Find the equation of a line that passes through the point (3,-5) and has a gradient of 2.

Answer:

Step-by-step explanation: x is the number of days she is booked.

List an equation

748+86x=734+87x

x=14

14 nights and plugging x into the equation 1952 points

Over the interval [-3, 1], the local minimum is 0,  Over the interval [-1, 0], the local maximum is 4.39,  Over the interval [0, 3], the local minimum is -32.

By plot the function on a graphing tool and visually identify the local minimum and maximum values over the specified intervals .A function that is continuous for an interval [a,b], a is not equal to b, then there is a local maximum and minimum if:

Local maximum: f(d) > f(x), ∀ x ≠ d, a ≤ d ≤ b

Local minimum: f(c)< f(x), ∀ x ≠ to c, a≤c≤b

we can proceed to solve each question:

Over the interval [-3, 1], the local minimum is 0,

since f(-2) < f(x), ∀ x ≠ -2,-3 ≤ x ≤ -1 .

Over the interval [-1, 0], the local maximum is 4.39,

since f(-0.8) > f(x), ∀ x ≠ -0.8, -1 ≤ x ≤ -1.

Over the interval [0, 3], the local minimum is -32,

since f(-2) < f(x), ∀ x ≠ -2.0 ≤ x ≤3.

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Answer:

0

4.39

-32

Step-by-step explanation:

on edge

Answer:

x = 1/4

Step-by-step explanation:

remove the parenthesis

collec like terms

caculate

move constant to the right

calculate

divide both sides

On solving the provided question we can say that - rate at which customers are entering the store in customers per minute is 4 minutes.

In order to calculate numerous unit values, a single unit value must first be determined. This is known as a unitary method. With the idea of dimensions and proportions, this strategy is mostly employed. The unit technique can be applied in either direct or indirect ways. A singular or unique entity is referred to by the word "unitary." The value will be determined using this procedure in terms of a single entity. The unit system, for instance, may be used to calculate the distance covered by a car on one liter of gasoline if it drives 44 km on two.

as per the question,

2 costumers enter over course of = 8 minutes

so, 1 costumers enter over course of = 8/2 =4 minutes

Hence,

rate at which customers are entering the store in customers per minute is 4 minutes.

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The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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Answer:

15πcm

Step-by-step explanation:

2πr = circumference

radius = 0.075m = 7.5cm

Circumference = 7.5X2π

15π cm

The formula for uranium oxide is UO2. This means that there are two oxygen ions attached to one uranium atom.

The unit cell consists of one uranium atom surrounded by 8 oxygen ions. This means that the uranium atom is in a cubic structure and the oxygen ions are located in the 8 holes of the cube. This is known as a body-centered cubic (BCC) structure. The general formula for a uranium oxide is UO2, which means that there are two oxygen ions attached to each uranium atom.

For example, if we consider a unit cell of uranium oxide with a cubic crystal structure, the formula would be UO2. This means that there is a uranium atom in the center surrounded by two oxygen atoms at each of the six corners of the cube. These atoms are covalently bonded to the uranium atoms to form the unit cell structure.

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Answer:

Question 1

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, or a right triangle)

Given:

⇒ BC² + 8² = 10²

⇒ BC² = 36

⇒ BC = 6 cm

Question 2

Given:

⇒ MB = AB - AM = 8 - x

As ΔABC ~ ΔMBN

⇒ AB : AC = MB : MN

⇒ 8 : 10 = (8 - x) : MN

\(\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}\)

\(\sf \implies \dfrac45=\dfrac{(8-x)}{MN}\)

\(\sf \implies MN=\dfrac54(8-x)\)

Question 3

D = (6, 8)

As ΔBAD ~ ΔMAP

⇒ AB : AD : BD = AM : AP : MP

⇒ 8 : 6 : 10 = x : AP : MP

\(\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}\)

\(\sf \implies AP=\dfrac34x\)

\(\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}\)

\(\sf \implies MP=\dfrac54x\)

Question 4

Perimeter of MNCDP = MN + NC + CD + PD + MP

As ΔABC ~ ΔMBN

⇒ AB : BC : AC = MB : BN : MN

⇒ 8 : 6 = (8 - x) : BN

\(\sf \implies \dfrac86=\dfrac{(8-x)}{BN}\)

\(\sf \implies BN=\dfrac34(8-x)\)

NC = BC - BN

\(\sf \implies NC=6-\dfrac34(8-x)\)

PD = 6 - AP

\(\sf \implies PD=6-\dfrac34x\)

Perimeter of MNCDP = MN + NC + CD + PD + MP

\(\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x\)

\(\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x\)

\(\sf \implies perimeter=10+8+6=24\)

"To determine if a function is even or odd, check if it satisfies the properties of evenness or oddness algebraically."

When determining whether a function is even or odd, we need to apply specific algebraic conditions to verify its symmetry properties. An even function satisfies the condition f(-x) = f(x) for all x in its domain, meaning that substituting -x into the function yields the same result as using x. On the other hand, an odd function satisfies the condition f(-x) = -f(x) for all x in its domain, indicating that substituting -x into the function results in the negative of the value obtained using x. By applying these algebraic tests, we can determine if a function exhibits evenness, oddness, or neither, which provides insight into its symmetry properties.

"To determine if a function is even or odd, check if it satisfies the properties of evenness or oddness algebraically."

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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The average rate of change of f(x) from x₁ = 5 to x₂ = 8 is approximately 0.15.

To compute the average rate of change of the function f(x) = √√(2x - 9) from x₁ = 5 to x₂ = 8, we need to calculate the difference in the function's values over the given interval and divide it by the difference in the corresponding x-values.

First, let's find the value of f(x₁):

f(x₁) = √√(2x₁ - 9) = √√(2(5) - 9) = √√(10 - 9) = √√1 = √1 = 1.

Next, let's find the value of f(x₂):

f(x₂) = √√(2x₂ - 9) = √√(2(8) - 9) = √√(16 - 9) = √√7.

Now, we can calculate the average rate of change using the formula:

Average Rate of Change = (f(x₂) - f(x₁)) / (x₂ - x₁)

Plugging in the values we found:

Average Rate of Change = (√√7 - 1) / (8 - 5)

Using a calculator or a math software, we can approximate the value:

Average Rate of Change ≈ (1.449 - 1) / 3 ≈ 0.449 / 3 ≈ 0.15 (rounded to two decimal places).

Therefore, the average rate of change of f(x) from x₁ = 5 to x₂ = 8 is approximately 0.15.

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Answer:

Step-by-step explanation:

h(t) = t2 - 8t + 12

Putting value of t = 0

h(0) = (0)2 - 8(0) + 12

= 0 - 0 + 12

= 12

Answer:

i'm sorry i don't know it

Step-by-step explanation:

hope u have a good day

Answer:

16

Step-by-step explanation:

\((9+V-4)-(5+V-16)\\=9+V-4-5-V+16\\=9+V-9-V+16\\=16\)

Answer:

Step-by-step explanation:

Let the amounts be x kg of Orange Blossom and 10 - x of Red Dragon.

According to question we set the following equation:

Answer:

Its enlargement

Step-by-step explanation:

Its enlargement!

hope it helps

Answer:

The reasoning isn't correct

Step-by-step explanation:

This is becuase the given amount for each frame is 42 dollars not 40 like it is listed in the equation. Another reason the reasoning from Jansen is wrong is because he wants to buy 98 frames, not 100 like it was listed in the equation.

The report's statement of "no significant difference" between treatments does not provide enough information to determine the total number of participants.

The statement "The data show no significant difference between the two treatments, t(10) = 1.65, p > 0.05" suggests that a t-test was conducted with 10 degrees of freedom, resulting in a t-value of 1.65 and a p-value greater than 0.05.

The p-value indicates the probability of observing such results if there were no true difference between the treatments. However, the report does not provide information about the sample size, making it impossible to determine the total number of individuals who participated in the study.

The conclusion regarding the sample size requires additional information that is not provided in the given report.

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A mother invests $6000 for her children's education, with a portion in a 4% CD account and the remainder in a 7% savings bond. The total interest earned is $360.

Let's assume the amount invested in the CD account is x dollars. Then, the amount invested in the savings bond will be the remaining amount, which is (6000 - x) dollars.

The interest earned from the CD account is given by 0.04x, while the interest earned from the savings bond is 0.07(6000 - x). The total interest earned after one year is $360, so we can set up the equation:

0.04x + 0.07(6000 - x) = 360

Simplifying the equation, we get:

0.04x + 420 - 0.07x = 360

-0.03x = -60

x = 2000

Therefore, the mother invested $2000 in the CD account (earning 4%) and $4000 in the savings bond (earning 7%) to accumulate a total interest of $360 after one year.

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6.022× \(10^2^3.\)particles are in one mole.

The correct option is 6.022× \(10^2^3.\)

Now, According to the question:

Avogadro's number

Avogadro's number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214076 × \(10^2^3.\) The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction.

Now, According to Avogadro's law, one mole of any substance contains a fixed number of particles i.e.,6.022× \(10^2^3.\)particles (atoms, molecules or ions) which is also known by the name Avogadro's number.

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Answer:

36 ounces or if over 150 lbs drink more water than 36 ounces

Step-by-step explanation:

For every pound of sweat you lose you need to drink 16 ounces of water!

The expression that can be used to represent the number of pears that can be bought with d dollars is d(c/5)

The first step is to determine the price of one pear. This can be determined by dividing c cents by 5 pears.

Cost of one pear = c/d

The second step is to multiply the cost of one pear by d dollars:  d(c/5)

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The calculation; (9.04-8.23+21.954+81.0) * 3.1416 should have three significant figures.

To determine the number of significant figures in a calculation, we follow these rules:

1. When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.

2. When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Let's calculate the expression:

(9.04 - 8.23 + 21.954 + 81.0) * 3.1416

First, perform the addition and subtraction:

(0.81 + 21.954 + 81.0) * 3.1416

= 103.764 * 3.1416

Next, perform the multiplication:

325.8512544

To determine the number of significant figures, we look at the original numbers involved in the calculation.

9.04 has three significant figures.

8.23 has three significant figures.

21.954 has five significant figures.

81.0 has three significant figures.

3.1416 has five significant figures.

Among these numbers, the number with the fewest significant figures is 81.0 with three significant figures.

Therefore, the result of the calculation, 325.8512544, should have three significant figures to match the least precise value.

In scientific notation, the result would be expressed as 3.26 x 10^2.

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The given calculation would yield a result with five significant figures because we base our significant digits off of the least precise term within the parentheses, which is 81.0. The result is then rounded according to this rule.

In the case of the calculation (9.04-8.23+21.954+81.0) * 3.1416, it's important to first consider the rule for significant figures in calculations - the result should be reported with the smallest number of decimal places in the numbers used in the calculation. The number 81.0 has two numbers after the decimal point, therefore, our final answer should have two numbers after the decimal point. When you calculate the inside of the parentheses, the result is 103.764. Multiplying that by 3.1416 would approximately yield 325.854. Rounding this to the least precise measurement (which is to two decimal places due to 81.0) would give us 325.85 which has five significant figures, effectively limiting our calculated value to five significant figures.

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To meet your requirements for a 7-day supply, you should combine 11 servings of Designer Whey and 2 servings of Muscle Milk.

Let x be the number of Designer Whey servings and y be the number of Muscle Milk servings.
Use the protein requirements to set up an equation:
18x + 32y = 262 (Designer Whey has 18g of protein per serving, and Muscle Milk has 32g per serving)
Use the carbohydrate requirements to set up a second equation:
2x + 16y = 54 (Designer Whey has 2g of carbohydrates per serving, and Muscle Milk has 16g per serving)
Now you have a system of two linear equations:
18x + 32y = 262
2x + 16y = 54
To solve this system, first simplify the second equation by dividing by 2:
x + 8y = 27
Rearrange the simplified equation to isolate x:
x = 27 - 8y
Substitute the expression for x from step 4 into the first equation:
18(27 - 8y) + 32y = 262
Distribute the 18 and simplify the equation:
486 - 144y + 32y = 262
Combine like terms and solve for y:
-112y = -224
y = 2
Substitute the value of y back into the expression for x from step 4:
x = 27 - 8(2)
x = 27 - 16
x = 11

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The solution to the system of equations using the elimination method is option (a) (2,0).

To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable "y" by multiplying the second equation by 2 and adding it to the first equation.

Multiplying the second equation by 2, we get:

4x - 20y = 8

Adding the modified second equation to the first equation, we have:

7x + 20y + 4x - 20y = 14 + 8
11x = 22
x = 2

Substituting the value of x into one of the original equations, let's use the second equation:

2(2) - 10y = 4
4 - 10y = 4
-10y = 0
y = 0

Therefore, the solution to the system of equations is x = 2 and y = 0, which corresponds to option (a) (2,0).

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Answer:

The value of the given expression to the nearest integer is 114,126.

Step-by-step explanation:

\(\displaystyle \sum^{29}_{n=2}80\left(1.23\right)^{n-2}\)

The given sigma notation means

As 80(1.23)ⁿ⁻² is exponential, the series is geometric.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}\)

Therefore, the first term, a, is 80 and the common ratio, r, is 1.23.

The formula for the sum of the first n terms of a geometric series is:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

As the exponent of the sigma notation is (n - 2) rather than (n - 1), and the given values of n are from n = 2 to n = 29, we need to find the sum of the first 28 terms.

Therefore, substitute a = 80, r = 1.23 and n = 28 into the sum formula:

\(\implies S_{28}=\dfrac{80\left(1-1.23^{28}\right)}{1-1.23}\)

\(\implies S_{28}=114125.755...\)

\(\implies S_{28}=114126\)

Therefore, the value of the given expression to the nearest integer is 114,126.

5/9 of 54 are the ones which have chocolate, so we need to multiply the fraction by 54

5/9 * 54 = 30

Since 30 pieces of candy have chocolate, then 24 don't have it. 2/3 of the last number are the ones which have gum, multiply 2/3 by 24 to get the answer:

2/3 * 24 = 16.

The answer is: 16 pieces of candy have gum

Answer:

B is your answer

Step-by-step explanation:

Answer:

3n + 8 < 5n

n > 4

Step-by-step explanation:

Let

n = cost of viewing videos

Plan A: $3 per video viewed, plus a flat rate of $8 per month

Total cost for plan A = 3n + 8

Plan B: $5 per video viewed and no additional flat rate

Total cost for plan B = 5n

Plan A is less than the cost of viewing n videos using Plan B

The inequality

3n + 8 < 5n

8 < 5n - 3n

8 < 2n

8/2 < n

4 < n

n > 4

From the given equations , the equation which represents the result of having variables terms on one side of the equal to sign and on the other side is the solution is given by q = 2.

As given in the question,

Equations which represents the result of having variables terms on one side of the equal to sign and on the other side is the solution is represented as follow:

Option A:

1 = 1

On the left hand side it is 1 which is a number and same is on the right hand side. Both are representing numbers .

Incorrect option.

Option B:

q = 2

On the left hand side it is 'q' which represents the variable and on the right hand side it is 2 which is solution.

Correct option.

Option C:

2 = 2

On the left hand side it is 2 which is a number and same is on the right hand side. Both are representing numbers .

Incorrect option.

Option D:

1 =2

On the left hand side it is 1 which is a number and 2 is on the right hand side again a number. Both are representing numbers .

Incorrect option.

Therefore, equation which represents the result of having variables terms on one side of the equal to sign and on the other side is the solution is given by q = 2.

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Answer:

The rate of change of the radius of the cone when the radius is 3 inches is 0.\(\overline 3\) inch/minute

Step-by-step explanation:

The given parameters are;

The radius of the cone = 3 inches

dV/dt = 9·π in.³/min

The height, h = 3 × Radius, r

The formula for the volume of a cone, V is V = 1/3×π×r²×h = 1/3×π×r²×3×r = π·r³

Therefore, we have;

dV/dt = dV/dr × dr/dt

dV/dr =3·π·r²

∴ dr/dt = dV/dt/(dV/dr) = 9·π/(3·π·r²) = 3/r²

When r = 3 inches, we have;

dr/dt = 3/r² = 3/(3²) = 1/3 inch/minute

The rate of change of the radius of the cone when the radius is 3 inches = 0.\(\overline 3\) inch/minute