Which is the logarithmic form of 25 = 52? log25 = 25 log252 = 5 log525 = 2 log52 = 25.

The probability that at least one bulb out of 12 will stop working during holiday season making all of lights go out on string is given by 0.2153.

Number of bulbs working throughout the holiday season = 12

Chance of each bulb working throughout the holiday season = 98%

Let A be the event that at least one bulb stops working during the holiday season, .

Making all of the lights go out, and let B be the event that all bulbs work throughout the holiday season.

Find P(A), the probability of event A.

Use the complement rule to find P(A),

P(A) = 1 - P(B)

To find P(B), we need to calculate the probability that each of the twelve bulbs works throughout the holiday season,

0.98¹² = 0.7847

So, the probability that all bulbs work throughout the holiday season is 0.7847.

This implies,

P(A) = 1 - P(B)

       = 1 - 0.7847

       = 0.2153

Therefore, probability that at least one bulb will stop working during  holiday season, making all of the lights go out on the string is 0.2153.

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Answer:

Arav is 30 and Pawan is 40

Step-by-step explanation:

We can call Arav's age x and Pawan's age x + 10, therefore we can write the following equation:

1/7((x + 10) - 5) = 1/5(x - 5)

1/7(x + 5) = 1/5(x - 5)

5(x + 5) = 7(x - 5)

5x + 25 = 7x - 35

-2x = -60

x = 30 so x + 10 = 40

Answer:

250

Step-by-step explanation:

We can approximate that the scientists counted \(\frac{18}{30}=\frac{3}{5}\) of the elk.

So, the best estimate of the elk population is \(150(5/3)=250\).

Answer:1,250

Step-by-step explanation:

Answer:

To find the volume of the figure made up of two rectangular prisms, we need to find the volume of each rectangular prism and add them together.

The first rectangular prism has a base of 2 cm by 8 cm and a height of 2 cm. Its volume can be found using the formula V = lwh, where l is the length, w is the width, and h is the height:

V1 = 2 cm x 8 cm x 2 cm = 32 cm^3

The second rectangular prism has a base of 3 cm by 8 cm and a height of 6 cm. Its volume can be found using the same formula:

V2 = 3 cm x 8 cm x 6 cm = 144 cm^3

To find the total volume of the figure, we can add the volumes of the two rectangular prisms:

Vtotal = V1 + V2 = 32 cm^3 + 144 cm^3 = 176 cm^3

Therefore, the volume of the figure made up of two rectangular prisms is 176 cubic centimeters.

Answer:

The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the formula for the volume of the cylinder is given by:

We have r = 10 inches and h = 5 inches

V = 500π cubic inches

Percent change in volume from cylinder A to cylinder B:

= 50%

Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

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Step-by-step explanation:

The quadratic form induced by the matrix D is given by:

Q(x) = x^T Dx = 3x₁² - 7x₄²

This represents a hyperbolic equation in four variables. To see why, we can rewrite the equation as:

(3/7)x₁² - x₄² = 1

This is the equation of a hyperboloid of two sheets centered at the origin in 4-dimensional space. The cross-sections of this hyperboloid with any plane that contains the origin will be hyperbolas. Therefore, the geometric figure that emerges from the quadratic form induced by the matrix D is a hyperbola.

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Answer:

the one with the most parts citric acid

Step-by-step explanation:

no tables were provided but if a cup is 3/4 water and 1/4 citric acid and the other is 1/4 water and 3/4 citric acid then it's the second one. Basically it the one with the most citric acid.

Answer:

Mango = 0.5, Peach = 1.75

Step-by-step explanation:

Let x represent the price of mango

Let y represent the price of peach

Melanie: 8x + 6y = 14.50

Jaya: 4x + 7y = 14.25

Isolate for a variable in one of the equations (just pick a random one, you don't have to pick mine)

4x + 7y = 14.25 => x = (14.25 - 7y)/4 = 3.5625 - 7/4y

Plug into other equation

8x + 6y = 14.50

8(3.5625 - 7/4y) + 6y = 14.5

28.5 - 14y + 6y = 14.5

28.5 - 14.5 = 14y - 6y

14 = 8y

y = 1.75

4x + 7y = 14.25

4x + 7(1.75) = 14.25

4x + 12.25 = 14.25

4x = 2

x = 0.5

First let's find how many kilometers the jeep traveled, by subtracting the odometer readings:

Now, to find the miles per gallon, we just need to divide the kilometers by the amount of gallons of gasoline:

So Harry got 17.8 miles per gallon with the Jeep.

Answer:

Step-by-step explanation:

Given is an isosceles triangle.

Sum of interior angles is 180°:

Correct choice is B

π(2ft)2(10ft) + π(2ft)2(13ft − 10ft) is used to calculate the total volume of grains that can be stored in the silo.(option-c)

The total volume of grains that can be kept in the silo is calculated as (2ft)2(10ft) + (2ft)2(13ft 10ft).(option-c)

The formula $V = gives the volume of a cylinder.

$, where $r$ denotes the base's radius and $h$ denotes its height. The equation $V = gives the volume of a cone.

$, where $r$ denotes the base's radius and $h$ denotes its height.

The silo is made up of a cone with a height of 3 feet and a radius of 2 feet, as well as a 10 foot tall cylinder with the same dimensions. Consequently, the silo's overall volume is V =

V = \(\pi (2ft)^2 (10ft) + \frac{1}{3} \pi (2ft)^2 (3ft)\)

V =\(\pi (4ft^2) (10ft) + \frac{1}{3} \pi (4ft^2) (3ft)\)

V = \(40 \pi ft^3 + 4 \pi ft^3\)

V = \(44 \pi ft^3\)(option-c)

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Answer:

The graph of the circle can be seen on the image at the end,and the circumference is 31.4 units.

Step-by-step explanation:

Remember that the equation of a circle of radius R and center (a, b) is:

(x - a)² + (y - b)² = R²

Here the center is (4, 1), and the radius is the distance between the points (4, 1) and (4, -4)

So the radius is: R = √( (4 - 4)² + (1 + 4)²)R = 5.

Then the circle equation is:(x - 4)² + (y - 1)² = 5²

And the graph can be seen on the image at the end.  Remember that the circumference of a circle of radius R is:C = 6.28*R

So, here the circumference is:C = 6.28*5 = 31.4

The output of the print statement will be "50".

In the given pseudo-code program, the variable x is assigned a value of 8, and the variable y is assigned a value of 50. Then, the program calls the auxiliary function sqr(x) and passes the value of x as an argument.

The sqr(x) function takes the input x and squares it by multiplying x with itself. In this case, since x is 8, sqr(x) will return the value 64.

After calling the sqr(x) function, the program executes the print statement, which outputs the value of y. Since y is assigned the value 50 and is not modified anywhere else in the program, the output of the print statement will be "50".

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Multiple regression analysis is applied when analyzing the relationship between one dependent variable and two or more independent variables. The goal is to determine the extent to which the independent variables predict the dependent variable.

Multiple regression analysis is a statistical technique used to explore and quantify the relationship between a dependent variable and multiple independent variables. It allows researchers to examine how changes in one or more independent variables impact the dependent variable, while controlling for the effects of other variables. By estimating the coefficients for each independent variable, the analysis provides insights into the strength, direction, and significance of their relationships with the dependent variable. This method is commonly employed in various fields, such as economics, social sciences, and business, to understand complex relationships and make predictions based on the interplay of multiple factors.

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Answer:

i bleive that it is 261 havent done this in a wile tho

Step-by-step explanation:

15×12=180 ( did not divide because there are two of the same triangle) and 9×9=81 add them together and you get 216

Answer:

4,-2,1

Step-by-step explanation:

Keep dividing the previous term by -1/2

So we get

4,-2,1

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

From the question, we have the following parameters that can be used in our computation:

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer: (b/2)^2 = \(\frac{289}{4} or 72.25\)

Step-by-step explanation:

x^2 = a

17x = b

-22 = c

To find which number would have been added use the following formula:

\((\frac{b}{2} )^{2}\)

\((\frac{17}{2} )^{2} = \frac{289}{4}\)

If solving this equation the easier way would be to use the quadratic formula instead of completing the square.

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = - 3x + 2.5

The value of the equation at x = 1 will be given as,

y = - 3 × (1) + 2.5

y = - 3 + 2.5

y = - 0.5

The value of the equation at x = - 1.5 will be given as,

y = - 3 × (-1.5) + 2.5

y = 4.5 + 2.5

y = 7

The value of the equation at x = 8.5 will be given as,

y = - 3 × (8.5) + 2.5

y = - 22.5+ 2.5

y = - 20

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

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Complete question:

Monica's claim is incorrect. Even though her interest rate is higher, she will earn less interest, $10.20, after one year than Paul because her initial deposit is lower.

Paul will earn more interest of $13.20 because he deposited more money, even though his interest rate is slightly lower.

To determine who will earn more interest in one year, we shall calculate the interest earned by each person using the simple interest formula.

The formula for simple interest is:

I = P * r * t

where:

I = the interest earned

P = the principal (the amount deposited)

r = the interest rate (as a decimal)

t =s the time (in years)

For Monica, we are given:

P = $300

r = 0.034 (the interest rate is 3.4%)

t = 1 (the interest earned in one year)

Plugging these values, we have:

I = 300 * 0.034 * 1 = $10.20

So, Monica will earn $10.20 in interest after one year.

For Paul, we are given:

P = $400

r = 0.033 (interest rate = 3.3%)

t = 1 (interest earned in one year)

Plugging the values, we get:

I = 400 * 0.033 * 1 = $13.20

So, Paul will earn $13.20 in interest after one year.

Therefore, Monica's claim is incorrect. Monica will earn $10.20 in interest after one year while Paul will earn $13.20 in interest after one year.

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The equation of the tangent line to the astroid at the point (-3√3, 1) is: y = -(3√3)^(1/3)x - 3(3√3)^(1/3) + 1

To find the equation of the tangent line to the astroid at the point (-3√3, 1), we need to first find the slope of the tangent line.

We can do this by taking the derivative of the equation of the astroid with respect to x, and then evaluating it at the point (-3√3, 1).

Taking the derivative of x²/³ + y²/³ = 4 with respect to x, we get:

(2/3)x^(-1/3) + (2/3)y^(-1/3) * dy/dx = 0

Solving for dy/dx, we get:

dy/dx = (-x^(1/3))/y^(1/3)

Substituting x = -3√3 and y = 1, we get:

dy/dx = (-(-3√3)^(1/3))/(1^(1/3)) = -(3√3)^(1/3)/1

So the slope of the tangent line at the point (-3√3, 1) is -(3√3)^(1/3).

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line. The point-slope form is:

y - y1 = m(x - x1)

Substituting x1 = -3√3, y1 = 1, and m = -(3√3)^(1/3), we get:

y - 1 = -(3√3)^(1/3)(x + 3√3)

Simplifying, the equation of the tangent line to the astroid at the point (-3√3, 1) is:

y = -(3√3)^(1/3)x - 3(3√3)^(1/3) + 1

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Answer:

T = 1.5s

Step-by-step explanation:

Hello,

To find the time the pincone hits the ground, we need to use the equation given.

Note that h = 0 when the pinecones hits the ground.

This question relates to motion under gravity.

h = -16t² + 36

0 = -16t² + 36

Make t² the subject of formula

16t² = 36

t² = 36 / 16

t² = 2.25

Take the square root of both sides

t = √(2.25)

t = 1.5s

The time it takes the pinecone to hit the ground is 1.5s.

Answer:

The first step is to subtract 9 from each side

Step-by-step explanation:

2x+9=21

The first step is to subtract 9 from each side

2x+9-9 = 21-9

2x = 12

Then divide by 2 on each side

2x/2 = 12/2

x = 6

Answer:

That would be to collect like terms

Step-by-step explanation:

Further explanation

\(2x+9=21\\\\Collect\: like\: terms\\2x = 21-9\\\\Simplify\\2x = 12\\\\Divide\:both\:sides\:of\:the\:equation\:by\:2\\\frac{2x}{2} = \frac{12}{2} \\Simplify\\\\x =6\)

Answer:

In Mathematics a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. ... Since q may be equal to 1, every integer is a rational Number.

Step-by-step explanation:

noodlde noodle

Answer:

Step-by-step explanation:

The function C(x) is 0 when x = 14

The expression C(x) = -19(x-14)² represents a quadratic function in standard form.

To find C(14), we need to substitute 14 for x in the equation and simplify.

C(14) = -19(14-14)²

Evaluate the difference

C(14)=  -19(0)²

So, we have

= -19(0)

This gives

= 0

So, when x = 14, the value of the function C(x) is 0.

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Complete question

Find C(14) in C(x) =-19(x-14)²​

Expression

\(bc + 1 - (8d - 4)\)

Equation

\( {w}^{4} = 81\)

Inequality

\(63 < 9k\)