Brian is running. The number of calories he has burned vanes directly with the number of minutes he has run. See the graph below.

She'll probably instruct you to clean your room, but there's a 1/5 or 0.2 (20%) probability she won't.

The likelihood or chance of an occurrence happening is known as probability. For instance, there is only one method to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we put.

P(A) = 4/5 (the probability of mom telling to clean the room)

P(not A) = 1 - P(A) = 1 - 4/5 = 1/5

Therefore, there is a 1/5 chance, or 0.2 percent, that she won't instruct you to clean your room.

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Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

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The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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Answer:

A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm

Calculate the volume using the value 22/7. 

Step-by-step explanation:

Answer:

$24,992

Step-by-step explanation:

The equation for simple interest is I = PRT where I is the interest earned, P is the principal deposited/borrowed, R is the rate as a decimal, and T is time in years.

I = (17,600)(0.084)(5)

I = 7,392

The total amount that must be repaid is the interest + the principal:

7,392 + 17,600 = 24,992

Please let me know if you have questions

Answer:

The number is 9.

Step-by-step explanation:

Using algebra, let c be the number you are finding.

2c -3 = 15

2c = 18

c = 9

Hence, the number is 9.

The new endpoints of the line segment after the segment is rotated by 90 degrees are (1, -2) and (4, -5).

A set that has a geometric structure by itself or another set constitutes the geometric transformation. A shape can change shape, but not appearance. After that, the shape might match or resemble its preimage. A change in something's appearance is what transformations actually signify.

Given that, the line is rotated by 90 degrees.

When a figure is rotated by 90 degrees clockwise the coordinated of the image transform using the following transformation:

(x , y) ↔ (y , -x)

The coordinates of the given line are:

(2, -1) and (5, -4)

Applying the transformation the coordinates of the rotated line segment are:

(2, -1) ↔ (1, -2)

(5, -4) ↔ (4, -5)

Hence, the new endpoints of the line segment after the segment is rotated by 90 degrees are (1, -2) and (4, -5).

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Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

Samantha got 85 questions right.

Step-by-step explanation:

90% of 50 is 45.

80% of 50 is 40.

40 + 45 = 85

:)

Answer:

95

Step-by-step explanation:

Im pretty sure It's 95 because if you get a 90% on a test with 50 questions, you would've gotten 45 correct. If you get an 80% on a test with 50 questions, you would've gotten 40 correct. Then add them.

Answer:

5

Step-by-step explanation:

The arc length is 59/360 of the circumference.

So, the circumference is 34(360/59), which is about 207.

Answer:

Ann traveled 165 miles on 5 gallons of gas

Step-by-step explanation:

First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.

a. The probability of x being no more than a: d. P(x≤a)

b. The probability of being at least a: e. P(x≥a)

c. The probability of z being at most a: b. P(x ≤a)

d. The probability of z being no less than a: c. P(x ≥a).

e. The probability of a being more than a: c. P(x>a)

f. The probability of 2 being exactly a: b. P(x =a)

Using mathematical symbols, probability notation is a means to represent events and their probabilities. In this instance, an is a specified value or constant, while x is utilised as a random variable. P(x=a), P(x>=a), P(x=a), P(x>a), P(xa), or P(x!=a) are the possible outcomes. Depending on the particular event under consideration, one may choose one of the inequality symbols (, >, =, >=, or =). For instance, P(x=a) denotes the likelihood that x will not exceed a, but P(x>a) denotes the likelihood that x will exceed a. To minimise confusion and assure accurate probability estimates, the proper notation must be used

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The answer for following questions are mentioned below.

Probability notation is a way of representing the probability of an event or a random variable using mathematical symbols and formulas. It typically involves using capital letters, such as P, to denote probability, and variables, such as x, to denote random variables.

a. The probability of x being no more than a:

d. P(x≤a)

b. The probability of being atleast a:

e. P(x≥ a)

c. The probability of z being at most a:

b. P(x ≤a)

d. The probability of z being no less than a:

c. P(x ≥a).

e. The probability of a being more than a:

c. P(x>a)

f. The probability of 2 being exactly a:

b. P(x =a)

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The biscuits should be placed 2.54 centimeters apart on the baking tray.

The unitary method is a way for solving a problem by the first value of a single unit and than finding the value by multiplying the single unit. Unitary method is a technique by which we can find the value of a single value from the value of more than one devices and the value of more than one unit from the value of a single unit. We can this method use for most of the calculations in math.

We are given that;

Elana must roll the dough into 7 inch rounds.

a) To convert this measurement to centimeters, we can use the conversion factor 1 inch = 2.54 centimeters. Therefore, 7 inches is equal to:

7 inches x 2.54 centimeters/inch = 17.78 centimeters

So, Elana must roll the dough into 17.78 centimeter rounds.

b) To rewrite all the ingredients using grams or milliliters, we need to know the density of each ingredient. Assuming that the density of each ingredient is the same as that of all-purpose flour (which is approximately 125 grams per cup), we can convert the measurements as follows:

1 cup flour = 125 grams flour

1/2 cup sugar = 100 grams sugar

2 teaspoons baking powder = 10 grams baking powder

1 teaspoon salt = 5 grams salt

1/2 cup cream = 120 milliliters cream (assuming a density of 1 gram per milliliter)

So, the rewritten ingredients are:

125 grams flour

100 grams sugar

10 grams baking powder

5 grams salt

120 milliliters cream

c) The recipe states that the oven should be preheated to 350 °F. To convert this temperature to Celsius, we can use the formula:

Celsius = (Fahrenheit - 32) x 5/9

So, the temperature in Celsius is:

Celsius = (350 - 32) x 5/9 = 176.67 °C

Therefore, Elana should heat the oven to 176.67 °C.

d) The recipe states that the biscuits should be placed on the baking tray 1 inch apart. To convert this measurement to centimeters, we can use the conversion factor 1 inch = 2.54 centimeters. Therefore, the biscuits should be placed on the baking tray:

1 inch x 2.54 centimeters/inch = 2.54 centimeters

Therefore, by unitary method answer will be 2.54 centimeters.

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From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

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Answer: 1. \(-\dfrac{5}{6}\)  2. \(-\dfrac{1}{3}\) . 3. \(-3\)

Step-by-step explanation:

Formula: Slope\(=\dfrac{y_2-y_1}{x_2-x_1}\)

1. (-2,2) (3,-3)

Slope \(=\dfrac{-3-2}{3-(-2)}\)

\(=\dfrac{-5}{3+2}\\\\=\dfrac{-5}{6}\)

Hence, slope of line passing through  (-2,2) (3,-3) is \(-\dfrac{5}{6}\) .

2. (-5,1) (4,-2)

Slope \(=\dfrac{-2-1}{4-(-5)}\)

\(=\dfrac{-3}{4+5}\\\\=\dfrac{-3}{9}\\\\=-\dfrac{1}{3}\)

Hence, slope of line passing through  (-2,2) and (3,-3) is \(-\dfrac{1}{3}\) .

3. (-1,5) (2,-4)

Slope \(=\dfrac{-4-5}{2-(-1)}\)

\(=\dfrac{-9}{2+1}\\\\=\dfrac{-9}{3}\\\\=-3\)

Hence, slope of line passing through (-1,5) and (2,-4) is -3.

The value of x is -3 and y is 7 for equilateral triangle having x+1, 2x+4 and 3x+y sides.

We can use the fact that an equilateral triangle has equal lengths on each of its three sides to determine the values of x and y.

Given:

First side=x+y

second side= 2x+4

third side=3x+y

An equilateral triangle has three equal sides, hence the following equations can be constructed:

x + 1 = 2x + 4

2x + 4 = 3x + y

Let's tackle each of these equations separately:

x + 1 = 2x + 4

We will subtract x from both sides and subtract 4 from both sides in order to solve this equation:

x + 1 - x = 2x + 4 - x

1 = x + 4

By taking 4 away from both sides, we arrive at:

1 - 4 = x + 4 - 4 , -3 = x

Therefore, x has been determined to be -3.

Now, substitute the value of x in the second equation:

2x + 4 = 3x + y

2(-3) + 4 = 3(-3) + y

-6 + 4 = -9 + y

-2 = -9 + y

y = -2 + 9

y = 7

So, we determined that y has a value of 7.

As a result, the values of x and y are, respectively, x=-3 and y=7

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Answer:

Step-by-step explanation:

In an equilateral triangle all sides are equal.

So each of these sides (and their equations are equal to each other.)

To find x - set the first two (as they only involve x) equal to each other and solve.

x + 1 = 2x + 4

x -x + 1 = 2x - x + 4

1 = x + 4

1- 4 = x + 4 - 4

-3 = x

Then substitute -3 for x in the last equation to find y, also setting it equal to one of the other equations.

3(x) + y = x + 1

3(-3) + y = -3 + 1

-9 + y = -2

-9 + 9 + y = -2 + 9

y = 7

so x = -3 and y equal 7

Answer:

768

Step-by-step explanation:

The point estimate of the population proportion is the midpoint of the confidence interval, which is the average of the lower and upper bounds:

Point estimate = (Lower bound + Upper bound) / 2

= (0.422 + 0.858) / 2

= 0.64

The margin of error is half the width of the confidence interval:

Margin of error = (Upper bound - Lower bound) / 2

= (0.858 - 0.422) / 2

= 0.218

To find the number of individuals in the sample with the specified characteristic x, we need to know the proportion of the sample with that characteristic. We can use the point estimate as an approximation:

x = n * point estimate

= 1200 * 0.64

= 768

Therefore, the number of individuals in the sample with the specified characteristic is 768.

Answer:

3628800

Step-by-step explanation:

There are 10 letters, so the answer is 10!

10*9*8*7*6*5*4*3*2*1= 3628800

Answer:

151,200 ways

151,200 waysThe letters of the word BOOKKEEPER can be arranged in 151,200 ways. The group can be arranged in 8640 ways with all students of the same major together. There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:  \(5t\sqrt{89}\)  miles

=======================================================

Explanation:

Draw a right triangle. The legs of this triangle represent the directions the two friends travel (one going east, the other going north).

The horizontal leg has side length 40t and the vertical leg has length 25t, where t is the number of hours.

I'm using the idea that distance = rate*time.

We'll use the pythagorean theorem to find the hypotenuse in terms of t.

\(a = 40t, \ b = 25t\\\\a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{(40t)^2+(25t)^2}\\\\c = \sqrt{1600t^2+625t^2}\\\\c = \sqrt{2225t^2}\\\\c = \sqrt{25*89t^2}\\\\c = \sqrt{25t^2}*\sqrt{89}\\\\c = 5t\sqrt{89}\\\\\)

At time t hours, the distance between the two friends is exactly \(5t\sqrt{89}\) miles.

Answer:

4(+5)(7+4)

Step-by-step explanation:

i think this is real

Answers:

1. 750

2. 750 + 5*20 = 850

By simply equating and entering the value, the ordered pair (1, 1) is a solution to the system of linear equations.

The statistic is said to be in its simplified sense when divided through its smallest equivalent fraction. What can be done to find the most basic form. Look for common factors in the denominator and denominator. Check a fractional integer to see if it's a power of two. A statement having two collinear and an equal indication in the middle is called the equation in mathematics. The simplified version of any equation provides the degrees of each variables in descending order. The normal format of a linear function is an x + b = 0. The general form of something like a linear equation with two variables is an x + b y + c = 0. (or something similar). Inequalities can be categorized as identity or conditional solutions. An identity stands true regardless of the value given to the variables.

given

= x + 4y = 3

y = −4x − 3

= x + 4(-4x-3) = 3

= x - 16x -12 = 3

= -15x = 15

x = -1

putting value of x

-1 + 4y = 3

4y = 4

y = 1

= By simply equating and entering the value, the ordered pair (1, 1) is a solution to the system of linear equations.

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

67

Step-by-step explanation:

Expressing the expansion of the logarithm in terms of log y, we can write: log(8x^2) = log(8) + 2*log(y), where y = x

Using the logarithmic identity that states log(a^b) = b*log(a), we can expand log(8x^2) as:

log(8x^2) = log(8) + log(x^2)

Note that a  logarithmic identity is a mathematical relationship or equation that involves logarithms.

We can further simplify log(x^2) as:

log(x^2) = 2*log(x)

Therefore, we can write:

log(8x^2) = log(8) + 2*log(x)

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Assuming \(f(x)=x^2\).

\(y=x^2\\x=-\sqrt y \vee x=\sqrt y\)

Since \(x\geq0\) only \(x=\sqrt y\) is valid.

Therefore

\(f^{-1}(x)=\sqrt{x}\)

Answer: 36˚

Step-by-step explanation:

180 - 3x = 2x

180 = 5x

.: x = 36˚

Answer: 14%

Step-by-step explanation: To find the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade, we divide the number of members who meet both criteria (14) by the total number of members (100) and multiply by 100 to get a percentage. Therefore, the probability is approximately 14%.

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