‼️WILL MARK BRAINLIEST‼️

WILL MARK BRAINLIEST

Answers

Answer 1

The experimental probability that the next person at the booth will win a prize is 40%.

How to calculate the probability

In this particular case, out of a total of 35 trials (people), there were 14 individuals who snagged a prize and the other 21 who did not. Consequently, we are able to calculate the experimental probability of the next person at the booth succeeding in winning a prize as such:

Number of Winners / Total Number of Participants

= 14 / 35

= 0.4 or 40%

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Related Questions

a study of two kinds of photocopying equipment shows that 61 failures of the first kind of equipment took on the average 80.7 minutes to repair with a standard deviation of 19.4 minutes, whereas 41 failures of the second kind of equipment took on the average 88.1 minutes to repair with a standard deviation of 18.8 minutes. construct a 98% confidence interval for the ratio of the variances of the two populations sampled.

Answers

To construct a confidence interval for the ratio of the variances of the two populations sampled, we can use the F-distribution. The formula for the F-statistic is: F = (s1^2 / s2^2) / (n1 - 1) / (n2 - 1) Where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Using the given data, we have:

s1 = 19.4
s2 = 18.8
n1 = 61
n2 = 41

The F-statistic is then:

F = (19.4^2 / 18.8^2) / (61 - 1) / (41 - 1) = 1.399

To find the confidence interval, we need to look up the critical values of the F-distribution with degrees of freedom (df) of (n1 - 1) and (n2 - 1) at the 1% level of significance.

Using a table or calculator, we find that the critical values are 0.414 and 2.518.

Thus, the confidence interval for the ratio of the variances is:

1 / (2.518 / sqrt(F)) < σ1^2 / σ2^2 < 1 / (0.414 / sqrt(F))

1 / (2.518 / sqrt(1.399)) < σ1^2 / σ2^2 < 1 / (0.414 / sqrt(1.399))

0.266 < σ1^2 / σ2^2 < 2.083

Therefore, we can be 98% confident that the ratio of the variances of the two populations sampled lies between 0.266 and 2.083.
To construct a 98% confidence interval for the ratio of the variances of the two populations sampled, we will use the F-distribution and the following formula:

CI = (s1^2 / s2^2) * (1 / Fα/2, df1, df2, F1-α/2, df1, df2)

Here, s1 and s2 are the standard deviations of the first and second kinds of equipment, and df1 and df2 are the degrees of freedom for each sample. Fα/2 and F1-α/2 are the F-distribution critical values at the α/2 and 1-α/2 levels, respectively.

Step 1: Calculate the variances (s1^2 and s2^2).
Variance1 = (19.4)^2 = 376.36
Variance2 = (18.8)^2 = 353.44

Step 2: Calculate the degrees of freedom (df1 and df2).
df1 = n1 - 1 = 61 - 1 = 60
df2 = n2 - 1 = 41 - 1 = 40

Step 3: Find the F-distribution critical values (Fα/2, df1, df2, F1-α/2, df1, df2) for a 98% confidence interval (α = 0.02).
F0.01, 60, 40 = 0.4611
F0.99, 60, 40 = 2.1080

Step 4: Calculate the confidence interval using the formula.
CI = (376.36 / 353.44) * (1 / 0.4611, 2.1080)
Lower limit = (376.36 / 353.44) * 0.4611 = 0.5925
Upper limit = (376.36 / 353.44) * 2.1080 = 2.2444

The 98% confidence interval for the ratio of the variances of the two populations sampled is (0.5925, 2.2444).

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Which type of relationship is indicated by the residual plot?

Onon-linear relationship

linear relationship

exponential relationship

quadratic relationship

cannot be determined

Answers

The non-linear relationship is the type of relationship that is indicated by the residual plot.

What is the non-linear relationship?

A non-linear relationship denotes a kind of connection between two variables whereby one variable does not consequentially result in a proportional transformation for the other.

To elaborate, instead of delineating a direct line, such an association is generally expressed as a curve, exponential formula, or other convoluted mathematical equations.

Notwithstanding, the rate of difference in these variables isn't fixed and may shift in tandem with changes to either one of their numerical values.

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T/F : The solution set of the linear system whose augmented matrix [a1a2a3b] is the same as the solution set of the equation x1a1+x2a2+a3x3=b

Answers

True.

the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.



The augmented matrix [a1 a2 a3 | b] corresponds to the system of linear equations:

a1x1 + a2x2 + a3x3 = b

The solution set of this system is the same as the solution set of the vector equation:

[x1, x2, x3] * [a1, a2, a3] = b

which can be written as:

x1a1 + x2a2 + x3a3 = b

Therefore, the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.

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Points A and B are 80km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 8 hours, but if they travel in opposite directions, they meet in 1 hour 20 mins. What are their speeds in km/hr?

Answers

The speeds of the car are 35 km/hr and 25 km/hr, if a car starts from A and another car starts from B at the same time. If both cars travel in the same direction, they cross in 8 hours, but if these cars travel in opposite directions, they meet each other in 1 hour 20 mins. A and B have a distance of 80 km.

Let the speed of the car at A be [tex]v_1[/tex]

the speed of the car at B be [tex]v_2[/tex]

In the first case, they travel in the same direction, the relative velocity is given by [tex]v_1-v_2[/tex]

[tex]v_1-v_2[/tex] = [tex]\frac{80}{8}[/tex]

[tex]v_1-v_2[/tex] = 10 -----(i)

In the second case, they travel in the opposite direction, the relative velocity is given by [tex]v_1+v_2[/tex]

[tex]v_1+v_2[/tex] = [tex]\frac{80}{1\frac{1}{3} }[/tex]

[tex]v_1+v_2[/tex] = [tex]\frac{80*3}{4}[/tex]

[tex]v_1+v_2[/tex] = 60 ------(ii)

Add equations (i) and (ii)

[tex]2v_1[/tex] = 70

[tex]v_1[/tex] = 35 km/hr

From equation (i)

[tex]v_2[/tex] = 25 km/hr

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Write in slope intercept form given the information. slope = -1; y-intercept = 8

Answers

In slope intercept form is y=mx+b m is slope which in your case is -1 and b is y-intercept which in your case is 8 so your answer is y=-1x+8

15 The line plot shows the weights of ten eggs laid by one hen. EGGS LAID BY ONE HEN



THE PICTURE



what is the total weight, in onces, of the four heaviest eggs?
A 4

B 7

C 8 1/2

D 8 3/4
Pls tell me the answer again!​

Answers

Answer:

I believe its 8 3/4

Step-by-step explanation:

What is the exact number of fractions equivalent to 4/5

Answers

The exact number of fractions equivalent to the given fraction is 8/10, 12/15 and 16/20, under the condition that the given fraction is 4/5.

In order to determine the equivalent fractions of 4/5, we are have to multiply the numerator and denominator by same numbers.

Then the exact numbers equivalent to the given fraction is

(4/5) × (2/2) = (4 × 2) / (5 × 2) = 8/10

(4/5) × (3/3) = (4 × 3) / (5 × 3) = 12/15

(4/5) × (4/4) = (4 × 4) / (5 × 4) = 16/20

Then, 8/10, 12/15, and 16/20 are equal to 4/5 when simplified, which means they are equivalent in nature.

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modeling with mathematics a web browser is open on your computer screen. a rectangular computer screen is shown displaying a rectangular web browser. the length of the computer screen is labeled x plus 7 inches. the length and width of the web browser are labeled x inches and x minus 2 inches respectively. a. the area of the browser window is 24 square inches. find the length of the browser window $x$ . in. b. the browser covers $\frac{3}{13}$ of the screen. what are the dimensions of the screen? length: in. width: in.

Answers

The dimensions of the screen are:

length = L = 12 inches

width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches

a. The area of the browser window is given by:

area = length * width

24 = x(x-2)

Simplifying and solving for x, we get:

[tex]x^2[/tex] - 2x - 24 = 0

(x - 6)(x + 4) = 0

Since the length cannot be negative, we take x = 6. Therefore, the length of the browser window is x = 6 inches.

b. Let L and W be the length and width of the computer screen, respectively. We are given that:

length of browser = x inches = L - 7 inches

width of browser = x - 2 inches

The area of the browser is:

area of browser = x(x-2) = (L-7)(L-9)

We are also given that the browser covers 3/13 of the screen, so:

area of browser = (3/13) * area of screen

x(x-2) = (3/13) * L * W

Substituting x = L - 7 and simplifying, we get:

(L-7)(L-9) = (3/13) * L * W

Expanding and simplifying, we get:

13L[tex]^2[/tex] - 182L + 546 = 3LW

Since L and W are positive, we can divide both sides by 3L to get:

W = (13L - 182) / 3

We also know that the browser covers 3/13 of the screen, so:

area of browser = (3/13) * area of screen

x(x-2) = (3/13) * L * W

6(4) = (3/13) * L * ((13L-182)/3)

24 = (L/3) * (13L-182)

8 = L(13L-182)/3

24 = L(13L-182)

13L^2 - 182L - 24 = 0

(L - 12)(13L + 2) = 0

Since the length cannot be negative, we take L = 12. Therefore, the dimensions of the screen are:

length = L = 12 inches

width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches

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pls help ASAPP v(if u dont know the answer then dont GUESS the answer. and no links please)

Answers

the answer is b or the second one

Answer:

Step-by-step explanation:

first do Pemdas and thats it

Sarah was mixing up some lemonade to sell for her lemonade stand. The recipe calls for 3 scoops of lemonade mix to make 2 gallons of lemonade.

If she has 21 scoops of lemonade mix in the container, how many gallons of lemonade can she make?
*

Answers

Sarah can make 14 gallons of lemonade with 21 scoops of lemonade mix.

Given information:

Sarah was mixing up some lemonade to sell for her lemonade stand.

The recipe calls for 3 scoops of lemonade mix to make 2 gallons of lemonade.

If 3 scoops of lemonade mix are needed to make 2 gallons of lemonade, then one scoop of lemonade mix can make 2/3 of a gallon of lemonade.

As per the multiplication,

So, with 21 scoops of lemonade mix, Sarah can make:

21 scoops x (2/3 gallon/scoop) = 14 gallons

Therefore, Sarah can make 14 gallons of lemonade with 21 scoops of lemonade mix.

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a sailfish can travel as fast as 68 miles per hour. at that rate, how far would a sailfish travel in 45 minutes

Answers

Therefore, a sailfish would travel 51 miles in 45 minutes if it maintained a speed of 68 miles per hour in the equation.

To calculate the distance traveled in a given time, we can use the formula distance = rate x time, where rate refers to the speed of travel and time refers to the duration of travel. In this scenario, we are given a rate of 68 miles per hour and a time of 45 minutes.

To use the formula, we first need to convert the time to hours since the rate is given in miles per hour. We do this by dividing the time by 60, since there are 60 minutes in an hour. In this case, 45 minutes divided by 60 minutes per hour gives us 0.75 hours.

Now, we can plug in the values for rate and time into the formula and solve for distance. Multiplying 68 miles per hour by 0.75 hours gives us a distance of 51 miles.

45 minutes / 60 minutes per hour = 0.75 hours

Then, we can use the formula: distance = rate x time

distance = 68 miles per hour x 0.75 hours

distance = 51 miles

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Help me find the volume! PLEASE ITS IMPORTANT!!!!

Answers

The volume of the given pyramid is approximately 780.975 cubic kilometers.

Given information:

The provided shape is a pyramid with a triangular base.

And the width of the base is 11.7 kilometers and the length of the base is 26.7 kilometers.

And the height of the pyramid is 15 kilometers.

To find the volume of a pyramid with a triangular base, we use the formula:

V = (1/3)Bh

where V is the volume, B is the area of the base, and h is the height of the pyramid.

In this case, we are given that the base of the pyramid is a triangle with a width of 11.7 kilometers and a length of 26.7 kilometers.

To find the area of this triangle, we use the formula for the area of a triangle:

B = (1/2)bh

where b is the width and h is the length of the base of the triangle.

Substituting the given values, we get:

B = (1/2)(11.7)(26.7)

B = 156.195 km²

Now, we substitute the values of B and h into the formula for the volume of a pyramid:

V = (1/3)(156.195)(15)

V = 780.975 km³.

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(Chapter 14) If f(x,y) --> L as (x,y) --> (a,b) along every straight line through (a,b), then limit as (x,y) approches (a,b) = L

Answers

Yes, the statement is true. This is a restatement of the definition of the limit of a function of two variables.

Formally, we say that the limit of f(x,y) as (x,y) approaches (a,b) is L if and only if for every number ε > 0, there exists a number δ > 0 such that if the distance between (x,y) and (a,b) is less than δ, then the distance between f(x,y) and L is less than ε. In symbols:

For every ε > 0, there exists a δ > 0 such that if 0 < sqrt((x-a)^2 + (y-b)^2) < δ, then |f(x,y) - L| < ε.

The condition that f(x,y) approaches L along every straight line through (a,b) is equivalent to saying that the limit of f(x,y) as (x,y) approaches (a,b) along any path is also L. This is a stronger condition than the usual definition of the limit, and implies that the limit exists and is equal to L.

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What is the surface area of a rubik's cube in cm² with side that measures 14cm?

Answers

The surface area of the Rubik's cube is 1176 cm².

Surface area is a measurement of the overall space occupied by an object's surface. Often, it is expressed in terms of square measurements like square meters (m²) or square feet (ft²).

A Rubik's cube has six faces, each of which is a square with sides equal to the length of a side of the cube. Therefore, the surface area of a Rubik's cube is six times the area of one of its faces.

The area of one face of the cube with a side of 14 cm is:

14 cm x 14 cm = 196 cm²

So, the total surface area of the Rubik's cube is:

6 x 196 cm²= 1176 cm²

Hence, the area will bed 1176 cm².

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help i need help super quick

Answers

the answer is c, i'm pretty sure

Hiya can someone pls help me ty due in few days thanks! <3

Answers

The distance from the wall, that the ladder slipped during the day, would be 21 cm.

How to find the distance ?

First, use the Pythagorean theorem to find the original height of the ladder from the wall:

50² + b² = 300²

2, 500 + b ² = 90, 000

b ² = 90, 000 - 2, 500

b = √ 87, 500

b = 295. 8 cm

We can then find the new distance from the wall to be :
= 50 + 70

= 120 cm

The new height of the ladder to show the slip would be:

120² + b² = 300²

14,400 + b ² = 90, 000

b ² = 90, 000 - 14, 400

b = √ 75, 600

b = 275 cm

The distance slipped is:

= 295. 8 - 275

= 21 cm

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if each complete revolution of the pedals moves the bike 5.20 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. neglect work done by friction and other losses. the pedals turn in a circle of diameter 34.4 cm.

Answers

Average force ≈ 0.208 times the total force exerted in a revolution.


To calculate the average force exerted on the pedals tangent to their circular path, we need to first find the circumference of the pedal circle and then determine the force exerted per revolution.

1. Calculate the circumference of the pedal circle:
Circumference = π * diameter
Circumference = π * 0.344 m (converted 34.4 cm to meters)
Circumference ≈ 1.081 m

2. Calculate the force exerted per revolution:
We are given that each complete revolution moves the bike 5.20 m along its path. The force exerted per revolution is directly proportional to the work done.
 
Work done = Force * distance
Force = Work done / distance
Force = Work done / (5.20 m / 1.081 m)

Since the work done by friction and other losses is neglected, we only need to know the ratio of distances to determine the average force exerted on the pedals tangent to their circular path. Therefore,

Average force = 1.081 m / 5.20 m
Average force ≈ 0.208 times the total force exerted in a revolution.

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write the equation of the line that
passes through (2,-6) and is perpendicular to y = 2/3x+4

Answers

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+4\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{2} }}[/tex]

so we're really looking for the equation of a line whose slope is -3/2 and it passes through (2 , -6)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{2}) \implies y +6 = - \cfrac{3}{2} ( x -2) \\\\\\ y+6=- \cfrac{3}{2}x+3\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x-3 \end{array}}[/tex]

(-3,6) (-2,9) write the equation in slope intercept form

Answers

Answer:

y = 3x + 15

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-3,6) (-2,9)

We see the y increase by 3 and the x increase by 1, so the slope is

m = 3

Y-intercept is located at (0,15)

So, the equation is y = 3x + 15

y = 3x + 15


The rate of change is 3 which you can find using rise over run or a different method. If you have a graph you can see where the two lines intersect (connect or touch each other) to find your y (initial value).

4. If W has a chi-square distribution with v degrees of freedom, find E(W) and V(w). if X, i = 1, 2,..,n is a random sample from a normal distribution with mean y and variance o, find E(S) and V(s).

Answers

Since S is the average of the random sample, the expected value (E(S)) and variance (V(S)) are: E(S) = µ and V(S) = σ² / n

For W with v degrees of freedom, we know that E(W) = v and V(W) = 2v.

Now, let's consider the random sample X = (X1, X2, ..., Xn) from a normal distribution with mean y and variance o. The sample variance S^2 is defined as:

S^2 = (1/n-1) * sum(i=1 to n) (Xi - y)^2

where y is the sample mean.

Using properties of the normal distribution, we can derive that E(S^2) = o * (n-1)/n and V(S^2) = (2o^2 * (n-1)^2)/(n(n-2)).

To find E(S) and V(S), we take the square root of E(S^2) and V(S^2) respectively. Thus:

E(S) = sqrt(o * (n-1)/n)

V(S) = sqrt((2o^2 * (n-1)^2)/(n(n-2)))


First, let's discuss the chi-square distribution. If W has a chi-square distribution with v degrees of freedom, the expected value (E(W)) and variance (V(W)) are as follows:

E(W) = v
V(W) = 2v

Now let's consider the random sample from a normal distribution. If X, i = 1, 2,...,n is a random sample from a normal distribution with mean y (µ) and variance σ², we can find the sample mean (S) as:

S = (ΣX_i) / n

Since S is the average of the random sample, the expected value (E(S)) and variance (V(S)) are:
E(S) = µ and V(S) = σ² / n

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help i need help with the question

Answers

The angle which is supplemental to the 6 is the angle 8, which makes option a correct.

What are angles formed by a pair of parallel lines cut by a transversal line?

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

Supplementary angles are a pair of angles that add up to 180 degrees. The angles 6 and 8 lie on a straight line which implies they are supplementary as the sum of angles on a straight line is also 180°

Therefore, the angle which is supplemental to the 6 is the angle 8, which makes option a correct.

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Someone please help me with this question.

Answers

The value of the angle x of the regular octagon is: x = 112.5°

How to find the interior angle of a polygon?

The formula for the Interior angle of a Polygon is:

θ = 180(n - 2)/n

We are given that the polygon has 8 sides. Thus:

θ = 180(8 - 2)/8

θ = 135°

Sum of angles in a triangle is 180° and as such, the base angles of the Isosceles triangle formed is:

base angle = (180 - 135)/2

= 22.5°

Thus:

x = 135 - 22.5

x = 112.5°

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i need help with this problem

Answers

The Surface Area of Cone is 124.344 cm².

We have,

Diameter= 11 cm

slant height = 7.2 cm

Radius = 5.5 cm

So, Surface Area of Cone

= πrl

= 3.14(5.5)(7.2)

= 124.344 cm²

Thus the Surface Area of Cone is 124.344 cm².

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A drawer contains 12 brown socks and 12 black socks, all unmatched. A man takes socks out at random in the dark. Answer the following questions. Question 7 Select the least number of socks that he must take out to be sure that he has at least two socks of the same color. 12 4 Question 8 Select the least number of socks that he must take out to be sure that he has at least two black socks. 3

Answers

For Question 7, the man must take out 4 socks to be sure that he has at least two socks of the same color. This is because he could potentially take out 3 brown socks and 3 black socks before getting a matching pair, but with 4 socks, there must be at least two of the same color.

For Question 8, the man must take out 3 socks to be sure that he has at least two black socks. This is because he could potentially take out all 12 brown socks before getting a black one, but with 3 socks, there must be at least one black sock and then a potential for a second.

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find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest.

Answers

The three consecutive integers are 10, 11, and 12.

To find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest, follow these steps:

1. Let the smallest integer be x. Then, the other two consecutive integers are x + 1 and x + 2.

2. The sum of their squares is x^2 + (x + 1)^2 + (x + 2)^2.

3. The given condition is that this sum is 65 more than three times the square of the smallest integer: x^2 + (x + 1)^2 + (x + 2)^2 = 3x^2 + 65.

4. Simplify the equation:
  x^2 + (x^2 + 2x + 1) + (x^2 + 4x + 4) = 3x^2 + 65

5. Combine like terms:
  3x^2 + 6x + 5 = 3x^2 + 65

6. Subtract 3x^2 from both sides to eliminate the x^2 terms:
  6x + 5 = 65

7. Subtract 5 from both sides:
  6x = 60

8. Divide by 6:
  x = 10

So, the three consecutive integers are 10, 11, and 12.

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can Someone please help me answer this? i really don't know what to do for this one and it due tmr and I got a bunch of questions lefttt ty for whoever helps :D

Answers

Health Club B costs $8 less in monthly membership fees than Health Club A.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.

For Club A, the monthly cost is given as follows:

$60.

For Club B, we have that each 4 months, the cost increases by $208, hence the monthly cost is given as follows:

208/4 = $52.

Which is $8 less than Club A.

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Students measured the length of several pencils and recorded their data in a table.

Pencil Lengths (Inches)

3
7
8
,

5
1
4
,

4
,

6
1
8
,

4
1
2
,

5
1
4
,

3
1
2
,

5
3
8
,

4
3
4
,

5
Part A
How many dots will the line plot have in all?

A.
2

B.
6

C.
7

D.
10

Part B
The students will make the line plot using one fractional unit. What fractional unit should the students use so that all of the data can be plotted above a label?

A.
tenths

B.
eighths

C.
fourths

D.
halves
HELP MEEEE

Answers

Answer: I don't know, sorry!

Step-by-step explanation:

If x belongs to the interval [0,2π], at which values of x does the tangent to the curve y=cosx have a slope of 1 ? Type answer as x=c, where c is constant. For multiple answers, separate with a comma. For example, x=1. x=2 If x belongs to the interval [0,2π], at which values of x does the tangent to the curve y=cosx have a slope of 21​ ? Type answer as x=c, where c is constant. For multiple answers, separate with a comma. For example, x=1, x=2 Note: You can eam partial credit on this problem. You have attempted this problem 0 times. You have 3 attempts left before new version will be requested. You have unlimited attempts remaining.

Answers

The value at which x does the tangent to the curve y=cosx have a slope of 1 is x =  3π/2.

To find the values of x at which the tangent to the curve y = cos(x) has a slope of 1, if x belongs to the interval [0,2π], we need to find the points where the derivative of the function is equal to 1. The derivative of y = cos(x) with respect to x is -sin(x). So, we need to solve the equation:

-sin(x) = 1

sin(x) = -1

Now, we want to find the values of x in the interval [0, 2π] that satisfy this equation. The sine function takes the value -1 at x = 3π/2. Therefore, x does the tangent to the curve y=cosx have a slope of 1 is x = 3π/2.

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the statistical power of a test is the probability that the test will correctly reject a false null hypothesis. that is, if a null hypothesis is false at the population level, the statistical power of a test is the probability that a researcher rejects the null hypothesis in his or her sample too. group of answer choices true false

Answers

The statement provided in the question is true. The statistical power of a test is the probability of correctly rejecting a false null hypothesis. It is the ability of a statistical test to detect a true effect, given that one exists. In other words, it is the likelihood that a study will be able to detect a difference or relationship between variables if such a difference or relationship truly exists in the population being studied.

The statistical power of a test depends on several factors, including the sample size, the effect size, and the level of significance chosen for the test. A larger sample size, a larger effect size, and a smaller level of significance all increase the power of a test. A low statistical power may indicate that the sample size is too small or that the test is not sensitive enough to detect the true effect.

Therefore, it is important to consider statistical power when designing and interpreting studies.

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You have two 5-gallon buckets. One is filled with water but has a slow leak, leaking out water 7 ounces per minute. The other is empty but is being used to catch water from a leaky faucet at a rate of 4 ounces per minute

Answers

Based on the mentioned informations, at the time when the first bucket is empty, it is calculated that the second bucket will contain approximately 365.72 ounces volume of water.

The first step is to convert the 5-gallon volume to ounces. There are 128 ounces in one gallon, so 5 gallons is equal to 640 ounces.

The water is leaking out of the bucket at a rate of 7 ounces per minute. Therefore, the amount of water remaining in the bucket after t minutes can be calculated as:

Remaining water in the bucket = 640 - 7t

We want to find out when the remaining water in the bucket reaches zero, so we set the above equation equal to zero and solve for t:

640 - 7t = 0

7t = 640

t = 91.43 minutes

Therefore, it will take approximately 91.43 minutes for the water level in the bucket to reach zero.

At the same time, the empty bucket is being filled with water from the leaky faucet at a rate of 4 ounces per minute. Therefore, the amount of water in the empty bucket after t minutes can be calculated as:

Water in the empty bucket = 4t

We want to find out how much water will be in the empty bucket at the time when the first bucket is empty, so we substitute t = 91.43 into the above equation:

Water in the empty bucket = 4 x 91.43

Water in the empty bucket = 365.72 ounces

Therefore, at the time when the first bucket is empty, the second bucket will contain approximately 365.72 ounces of water.

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The complete question is :

If the bucket that is filled with water initially contained 5 gallons of water and the leak in that bucket started at time zero, how long will it take for the water level in the bucket to reach zero, and how much water will be in the empty bucket at that time assuming that both leaks continue at the same rate of 7 ounces per minute and 4 ounces per minute, respectively?

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