The CEO of a cell-phone company has recently noticed a 26% sales decrease in the month of July compared to June. Let n represent June’s sales. If y represents July’s sales, which equation can be used to determine the sales in July?

Answer:

It will take 125 minutes or 2 hours and 5 minutes.

Step-by-step explanation:

We can use a proportion.

7 pages is to 5 minutes as 175 pages is to x minutes

7 : 5 = 175 : x

7/5 = 175/x

7x = 5 * 175

7x = 875

x = 125

It will take 125 minutes or 2 hours and 5 minutes.

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Answer:

yes

Step-by-step explanation:

Given the graph of any function, an x-intercept is simply the point, or points where the graph crosses the x-axis. There might be just one such point, no such point, or many, meaning a function can have several x-intercepts.

The most distance Talia can go each day while staying within her budget is 320 miles.

In this case, our goal is to write an inequality before moving on to solve it.

We begin with the daily rental fee and the cost per mile.

This is stated as $30 per day and $0.20 per mile in the question.

She is required to spend a total of $94.

This means that the total cost of the rental automobile and the cost per mile must be $94 or less.

Let m be the maximum number of miles she can travel.

Hence, we may write the inequality as follows: 30 + 0.2 m 94.

This inequality is what we can now solve;

0.2m ≤ 94 - 30

0.2m ≤ 64

m ≤ 64/0.2

320 miles = m

The most distance Talia can go each day while staying within her budget is 320 miles.

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84 degrees

Step-by-step explanation:

180=60+36+x

180=96+x

-96 -96

x=84

Answer:

Step-by-step explanation:

Each grandchild will receive 655/13 = 50 with 5 coins left over. She can keep the 5 coins and start again.

Answer

Answer:

50 coins for each grandchild

5 left over.

Step-by-step explanation:

13x50=650

655-650=5

The conclusion results in a Type I error.

To determine whether the conclusion results in a Type I error, a Type II error, or a correct decision, we need to analyze the given information.

In this scenario, the test is conducted to compare a hypothesized population mean, denoted as μ, with a specific value of 58. The null hypothesis (H₀) states that μ is equal to 58, while the alternative hypothesis (H₁) suggests that μ is not equal to 58.

A significance level, denoted as α, is set at 0.05, which means that the researcher is willing to accept a 5% chance of making a Type I error - rejecting the null hypothesis when it is actually true.

The test statistic, z, is calculated to assess the likelihood of the observed data given the null hypothesis. In this case, the test statistic value is z = -2.14.

Since the test statistic is negative and falls in the rejection region of a two-tailed test, we can compare its absolute value to the critical value for a significance level of 0.05.

Looking up the critical value in the standard normal distribution table, we find that for a two-tailed test with α = 0.05, the critical value is approximately 1.96.

Since |z| = |-2.14| = 2.14 > 1.96, we have sufficient evidence to reject the null hypothesis.

Now, if the true value of μ is actually 58, and we reject the null hypothesis that μ = 58, it means we have made a Type I error - concluding that there is a difference when, in reality, there is no significant difference.

Therefore, the conclusion in this case results in a Type I error.

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To answer this question, we can use a one-sample t-test to determine whether the mean amount of vitamin c per tablet is significantly different from the claimed average of 200 milligrams. The null hypothesis is that the mean amount of vitamin c per tablet is equal to 200 milligrams, while the alternative hypothesis is that it is less than 200 milligrams.
We can calculate the test statistic using the formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

In this case, the sample mean is 194.3 milligrams, the population mean is 200 milligrams, the sample standard deviation is 21 milligrams, and the sample size is 70 tablets. Plugging in these values, we get:
t = (194.3 - 200) / (21 / sqrt(70)) = -2.47

Using a t-table with 69 degrees of freedom (70 minus 1), we can find the p-value associated with this test statistic. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the one we observed, assuming the null hypothesis is true. Looking up -2.47 in the t-table, we find a two-tailed p-value of approximately 0.016. However, since our alternative hypothesis is one-tailed (we are only interested in whether the mean amount of vitamin c is less than 200 milligrams), we need to divide this p-value by 2 to get the appropriate one-tailed p-value.

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The conserved quantity along geodesics is d/dξ (ds/dξ)² = 0. The required metric is, ds² = - dt² + dx² = a²cosh²(at)(dT)² - a²sinh²(at)(dX)² = a²(T)² - (X)²

(1,1) are the coordinates of 2-dimensional Minkowski space and (T, X) are coordinates in a frame that is accelerating. They are related via t = ax sinh(aT) r = ax cosh(at)

(i) Finding the metric in the accelerating frame by transforming the metric of Minkowski space ds² = -dt² + dx² to the coordinates (T, X) is,

We have the transformation relation as,

t = ax sinh(aT)

r = ax cosh(aT)

The inverse transformation relations will be,

T = asinh(at)

x = acosh(at)

We will calculate the required metric using the inverse transformation.

The chain rule of differentiation is used to calculate the derivative with respect to t.

dt = aacosh(at)dX

dr = - aasinh(at)dt

So the required metric is,

ds² = - dt² + dx² = a²cosh²(at)(dT)² - a²sinh²(at)(dX)² = a²(T)² - (X)²

(ii) The geodesic Lagrangian in the (T, X) coordinates is given by,

L = ½ (ds/dξ)²,

where ds² = a²(T)² - (X)².

The conserved quantity along geodesics is d/dξ (ds/dξ)² = 0.

(iii) From the condition L = -1, we get,

-1 = ½ (ds/dξ)²,

which gives ds/dξ = i.

We have ds² = -dt² + dx² = - a²cosh²(at)(dT)² + a²sinh²(at)(dX)² = - a²(T)² + (X)².

Substituting ds/dξ = i in the above equation, we get dX/dT = ±i.

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The distance between the ship and the base of the lighthouse can be calculated using trigonometry. By applying the tangent function to the angle of depression, we can determine that the ship is approximately 54.49 feet away from the base of the lighthouse.

To determine the distance between the ship and the base of the lighthouse, we can use trigonometry. The angle of depression of 15° represents the angle formed between the horizontal line from the top of the lighthouse and the line of sight to the ship in the ocean. We can consider the height of the lighthouse (158 ft) as the opposite side of the right triangle, and the distance between the ship and the base of the lighthouse as the adjacent side.

Using the tangent function, we can set up the equation tan(15°) = opposite/adjacent, where the opposite side is 158 ft and the angle is 15°. Rearranging the equation, we have tan(15°) = 158/adjacent. Solving for the adjacent side, we find that the ship is approximately 545.51 feet away from the base of the lighthouse.

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Answer:

7

Step-by-step explanation:

Sum of angles on a straight line is 180°

12x - 8 + 104 = 180°

12x + 96° = 180°

12x = 180° - 96°

12x = 84

12 12

x = 7

Answer:

B. <

Brainlist Pls!

Look at the example pics below:

Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

Answer:

Let P be the event that a home has a pool, and B be the event that a home has at least 3 bedrooms. We want to find P(P|B), the probability that a home has a pool given that it has at least 3 bedrooms.

By Bayes' theorem, we have:

P(P|B) = P(B|P) * P(P) / P(B)

We are given:

P(P) = 0.38, the probability that a home has a pool

P(B) = 0.70, the probability that a home has at least 3 bedrooms

P(P and B) = 0.25, the probability that a home has both a pool and at least 3 bedrooms

To find P(B|P), the probability that a home has at least 3 bedrooms given that it has a pool, we use the conditional probability formula:

P(B|P) = P(B and P) / P(P)

We know P(B and P) = P(P and B) = 0.25, and P(P) = 0.38, so:

P(B|P) = 0.25 / 0.38 = 0.6579 (rounded to four decimal places)

Now we can use Bayes' theorem to find P(P|B):

P(P|B) = P(B|P) * P(P) / P(B)

= 0.6579 * 0.38 / 0.70

= 0.3555 (rounded to four decimal places)

Therefore, the probability that a home has a pool given that it has at least 3 bedrooms is approximately 0.3555.

Answer:

Therefore,

P(A|B) = P(A and B) / P(B) = 0.25 / 0.70 ≈ 0.357

So the probability that a home has a pool, given that it has at least 3 bedrooms, is approximately 0.357 or 35.7%.

Step-by-step explanation:

We are given that 38% of the homes have pools, 70% have at least 3 bedrooms, and 25% have both a pool and at least 3 bedrooms.

We are asked to find the probability that a home has a pool, given that it has at least 3 bedrooms. Let P(A) represent the probability of a home having a pool, and P(B) represent the probability of a home having at least 3 bedrooms. We need to find P(A|B), the conditional probability of a home having a pool given that it has at least 3 bedrooms.

Using Bayes' theorem, we have:

P(A|B) = P(A and B) / P(B)

We are given that 25% of the homes have both a pool and at least 3 bedrooms, which means that P(A and B) = 0.25. We are also given that 70% of the homes have at least 3 bedrooms, which means that P(B) = 0.70.

The upper bound of the volume of water left in the fish tank is 40 liters.

In the given statement is :

A fish tank contains 70 liters of water, rounded to 1 significant figure. 30 liters of water, rounded to 1 significant figure, are removed from the tank.

Work out the upper bound of the volume of water left in the fish tank.

Now, According to the question:

Initial water in tank = 70 liters

Amount of water removed = 30 liters

Hence, To calculate the upper bound of the volume of water left in the fish tank;

= 70 - 30

= 40 liters

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Step-by-step explanation:

Force = Mass × Acceleration

Hope it helps :)

★ As per newton's second law of motion, force is measured as the product of mass and acceleration\(.\)

F denotes force

m denotes mass

a denotes acceleration

➤ Force is a polar vector quantity as it has point of application.

It has both magnitude as well as direction.

The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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Since the base case holds and the induction step is valid, by mathematical induction, the number 2²ⁿ2²ⁿ⁻¹ 1 can be expressed as the product of at least n prime factors, not necessarily distinct.

To prove that the number

2²ⁿ2²ⁿ⁻¹ 1

can be expressed as the product of at least $n$ prime factors, not necessarily distinct, we can use mathematical induction.
First, let's consider the base case where n = 1.

In this case, the number is

2² 2²⁺¹⁻¹ 1 = 2² 2¹ 1 = 8.

As 8 can be expressed as 2 times 2 times 2, which is the product of 3 prime factors, the base case holds.
Now, let's assume that for some positive integer k,

the number

$2²ˣ 2²ˣ⁻¹1

can be expressed as the product of at least k prime factors.
For

n = k + 1,

we have

2²ˣ⁺¹ 2²ˣ⁺¹⁻¹ 1

= 2²ˣ⁺¹ 2²ˣ 1

= (2²ˣ 2²ˣ⁻¹1)^2.

By our assumption,

2²ˣ 2²ˣ⁻¹ 1

can be expressed as the product of at least k prime factors. Squaring this expression will double the number of prime factors, giving us at least 2k prime factors.
Since the base case holds and the induction step is valid, by mathematical induction, we have proven that the number 2²ⁿ 2²ⁿ⁻¹ 1 can be expressed as the product of at least n prime factors, not necessarily distinct.

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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The error term is a random variable with an expected value of zero.2. The error term is normally distributed

The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.

The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.

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14 ft to 21 ft = 2 ft to 3 ft

The vertex form of a quadratic function is given by:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

Since the graph of f(x) = x^2 was translated 6 units to the left to create the graph of g, the vertex of g is at the point (h - 6, k).

The vertex of f(x) = x^2 is at (0, 0), so the vertex of g is at (-6, 0).

Since the vertex is at (-6, 0), the equation of g in vertex form is:

g(x) = a(x + 6)^2 + 0

We can find the value of "a" by using another point on the parabola. For example, if we know that g(-3) = 9, then we can substitute these values into the equation and solve for "a":

9 = a(-3 + 6)^2

9 = 9a

a = 1

So the equation of g in vertex form is:

g(x) = (x + 6)^2

The unit of the right-hand side of the equation is s⁰ * s⁻¹ = s⁻¹.The SI unit of the quantity f is s⁻¹.

Given that the motion y(x, t) of a vibrating system is described by

                                     y(x, t) = A0e^(-πt) sin((2πx/λ)−2πft).

Denoting units with fractions using the "/" operator and units with products using the "*" operator, numbers.

We are given that

                                          y(x, t) = A0e^(-πt) sin((2πx/λ)−2πft)where x denotes a distance in meters and t denotes a time in seconds.

The SI unit for time t is the second (s).We need to find the unit of the quantity f, given that the formula is

                                        y(x, t) = A0e^(-πt) sin((2πx/λ)−2πft)

Comparing the argument of sin in the above equation,(2πx/λ) − 2πft

The unit of the first term is m/m = 1The unit of the second term is s⁻¹ * s = s⁻¹

Therefore, the unit of the argument of sin is s⁻¹.

Now, sin(x) is a dimensionless quantity.

Hence, the unit of A₀e^(-πt) is s⁰ or 1.

Therefore, the unit of the right-hand side of the equation is s⁰ * s⁻¹ = s⁻¹.The SI unit of the quantity f is s⁻¹.

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The common ratio 'r' is not constant, meaning that the series is not geometric.

Each term in a geometric series is created by multiplying the previous term by a fixed constant known as the common ratio.

To determine if the geometric series (4, -7, 49, -343, 16) is convergent or divergent, we need to find the common ratio 'r' of the series.

r = (next term) / (current term)

r = (-7) / 4 = -1.75

r = 49 / (-7) = -7

r = (-343) / 49 = -7

r = 16 / (-343) = -0.0466...

We can see that the common ratio 'r' is not constant, meaning that the series is not geometric, and therefore we cannot determine if it is convergent or divergent.

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Answer:

\(\mathrm{a=-50,\ d=7,\ general\ formula=7(n-1)-50}\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{Given,}\\\mathrm{15^{th}\ term(t_{15})=48}\\\mathrm{or,\ a+14d=48.........(1)}\\\mathrm{And\ 40^{th}\ term(t_{40})=223}\\\mathrm{or,\ a+39d=223......(2)}\\\mathrm{n^{th}\ term(t_n)=\ ?}\\\mathrm{Subtracting\ equation(1)\ from\ (2),}\\\mathrm{25d=175}\\\mathrm{or,\ d=7}\\\mathrm{Now,\ a+14d=48\ or,\ a=48-14d=48-14(7)}\\\mathrm{\therefore a=-50}\)

\(\mathrm{t_n=a+(n-1)d}\\\mathrm{or,\ t_n=-50+(n-1)7}\\\mathrm{\therefore general\ formula=7(n-1)-50}\)

Looking at the given diagram,

angle 9x - 1 and angle y - 20 are linear pairs. they lie on a straight line. The sum of the angles on a straight line is 180 degrees. It means that

9x - 1 + y - 20 = 180

y = 180 + 1 + 20 - 9x

y = 201 - 9x equation 1

Also, angle 5x - 15 and angle y - 20 are vertically opposite angles. Vertically opposite angles are equal. It means that

5x - 15 = y - 20 equation 2

Substituting equation 1 into equation 2, it becomes

5x - 15 = 201 - 9x - 20

Collecting like terms, it becomes

5x + 9x = 201 - 20 + 15

14x = 196

x = 196/14

x = 14

y = 201 - 9x = 201 - 9 * 14

y = 201 - 126

y = 75+