Driving at a constant speed, Sharon usually
takes 180 minutes to drive from her house to
her mother's house. One day Sharon begins
the drive at her usual speed, but after driving
1 of the way, she hits a bad snowstorm and
reduces her speed by 20 miles per hour. This
time the trip takes her a total of 276 minutes.
How many miles is the drive from Sharon's
house to her mother's house?

Answer:

So the lengths of the legs are approximately 8.6 cm and 15.6 cm.

Step-by-step explanation:

Let's call the smaller leg "x" and the larger leg "x + 7". According to the Pythagorean theorem, we know that:

x^2 + (x + 7)^2 = 17^2

Expanding the square on the left side and simplifying, we get:

2x^2 + 14x - 210 = 0

Dividing both sides by 2, we get:

x^2 + 7x - 105 = 0

Now we can solve for x using the quadratic formula:

x = (-7 ± sqrt(7^2 - 4(1)(-105))) / 2(1)

x = (-7 ± sqrt(649)) / 2

x ≈ -15.6 or x ≈ 8.6

Since we're dealing with lengths of sides in a triangle, we can't have a negative value for x. So we discard the negative solution and conclude that the smaller leg is approximately 8.6 cm.

To find the larger leg, we add 7 to x:

x + 7 ≈ 15.6 cm

The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.

To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.

To know more about number click-
https://brainly.com/question/24644930
#SPJ1

The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.

138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.

Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.

To know more about number click-
brainly.com/question/24644930
#SPJ1

For a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.

L'Hospital's rule applies to limit expressions of the form 0/0 or infinity/infinity. Specifically, if we have a limit expression of form f(x)/g(x), where f(x) and g(x) both approach 0 or infinity as x approaches a certain value, then L'Hospital's rule may be applied to find the limit of the expression.

It is important to note that L'Hospital's rule can only be applied if the limit of the derivative of f(x) divided by the derivative of g(x) exists and is finite, or if the limit of the derivative of f(x) divided by the derivative of g(x) approaches infinity or negative infinity.

Therefore, for a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.

Find out more about L'Hospital's rule

at brainly.com/question/30300388

#SPJ4

√9+25 = 28

π-4 = -0.8571

³√-27 = -3

2 / 3 = 0.6667

18÷2 = 9

√-27​ = 5.196

In mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).

We have √9+25 = 28

find the square root of 9 = 3

3 + 25 = 28

π-4 = 3.14 - 4

= -0.8571

³√-27 = ³√3³

= 3

2÷3 = 0.6667

18÷2 = 9

Read more on surds here:https://brainly.com/question/840021

#SPJ1

question:

given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27​

find the value of the terms

Answer:

(15+x)÷4 = 80-x

by criss cross we'll get:

15+x = 4(80-x)

15+x = 320-4x

x+4x=320-15

5x = 305

x = 61

According to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).

In mathematics, multiplication is an arithmetic operation that combines two or more numbers to produce a product. It is represented by the symbol "×" or "*", or by placing the numbers next to each other with no symbol between them.

Mary is 21 years old, so according to the rating factor table, her rating factor is 1.22 for a female.

For liability insurance, Mary has chosen the 50/100/25 coverage, which means $50,000 for bodily injury per person, $100,000 for bodily injury per accident, and $25,000 for property damage per accident. The premium for this coverage is $385.

For collision and comprehensive insurance, Mary has chosen a $500 deductible, so her premiums are $102 for collision and $87 for comprehensive.

To find the total annual premium, we add up the premiums for liability insurance and collision/comprehensive insurance:

Total premium = Liability premium + Collision premium + Comprehensive premium

Total premium = $385 + $102 + $87

Total premium = $574

Therefore, according to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).

To know more about multiplication visit :

https://brainly.com/question/1135170

#SPJ1

The rate of change (or slope) of this linear function is -1/2.

A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.

The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.

Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.

The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:

slope = (change in y) / (change in x)

Let's use the points (0, -3) and (2, -4) to calculate the slope:

slope = (-4 - (-3)) / (2 - 0)

slope = -1 / 2

Therefore, the rate of change (or slope) of this linear function is -1/2.

To know more about slope visit:

https://brainly.com/question/20828026

#SPJ1

Answer:

What is the Value of Tan 270 Degrees? The value of tan 270 degrees is undefined. Tan 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .) ⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .

please marke a a brainalist pls

Therefore, the only statement that is true is: "The new area is 6 times the original area."

Area is a measure of the size or extent of a two-dimensional surface or region, such as the surface of a square, rectangle, circle, triangle, or any other shape. It is expressed in square units, such as square meters, square feet, or square centimeters.

Here,

If the side lengths of a square are tripled, the new side length will be 2 mm x 3 = 6 mm.

The original area of the square is:

Area = side length x side length = 2 mm x 2 mm = 4 mm²

The new area of the square with tripled side lengths will be:

New area = new side length x new side length = 6 mm x 6 mm = 36 mm²

Therefore, the new area of the square will be 36 mm².

To determine which of the following statements about its area will be true, we need to see which statements are true for the new area of 36 mm²:

A. The new area is 6 times the original area. This statement is true because 36 mm² is 6 times larger than 4 mm².

B. The new area is 3 times the original area. This statement is false because 36 mm² is 9 times larger than 4 mm², not 3 times larger.

C. The new area is equal to the original area. This statement is false because the new area of 36 mm² is much larger than the original area of 4 mm².

To know more about area,

https://brainly.com/question/22469440

#SPJ1

Complete question:

look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?

The ratio of the new area to the old area will be 2:1

The ratio of the new area to the old area will be 6:1.

The ratio of the new area to the old area will be 1:2.

The ratio of the new area to the old area will be 4:1.

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.

given

AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.

We can apply the Pythagorean theorem to segment AB as follows:

[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]

AB² = 50

AB = √50 = 5√2

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ1

The set of all n×n invertible matrices with the standard operations of matrix addition and scalar multiplication is (b) not a subspace.

A Subspace is defined as a subset of a vector space that is itself a vector space under the same operations of addition and scalar multiplication defined on the original vector space.

To be a subspace of Mₙ,ₙ, a subset of Mₙ,ₙ must satisfy three conditions:

(i) The subset must contain the zero matrix,

(ii) The subset must be closed under matrix addition, meaning that if A and B are in the subset, then (A + B) is also in the subset.

(iii) The subset must be closed under scalar multiplication, meaning that if A is in the subset and c is any scalar, then cA is also in the subset.

The set of all n×n invertible matrices does not contain the zero matrix, as the zero matrix is not invertible.

Therefore, it fails to meet the first condition and cannot be a subspace, the correct option is (b).

Learn more about Subspace here

https://brainly.com/question/13106912

#SPJ4

The given question is incomplete, the complete question is

Determine whether the subset of Mₙ,ₙ is a subspace of Mₙ,ₙ with the standard operations of matrix addition and scalar multiplication.

The set of all n×n invertible matrices is

(a) Subspace

(b) Not a subspace.

The width of the top of the bookcase should be approximately 12.2 inches to give Bria's soap carving collection an area of 300 square inches.

Simply multiply the length and width measurements to get the area of your square or rectangular area in square inches.

Assume the bookcase's top is rectangular, with length "L" and width "b". Because the area of a rectangle is the product of its length and width, we get:

L * b = 300

To find "b," we can rearrange the equation as follows:

b = 300 / L

We don't have enough information to directly solve for "L," but we can make an educated guess based on the figure provided. Based on the illustration, the bookcase appears to be roughly twice as long as it is wide. So let us suppose:

L ≈ 2b

When we plug this into the equation above, we get:

b = 300 / (2b) (2b)

To simplify, we have:

b^2 = 150

When we take the square root of both sides, we get:

b ≈ 12.2

We have, rounded to the nearest tenth of an inch:

b ≈ 12.2 inches

As a result, the width of the top of the bookcase should be approximately 12.2 inches in order to give Bria's soap carving collection a 300-square-inch area.

To know more about Area of Square Inches visit:

https://brainly.com/question/7742557

#SPJ1

Answer:

Assuming that (gof)(5) means (g(f(5))):

(gof)(5) = g(f(5)) = g(3x + 7) = 5x + 2

Therefore, (gof)(5) = 5(3x + 7) + 2 = 15x + 17.

The intersection of two parallel lines; x = 10 metres.

Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.

The alternate interior angles are equal because of the parallel lines characteristic.

Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.

Setting these two angles equal to each other, we can get:

x+20 = 2x+10

Simplifying this equation, we get:

x = 10.

To know more about parallel lines visit:-

https://brainly.com/question/16701300

#SPJ1

FALSE. Every random sample of the same size from a given population will not produce exactly the same confidence interval for μ.

The confidence interval is a statistical measure used to estimate the range of values within which a population parameter is likely to fall. The confidence interval is calculated based on the sample mean and standard deviation, as well as the level of confidence desired.

Suppose we take a random sample of size n from a population, and calculate the confidence interval for the population mean using this sample. The sample mean and the sample standard deviation will be used to estimate the true population mean and the population standard deviation, respectively. However, as the sample is random, each sample—despite being drawn from the same population—will have different values for the sample mean and standard deviation. Thus, different samples will produce different confidence intervals for the population mean.

Moreover, the size of the sample also affects the width of the confidence interval; larger samples tend to produce more precise estimates of the population mean, while smaller samples yield larger confidence intervals. Therefore, random samples of different sizes from a given population will also produce different confidence intervals.

In summary, the confidence interval is a statistical measure that provides a range of likely values for the population parameter, such as the population mean. While it can be calculated using any random sample from a population, different samples of the same size or different sizes will generally produce different confidence intervals.

To know more about confidence interval click here:

brainly.com/question/24131141

#SPJ4

The sine function with the desired features is given as follows:

F(x) = sin(3.5π(x + π/2)) + 1.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are listed as follows:

The function has an amplitude of 1, hence the parameter A is given as follows:

A = 1.

The period is of 4/7, hence the coefficient B is given as follows:

2π/B = 4/7

4B = 14π

B = 3.5π.

The function contains the point (-π, 2), hence the phase shift and the vertical shift are given as follows:

Hence the function is:

F(x) = sin(3.5π(x + π/2)) + 1.

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The answer of the given question based on finding the missing length of a triangle the answer is , None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

In geometry,  triangle is  two-dimensional polygon with three straight sides and three angles. It is one of  basic shapes in geometry and can be defined as  closed figure with three line segments as its sides, where each side is connected to two endpoints called vertices. The sum of  interior angles of  triangle are 180° degrees.

Triangles are classified based on length of their sides and  measure of their angles. A triangle can be equilateral, isosceles, or scalene based on whether all sides are equal, two sides are equal, or all sides are different, respectively.

To find the missing length indicated, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this triangle, we can see that the two legs have lengths of 9 and 16, and the hypotenuse has length X. So we can write:

9²+ 16² = X²

Simplifying the left-hand side:

81 + 256 = X²

337 = X²

Taking the square root of both sides (and remembering that X must be positive, since it is a length):

X = sqrt(337)

X ≈ 18.3575

So the missing length indicated is approximately 18.3575. None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

To know more about Pythagorean theorem visit:

https://brainly.com/question/14930619

#SPJ1

The graph's function limit at x=4 is 6.

In mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.

The formal definition of the limit of a function f(x) as x approaches a value a is as follows:

For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.

Limit f(x) at x tend to 4⁺ =6.

Limit f(x) at x tend to 4⁻ =6

Hence, the graph's function limit at x=4 is 6.

To know more about function, visit:

https://brainly.com/question/12431044

#SPJ1

The product of the number 3/4 and 8 1/2 is 51/8.

A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.

The given numbers are 3/4 and 8 1/2.

Convert the mixed number to an improper fraction:

8 1/2 = (8 x 2 + 1) / 2 = 17/2

Then, we can multiply the fractions:

3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8

Hence, the product of 3/4 and 8 1/2 is 51/8.

Learn more about improper fraction here:

https://brainly.com/question/21449807

#SPJ1

The slope of this linear function is equal to: B. -2/9.

The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.

The value of each expression is: C. a) 2, b) 1/2, c) 2/9.

In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (8 - 10)/(6 - (-3))

Slope (m) = (8 - 10)/(6 + 3)

Slope (m) =

Slope (m) = -2/9.

In Mathematics, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given parameters, we have:

Volume of cylinder, V = 3.14 × 5² × 10

Volume of cylinder, V = 785 m³

(√2)² = 2

(1/√2)² = 1/2

(√2/3)² = 2/9

Read more on cylinder here: brainly.com/question/14060443

#SPJ1

When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is used to determine how likely or unlikely an occurrence is to occur. An event's likelihood is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of occurrence. The symbol P stands for the probability of an occurrence A. (A). It is determined by dividing the number of positive results of event A by all the potential outcomes.

given

(a) The result of rolling 3 or 6 times is 6 + 9 = 15.

Experimental chance = (Total number of rolls) / (Number of times 3 or 6 were rolled) = 15/40 = 0.375

(b) The theoretical likelihood of rolling either a 3 or a 6 on a fair number cube is equal to the total of those odds, which is 1/6 + 1/6 = 1/3 = 0.333. (rounded to three decimal places).

(c) When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Answer:

52

Step-by-step explanation:

10.40 TIMES 3

The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.

A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.

The intervals of the piecewise function are;

f(x) = √(x + 5) if x < -2

f(x) = |x + 1| -2 ≤ x ≤ 2

f(x) = (x - 2)² if x > 2

The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²

The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2

The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.

The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.

The correct option for the graph of the piecewise function is therefore the third option.

Please find the attached the graph of the piecewise function created with MS Excel

Learn more on the graph of piecewise functions here: https://brainly.com/question/29192595

#SPJ1

Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:

lwh = 600

For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:

l(3w)h = 3lwh = 3(600) = 1800 cubic feet

Therefore, the volume of the neighbor's pool is 1800 cubic feet.

Step-by-step explanation:

Answer:

Anna had 23 sweets in her bag at the start of the day.

Step-by-step explanation:

Let's use working backwards to find out how many sweets were in the bag at the start of the day.

At the end of lesson 4, Anna had 1 sweet left in her bag. So, before she gave a sweet to her teacher in lesson 4, she had 2 sweets left in her bag.

In lesson 3, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 3, she had 2 x 2 + 1 = 5 sweets in her bag.

In lesson 2, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 2, she had 5 x 2 + 1 = 11 sweets in her bag.

In lesson 1, she gave out half of the sweets in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 1, she had 11 x 2 + 1 = 23 sweets in her bag.

Therefore, Anna had 23 sweets in her bag at the start of the day.

Answer:

Step-by-step explanation:

The appropriate 0.5 adjusted formula for normal approximation is option (d) p(x > 8.5)

The appropriate 0.5 adjusted formula for normal approximation to approximate binomial probabilities when n is large is

P(Z > (x + 0.5 - np) / sqrt(np(1-p)))

where Z is the standard normal variable, x is the number of successes, n is the number of trials, and p is the probability of success in each trial.

To approximate binomial probability p(x > 8) when n is large, we need to use the continuity correction and find the appropriate 0.5 adjusted formula for normal approximation. Here, x = 8, n is large, and p is unknown. We first need to find the value of p.

Assuming a binomial distribution, the mean is np and the variance is np(1-p). Since n is large, we can use the following approximation

np = mean = 8, and

np(1-p) = variance = npq

8q = npq

q = 0.875

p = 1 - q = 0.125

Now, using the continuity correction, we adjust the inequality to p(x > 8) = p(x > 8.5 - 0.5)

P(Z > (8.5 - 0.5 - 8∙0.125) / sqrt(8∙0.125∙0.875))

= P(Z > 0.5 / 0.666)

= P(Z > 0.75)

Therefore, the correct option is (d) p(x > 8.5)

Learn more about binomial probability here

brainly.com/question/29350029

#SPJ4

The given question is incomplete, the complete question is:

To approximate binomial probability p(x > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. a) p(x > 7.5) b)  p(x >= 9) c) p(x > 9) d) p(x > 8.5)

Answer: The total number of ways the photography student can choose 4 photos out of 21 is given by the combination formula:

Step-by-step explanation: C(21, 4) = (21!)/((4!)(21-4)!) = 5985

Out of the 21 photos, 9 were photos of babies. The number of ways the student can choose 4 baby photos out of 9 is given by:

C(9, 4) = (9!)/((4!)(9-4)!) = 126

Therefore, the probability that all 4 photos chosen are of babies is:

P = (number of ways to choose 4 baby photos)/(total number of ways to choose 4 photos)

P = C(9, 4)/C(21, 4)

P = 126/5985

P ≈ 0.021

So, the probability that all 4 photos chosen are of babies is approximately 0.021 or 2.1%.

The sum of the distinct prime factors is 16.

There are overall 24 factors of 792 among which 792 is the most significant factor and its prime factors are 2, 3, and 11.

Hence sum = 2 + 3 + 11 = 16