During a rainstorm, a pail collects 1 3 of an inch of water in 5 6 of a minute. At what rate is the pail collecting water?.

Value of x is 1.411

Given Eq.

[tex]9^{x+2} = 2^{5x-4} \\\\[/tex]

Applying exponent rules

[tex](x+2)ln(9) = (5x-4)ln(2)\\[/tex]

Solving for x

[tex]x = \frac{4ln(6)}{5ln(2)-2ln(3)}[/tex]

[tex]x = \frac{1.791}{5(0.693)-2(1.098)}[/tex]

[tex]x = \frac{1.791}{3.465-2.196} \\[/tex]

[tex]x = \frac{1.791}{1.269}[/tex]

[tex]x = 1.411[/tex]

Value of x is 1.411

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Answer:

x = 62

y = 41

Step-by-step explanation:

y + 21 = x

x + y + 77 = 180

2y+77 = 180

2y = 82

y = 41

x = 62

The probability of both the dice showing prime numbers is 1/4.

Prime numbers:

The numbers which have only two factors,  one and itself are known as prime numbers.

A dice has 6 faces numbering from 1 to 6.

Prime numbers from 1 to 6 are 2, 3, and 5.

Probability of one dice showing a prime number

                 = (number of favorable outcomes) / (total number of outcomes)

                 = 3/6

                 = 1/2

Probability of two dice showing a prime number = (1/2) x (1/2)

                                                                                 = 1/4

Therefore, the probability of both the dice showing a prime number is 1/4.

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The slope of a line is m=−3

The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).

Given that

the slope of 6x+2y=−32:

slope using the standard form:

slope m of a line of the form Ax+By=C equals –A/B

A=6, B=2

m=−6/2

simplify

m=−3

Therefore the slope of a line is m=−3

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Answer:

C

Step-by-step explanation:

Check the picture below.

The dimensions of the rectangle which form the dining room is 7 by 5 meters.

The perimeter of the rectangle is 24 meters.

The total length of a shape's boundaries is its perimeter. The total lengths of all other edges and sides are added to find a shape's perimeter.

Let the length be a and the width be b.

Hence 2(a + b) = 24

or, a+b = 12

Now the area of the rectangle is given as 35 square meters.

Therefore ab = 35

now we will use these two equations to find the dimension of the rectangle

a+b = 12

or, a = 12 - b

again:

ab = 35

or, (12 - b)b = 35

or, 12 b - b² = 35

or,  - b² +12b -35 = 0

or,   b² - 12b + 35 = 0

or,  (b-7) (b-5) = 0

either b = 7 or b = 5 .

Therefore the value of a from the equations is 5 or 7.

Therefore the dimensions of the dining room are 7 by 5 meters.

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Answer:

4 answers

Step-by-step explanation:

y = |x² - 4|

3 = |x² - 4|

3 = x² - 4     and -3 = x² - 4

3+4=x² - 4 + 4          and -3+4=x² - 4 + 4

7=x² and 1=x²

x=[tex]\sqrt{7}[/tex] and x=-[tex]\sqrt{7}[/tex] since x²=7

x=-1 and x=1 since x²=1

x= -[tex]\sqrt{7}[/tex], [tex]\sqrt{7}[/tex], -1, 1 ==> 4 answers

If the point D (8. -5) is reflected over the y-axis, the coordinates of D' would be: (-8, -5).

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to point D, the coordinates of the vertices of point D' include the following:

(x, y)                    →            (-x, y)

Point D = (8, -5)   →  Point D' = (-8, -5)

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Answer:

x = 2

y = 0

Step-by-step explanation:

Here are the simultaneous equations:

[tex]y=2-x\\6x+5y=11\\x+2y=2\\2x+y=1\\[/tex]

There are only two unknown values, so only two equations are needed to find the answer. I will use these:

[tex]y=2-x\\x+2y=2[/tex]

Substitute the first equation into the y in the second equation:

[tex]x+2(2-x)=2[/tex]

Simplify

[tex]x+4-2x=2\\x=2[/tex]

Use the value of x to find y in equation 1:

[tex]y=2-x\\y=2-2\\y=0[/tex]

Answer:

7x10x13=910=910 kilograms

Step-by-step explanation:

Answer:

[tex]-\frac{5}{32}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2(2)^4}-\frac{3}{4(2)^2} \\\frac{1}{32} - \frac{3}{16} = -\frac{5}{32}[/tex]

Singh percent error is approximately 13%.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.

Mrs. Singh is making snack packs for her class to eat on their field trip. She estimates that she will need 35 snack packs.  The day of the field trip 4 students are absent and Mrs. Singh actually only needs 31 snack packs.

Therefore, Singh's percent error can be calculated as follows:

percent error = 35 - 31 / 31 × 100

percent error =  4 / 31 ×100

percent error = 400 / 31

percent error = 12.9032258065

percent error ≈ 13%

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The numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that the numbers are,6.42,6.53,6.497,6.66,6.453,6.486.

Ascending order refers to a list of numbers that are arranged from least to greatest. The numbers are arranged in ascending order in this form. The first figure must be less than the second figure. It is referred to in descending order when the numbers are listed from greatest to least.

Thus, the numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.

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The nearby tower that casts a shadow that is 39.5 m long is 85 m tall.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

The ratio of the shadow of a pole to its length is 1.4 m : 3 m.

At the same time, the ratio of the shadow of a tower to its length should  also be equal to the ratio of the shadow of a pole to its length, which is 1.4 : 3.

Let x = length of the tower

Using proportion, determine the length of the tower by solving for x.

1.4 : 3 = 39.5 m : x

x = 39.5(3)/1.4

x = 84.64

Round off to the nearest meter.

length of the tower = 85 meters

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The amount that it will cost to paint the walls, given the cost per square foot and the dimensions of the rectangular walls is $828

First, find the area of the rectangular walls by the formula for the area of a rectangle which is:

= Length x Width

The area of the rectangles is therefore:

= 12 x 23

= 276 feet ²

The area of the two rectangular walls is:

= 276 + 276

= 552 feet ²

The cost to paint the walls is:

= Area of walls x cost per square feet to paint

= 552 x 1.50

= $828

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The rectangular form of Θ = 3π/4 will be; y + x = 0.

Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

On converting the rectangluar to polar form of the complex number;

x = rcosθ and y = rsinθ

z = r(cosθ+isinθ)

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Given the Θ = 3π/4

Therefore, θ = tan⁻¹y/x  = 3π/4

y/x  = tan (3π/4)

Now multiply both side by x

yx/x  = tan (3π/4) x

y =  tan (3π/4) x

Thus, y = -x

in rectangular form y + x = 0

Hence, the rectangular form of Θ = 3π/4 will be; y + x = 0.

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Answer: There were 18 oz. in the full bottle.

Step-by-step explanation:

If there are 6 oz. left, and Sasha drank 1/3 of half the bottle, then that means she drank 3 oz, since 6 is 2/3 of 9, which means that half of the bottle was 9 oz. 9 oz. is half of 18 oz, which means that there were 18 ounces in the full bottle.

Total students who graduated this year from this university is 3000.

This is a normal distribution problem with

Mean , μ = $20,000

Standard deviation, σ = $8,000

If 189 of the recent graduates have salaries of at least $32240.

Then, We first find the percentage of LU graduates with salaries more than $32240.

Required probability = P(x ≥ 32240)

We first normalize or standardize $32,240, then as we know,

z = (x - μ)/σ

= (32240 - 20000)/8000 = 1.53

The required probability:

P(x ≥ 32240) = P(z ≥ 1.53)

We'll use data from the normal probability table for these probabilities

P(x ≥ 32240) = P(z ≥ 1.53) = 1 - P(z < 1.53)

= 1 - 0.93699

= 0.06301

= 6.301%

So, 6.301% of the graduates this year = 189

Total Number of graduates this year = (189/0.06301) = 2999.5 = 3000 graduates this year.

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A) Chi-square test can be used if one of the samples has a value of less than five is the correct option.

Chi-square distribution and Chi-square test for independence:

The assumptions for the chi-square test are:

Hence, options (b), (c), and (d) are the assumptions that are true for chi-square test. Therefore, the options (b), (c), and (d) are considered incorrect.

Hence, option (a), that is, “a Chi-square test can be used if one of the samples has a value of less than five” is the correct option.

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Answer:

-24

Step-by-step explanation:

-3[-4(3-10)-12]/-2(-1)

-3[-4(-7)-12]/2

-3[28-12]/2

-3[16]/2

-48/2

-24

Hopes this helps

The difference quotient for the given quadratic equation is:

d = (2h + 4x + 4)

Here we have the quadratic function:

f(x)= 2x² + 4x - 3

And we want to get the difference quotient that is defined as:

d =  ( f(x + h) - f(x))/(h)

Replacing our function there, we get:

d = ( 2(x + h)² + 4*(x + h) - 3 - (2x² + 4x - 3)/h

d = (2x² + 2h² + 4xh + 4x + 4h - 3 - 2x² - 4x + 3)/h

d = (2h² + 4xh + 4h)/h

d = (2h + 4x + 4)

That is the difference quotient.

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Answer:

Step-by-step explanation:

Define Variables:

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangos cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangos cost $8, then:

2p+3m=8

Write System of Equations:

5p+6m=17.75

2p+3m=8

System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangoes cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangoes cost $8, then:

2p+3m=8

System of Equations:

5p+6m=17.75

2p+3m=8

Therefore System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

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Answer: 30 weeks

Step-by-step explanation:

let w = number of weeks

you have = 60 + 7w

she has = 120 + 5w

60+7w = 120 + 5w

7w-5w = 120-60

2w = 60

w = 30 weeks

The correct option is option (B) .

In a Multiple regression Model , the value of adjusted r-Squared is positive.

Adjusted r-Squared :

Adjusted r-squared is a modified version of r-squared adjusted for the number of predictors in the model. The fitted r-squared increases only if the new term improves the model beyond what would be expected by chance. This is reduced if the predictor happens to not improve the model more than expected.

The formula for r-squared,

Adjusted r-squared= 1 - [ ( 1 -r²)(n-1)/(n-k-1)]

where

N --> number of points in the data sample.

K --> number of independent regressors, i. number of variables in the model excluding or constant.

r²--> Indicates how well a term (data point) fits a curve or line.

r-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%.

100% r-squared means that all movements in the security are completely explained by movements in the index.

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The rate when his distance from second base changes and it is two third of the way to first base is - 13.86 feet/s.

let us consider the following values

distance between batter to Second base = d feet

distance between batter to First base

= x feet

distance between first to second base

= 90 feet

Using the Pythagorean theorem:

d² = x² + 90²

Knowing that the velocity of the bat to first base is 25 ft/s,

the distance x can be written as: x

= 90 - 25t

The equation for is,d² = 90²+(90 -25t)²--(1)

we want to find the rate of change of d.

let it be d' and from implicit differentiation:

2d.d' = 2(90-24t) × (-25)

d' = -50(90 - 25t) / (2d)

d' = -25 (90 - 24t) / d ---(*)

We can determine t and d from the fact that the batter is two third to his first base: d = √90^2 + 60^2 = √1 = 108.2 feet

putting the values of d in (1) we get,

=> 90 - 25t = 60 => 25t = 30 => t = 6/5.

Substitute d' in the formula equation (*)

d' = -25 (90 - 24t) / d = -25(90-30)/108.2

d'= - 13.86

d' = - 13.86 feet/s

negative sign means decreasing distance from second base (as it approaches the first

bases, it approaches the second base).

Hence,The required speed is 13.86 feet/s

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The number of students that are in both the Categories A and B are 16 students.

In the question ,

it is given that ,

the total number of students in category A and category B is 32 students .

which is represented as A union B ,

that is n(AUB) = 32 ,

the number of students in category A = n(A) = 24

the number of students in category B = n(B) = 24

we need to find the number of students that are in both category ,

that is n(A∩B) .

we know that ,

n(AUB) = n(A) + n(B) - n(A∩B)

Substituting the values , we get

n(A∩B) = 24 + 24 - 32

= 48 - 32

= 16

Therefore , The number of students that are in both the Categories are 16 students.

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