3 +14p^2+12p

b) (7y^3-5y)-(5y-7y^3)

Opening bracket

7y^3-5y-5y+7y^3

Combining like terms

14y^3-10y

c) (6z^4+15-7z^3)+(-2z^4+8z^3-5z^5)

Opening bracket

6z^4+15-7z^3-2z^4+8z^3-5z^5

-5z^5 +4z^4+1z^3+15

d) (-3n²-14n+1)-(-7n+2-6n²)

Opening bracket

-3n²-14n+1+7n-2+6n²

3n²-7n-1

e) (7b^3-14-8b^4) − (−3b^4+7b³ +4)

Opening bracket

7b^3-14-8b^4+3b^4-7b³-4

-5b^4-18

f) (-3n^2-4n+2n⁴) + (3n^2+ 19n-7n^4)

Opening bracket

-3n^2-4n+2n⁴+3n^2+ 19n-7n^4

-5n⁴+15n

Answer:

Page 1

1)

a) - 5x^4+3

Degree: 4

Number of terms: 2

b) 5x² + 30x+25

Degree: 2

Number of Terms: 3

c) 16r^4p

Degree: 4

Number of Terms: 1

d) 9m²n + 12mn +4m -6n+19

Degree:2

Number of Terms:5

Note:

Degree: the highest exponent of the variable x)

Number of terms: It is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or - signs, or sometimes by divide

Page 2:

Add or subtract the following polynomials.

a) (3p^3+6p^2+14p)+(-5p^3-2p+8p^2

opening bracket

3p^3+6p^2+14p+(-5p^3-2p+8p^2)

3p^3+6p^2+14p-5p^3-2p+8p^2

Combining like terms

-2p^3 +14p^2+12p

b) (7y^3-5y)-(5y-7y^3)

Opening bracket

7y^3-5y-5y+7y^3

Combining like terms

14y^3-10y

c) (6z^4+15-7z^3)+(-2z^4+8z^3-5z^5)

Opening bracket

6z^4+15-7z^3-2z^4+8z^3-5z^5

-5z^5 +4z^4+1z^3+15

d) (-3n²-14n+1)-(-7n+2-6n²)

Opening bracket

-3n²-14n+1+7n-2+6n²

3n²-7n-1

e) (7b^3-14-8b^4) − (−3b^4+7b³ +4)

Opening bracket

7b^3-14-8b^4+3b^4-7b³-4

-5b^4-18

f) (-3n^2-4n+2n⁴) + (3n^2+ 19n-7n^4)

Opening bracket

-3n^2-4n+2n⁴+3n^2+ 19n-7n^4

-5n⁴+15n

Step-by-step explanation:

The car travels a Distance of 120 ft in the time it takes to come to a rest.

A) Determine and graph the position function for t > 0

Given that: Deceleration of car, a(t) = -15 ft/s²Velocity of car, v(0) = 60 ft/sInitial position of car, s(0) = 0

We know that:v(t) = v(0) + a(t) * tHere, v(0) = 60 ft/sa(t) = -15 ft/s²v(t) = 60 - 15tThen, s(t) = s(0) + v(0)t + (1/2)a(t)t²Putting in the values, we get:s(t) = 60t - 7.5t²

Thus, the position function for t > 0 is s(t) = 60t - 7.5t²

.Graph: We can use the above formula for position function to create a graph using a graphing calculator. The graph will look like this:

B) How far does the car travel in the time it takes to come to a rest?When the car comes to rest, its final velocity (v) will be 0. We can find the time taken to come to rest as follows:0 = 60 - 15t15t = 60t = 60/15 = 4 seconds

The car travels for 4 seconds before coming to rest.

We can find the distance travelled during this time as follows:Distance travelled, s = s(4) = 60(4) - 7.5(4²) = 240 - 120 = 120 ft

Therefore, the car travels a distance of 120 ft in the time it takes to come to a rest.

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The probability that this area will be hit by exactly 15 hurricanes in 2 years is 0.0428 and the probability that this area will be hit by at most 9 hurricanes in 2 years is 0.4235.

(a) Probability that this area will be hit by exactly 15 hurricanes in 2 years even, λ = 6 × 2 = 12

The probability distribution function is given by: P(x) = (e-λλx) / x!P(15) = (e-121215) / 15!P(15) = 0.0428Therefore, the probability that this area will be hit by exactly 15 hurricanes in 2 years is 0.0428.

(b) Probability that this area will be hit by at most 9 hurricanes in 2 years here, we need to find the probability of P(x ≤ 9). We can find this by using the complement of the given probability.

Therefore,P(x > 9) = 1 – P(x ≤ 9)

Probability distribution function is given by:P(x) = (e-λλx) / x!Given, λ = 6 × 2 = 12Thus, the probability distribution function is: P(x) = (e-1212x) / x!P(x > 9) = ∑P(x = r) from r = 10 to ∞P(x > 9) = ∑ (e-1212x) / x! from r = 10 to ∞P(x > 9) = 1 – P(x ≤ 9)P(x > 9) = 0.4235

Therefore, the probability that this area will be hit by at most 9 hurricanes in 2 years is 0.4235.

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Answer:

Step-by-step explanation:

so true bestie

Answer:268

Step-by-step explanation:

Answer:

5.49430941

Step-by-step explanation:

Multiply together.

i hope this helps, good luck :)

Answer:

The answer is 12

Step-by-step explanation:

let Linda's present age = x

Linda =x

(4x+6)=3(x+3)

4x+6= 3x+18

x=12

Answer: Check Explanation

Step-by-step explanation:

The current area is 12x4 which is 48yards^2. 60 percent of that is 48x0.4=19.2. Now you can just put some random numbers that when multiplied = 19.2. For ex. 2 and 9.6, 4 and 4.8.

To determine the possible values of x that make the triangle with sides x, x, and 6 an acute triangle, we need to consider the triangle inequality theorem.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the longest side is given as 6. Therefore, the sum of the lengths of the other two sides (both x) must be greater than 6.

Mathematically, we can express this as:

2x > 6

Dividing both sides of the inequality by 2, we have:

x > 3

So, any value of x greater than 3 will make the triangle valid.

In interval notation, the solution would be x ∈ (3, ∞) or x > 3.

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11.25/3 = 3.75

30/3.75 = 8

14 x 3.75 = 52.5

Let me know if this is the correct answer. :)

The paint cans and the spaces serve as examples of equivalent ratios. 5.5 cans of paint will be required to cover 2200 sq. unit.

Two ratios that have the same values are said to be equivalent. The same number can be used to multiply or divide both sums to get an equivalent ratio. The method is the same as determining equivalent fractions. When two or more ratios are reduced to their most basic form, they have the same value. Examples of equivalent ratios are 1:2, 2:4, and 4:8. In their most basic form, all three ratios have the same value, which is 1:2. They are in proportion if two ratios are equal. Equations in algebra are said to be equivalent if their solutions or roots are equal. When the same amount or expression is added to or removed from both sides of an equation, the result is the same.

To paint a 2200 square unit space, 5.5 cans are required.

The given parameter is:

Cans: Area\(=1:400\)

Express as fraction

Cans/Area\(=1/400\)

Multiply both sides by Area

Cans\(=\frac{1}{400}*Area\)

When the area is 2200, we have:

Cans\(=\frac{1}{400}*2200\)

Cans\(=5.5\)

5.5 cans are therefore required to paint a 2200 units square space.

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To determine the loan amount Molly needs, subtract the down payment and cash allowance from the total cost of the car.

Loan amount = Total cost - Down payment - Cash allowance

To calculate Molly's monthly payment, use the Loan Calculator with the loan amount, loan term in months, and the APR of 1.9%.

To find the total interest paid, subtract the loan amount from the product of the monthly payment and the loan term.

To calculate the total cost of the car, add the down payment, cash allowance, loan amount, and total interest paid.

To calculate the loan amount Molly needs, we subtract the down payment and cash allowance from the total cost of the car. Let's assume the total cost is $X.

Loan amount = Total cost - Down payment - Cash allowance = X - $2500 - $500 = X - $3000.

To calculate Molly's monthly payment using the Loan Calculator and the 1.9% APR offer, we need to know the loan amount, the loan term in months, and the APR. Let's assume the loan term is Y months.

Using the Loan Calculator, we can determine the monthly payment based on the loan amount, loan term, and APR.

To calculate the total interest Molly will pay using this plan, we can multiply the monthly payment by the loan term in months and subtract the loan amount. This will give us the total interest paid.

Total interest = (Monthly payment * Loan term) - Loan amount.

To calculate the total cost of the car for Molly using this plan, we add the down payment, cash allowance, and the total interest paid to the loan amount.

Total cost = Loan amount + Down payment + Cash allowance + Total interest.

Please provide the values of X and Y to calculate the specific amounts.

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Answer:

AC ≈ 9.52 m

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos15° = \(\frac{BC}{AC}\) = \(\frac{9.2}{AC}\) ( multiply both sides by AC )

AC × cos15° = 9.2 ( divide both sides by cos15° )

AC = \(\frac{9.2}{cos15}\) ≈ 9.52 m ( to 3 sf )

Jim Russell’s $1,500 deposit could earn $18.87 in 12 months in a savings account paying 1.25% daily interest. How much more interest could Jim earn in a 3-month CD that pays 3.26% simple interest every 3 months during the 12-month period? EXAMPLE 4Find the effective rate of interest to the nearest hundredth percent on $1,000 deposited in an account that pays 5% annualinterest, compounded quarterly. Use the compound interest table below to help woth the calculations.Find the difference between the deposit and the compound amount.4

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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Let the number be n

\(\\ \sf\longmapsto 2(n+10)=60\)

\(\\ \sf\longmapsto n+10=60/2\)

\(\\ \sf\longmapsto n+10=30\)

\(\\ \sf\longmapsto n=30-10\)

\(\\ \sf\longmapsto n=20\)

Answer:

18%

Step-by-step explanation:

\(x = y*\frac{60}{100} =y*0.6=0.6y\\x=0.6y\)

\(y = z*\frac{30}{100} =z*0.3=0.3z\\y=0.3z\)

x is what percent of z?

Since x = 0.6y and y = 0.3z:

\(\%=\frac{x}{z} *100\\\\\%=\frac{0.6y}{z}*100\\ \\\%=\frac{0.6(0.3z)}{z} *100\\\\\%=\frac{0.18z}{z} *100\\\\\%=0.18*100\\\\\%=18\)

Answer:

20

Step-by-step explanation:

A period is how long a wavelength takes.

By picking the maximum y point, you look for the X difference between the first maximum and the second one.

NOTE: I may not be reading your graph correctly as the resolution is quite low, but I got it.

Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.

The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.

The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.

Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.

Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.

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Based on the described sampling approach, it should be concluded that the responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. (Option D).

Voluntary response sample refers to a response sample in which the researcher puts out a request for population members to join the sample, and the decision of whether or not to be in the sample resides with the people. As it is a sample comprising of voluntarily participants, people who chose to participate usually do so as they have a strong opinion on the subject of the survey. Typically, voluntary response samples oversample members with strong opinions and under sample members with little to no opinion on the subject of the survey. Hence, inferences from a voluntary response sample are not as reliable as conclusions based on a random sample of the entire population under consideration.

Note: Question is incomplete. The options were missing which are a. Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes. b. The cafeteria staff should not use the results to draw any conclusions since some students may not have filled out a comment card, which is nonresponse. c. If the students recorded their grade level with their response, the staff could make the original sample a stratified sample and use the responses to learn what proportion of each grade recommends major changes to food selection. d. The responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. e. The opportunity to fill out comment cards should be offered to students at all high schools in the school district to get a larger sample size, which will make the results more reliable

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The rate of change of a circle diameter with respect to radius is 0.

The rate of change of a circle diameter with respect to radius (D2(r)) can be calculated by using the formula dD2/dr. This formula states that the rate of change of a function at a given point is equal to the derivative of the function at that point.

To calculate the rate of change of a circle diameter with respect to radius, we must first calculate the derivative of the circle diameter with respect to radius. The formula for diameter of a circle is D = 2r, where r is the radius of the circle. Taking the derivative of the equation with respect to r gives us dD/dr = 2. This means that the rate of change of a circle diameter with respect to radius is 2.

We can also calculate the rate of change of a circle diameter with respect to radius using the formula dD2/dr. This formula states that the rate of change of a function at a given point is equal to the second derivative of the function at that point. Taking the second derivative of the equation for the diameter of a circle with respect to radius gives us d2D/dr2 = 0. This means that the rate of change of a circle diameter with respect to radius is 0.

Therefore, the rate of change of a circle diameter with respect to radius is 0.

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