A person cycles from their home to a library which is 8 kilometers away. It takes them 20 minutes to reach the library. They stay there for 30 minutes to read, and then
walk to their friend's home which is 4 kilometers from the library and reach there in 20 minutes. Which graph best represents this situation?

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 3 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (2, - 4 ) into the partial equation

- 4 = [tex]\frac{1}{2}[/tex] (2) + c = 1 + c ( subtract 1 from both sides )

- 5 = c

y = [tex]\frac{1}{2}[/tex] x - 5 ← equation of parallel line

The point (1, 1/2) lie on the equation  y(x² + 1) = 1.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x, y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, A function y(x² + 1) = 1.

y = 1/(x² + 1).

When x = 1, y = 1/2.

When x = - 1, y = 1/2.

So, The points that lie on the equation y(x² + 1) = 1 is (1, 1/2).

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Step-by-step explanation:

Cross multiply to solve for "a":

6 * a = 8 * 8

Simplify the right side:

6 * a = 64

Divide both sides by 6 to isolate "a":

a = 64 / 6

Simplify:

a = 10.67

The required probability is 0.8945 that a sample of 29 smoke detectors will have a mean lifetime between 57 and 64 months.

To find the probability that a sample mean is between 57 and 64 months, we need to find the standard deviation of the sample mean, which is given by the standard deviation of the population divided by the square root of the sample size.

The standard deviation of the sample mean = standard deviation of the population / square root of sample size = 8 / √(29) = 8 / 5.385 = 1.48

Next, we need to standardize the interval of 57-64 months by subtracting the mean and dividing it by the standard deviation of the sample mean.

z₁ = (57 - 60) / 1.48 = -2.03

z₂ = (64 - 60) / 1.48 = 1.35

Finally, we can use a standard normal table to find the area under the normal curve between z₁ and z₂, which gives us the probability of a sample mean falling in the interval (57, 64).

P(57 < X < 64) = P(-2.03 < Z < 1.35) = 0.9790 - 0.0845 = 0.8945

Therefore, the final answer is 0.8945, rounded to four decimal places.

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Answer: 16

Step-by-step explanation:

To get from 3 to 12, you multiply by 4

To get from 5 to 20, you multiply by 4

So you just multiply 4 by 4 to get x

Answer:

x = 16

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] = 4 ( multiply both sides by 4 to clear the fraction )

x = 16

The percent decrease in the boiling point of water from sea level to 7,500 feet is equal to 18.7%.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the percent decrease in the boiling point of water from sea level to 7,500 feet, we would determine the difference in temperature as follows;

Difference in temperature = 212°F - 198°F

Difference in temperature = 14°F

Percentage decrease = 14/7500 × 100

Percentage decrease = 0.00187 × 100

Percentage decrease = 18.7%.

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Answer: [tex]533 yd^{2}[/tex]

Step-by-step explanation:

The surface area of the base is:

(20 x 17.3) / 2

= 346 / 2

= 173

The surface area of one of the three identical triangles is:

(20 x 12) / 2

= 240 / 2

= 120

So in total, your answer would be one base plus three of those identical triangles:

173 + (3 x 120)

= [tex]533 yd^{2}[/tex]

Answer: The answer is 101

Answer:

Below

Step-by-step explanation:

Area is base ( which is 6 m) times the height ( which is 8m)

6 x 8 = 48 m^2

Answer: x<3

Step-by-step explanation:

Bring the 11 to the other side of the equation, and subtract.

5x<15.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{11 + 5x < 26}[/tex]

[tex]\mathsf{5x + 11 < 26}[/tex]

[tex]\large\textbf{Subtract 11 to both sides:}[/tex]

[tex]\mathsf{5x + 11 - 11 < 26 - 11}[/tex]

[tex]\large\textbf{Simplify it}[/tex]

[tex]\mathsf{5x < 26 - 11}[/tex]

[tex]\mathsf{5x < 15}[/tex]

[tex]\large\textbf{Divide 5 to both sides}[/tex]

[tex]\mathsf{\dfrac{5x}{5} < \dfrac{15}{5}}[/tex]

[tex]\large\textbf{Simplify it}[/tex]

[tex]\mathsf{x < \dfrac{15}{5}}[/tex]

[tex]\mathsf{x < 3}[/tex]
[tex]\large\textbf{You have an \boxed{\rm{\bf o p e n e d}} circle shaded to the left}[/tex]

[tex]\huge\boxed{\mathsf{x < 3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

A. 12 cm, 5 cm, 17 cm

Step-by-step explanation:

For any three given lengths to be the sides of a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check each of the options:

A. 12 cm, 5 cm, 17 cm: 5 + 12 = 17, which is greater than 17, so this is a valid triangle.

B. 10 cm, 15 cm, 24 cm: 10 + 15 = 25, which is greater than 24, so this is a valid triangle.

C. 9 cm, 22 cm, 11 cm: 9 + 11 = 20, which is not greater than 22, so this is not a valid triangle.

D. 21 cm, 7 cm, 6 cm: 7 + 6 = 13, which is not greater than 21, so this is not a valid triangle.

Therefore, the three lengths that could be the sides of a triangle are A (12 cm, 5 cm, 17 cm) and B (10 cm, 15 cm, 24 cm).

Answer: -1.5, -4/3, 3/2, 3/2

Step-by-step explanation:

First, convert the numbers to decimals or fractions.

-1.5

3/2 = 1.5

3/2 = 1.5

-4/3 = -1.3

Therefore, on a number line, the numbers would be in the following order:

-1.5, -4/3, 3/2, 3/2

The height of the cell phone tower in feet is solved to be 23 feet

The height of the cell phone tower is calculated using the concept of similar triangle and the equation is as follows

A ​2-ft vertical post casts a 10​-in shadow

2 / 10

nearby cell phone tower casts a 115​-ft shadow

let the height be x

x / 115

equating the proportions

2 / 10 = x / 115

cross multiplying

10x = 2 * 115

x = 2 * 115 / 10

x = 23 ft

The height of the tower is 23 feet

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The multiplication expression with eight rational factors are ''positive''.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.

Since, Multiplication of four positive numbers are always gives a positive number and multiplication of four negative numbers are always gives a positive number.

Hence, The multiplication expression with eight rational factors are positive.

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Answer:

4/161

Step-by-step explanation:

2×2
____
23×7

=4
161

=4
161

Answer:

He sleeps about 9 hours at night.

Step-by-step explanation:

If Sean's baby brother sleeps 13 hours a day, and takes 2 two-hour naps during the day, he sleeps 2 * 2 = 4 hours during the day.

SOOO, he sleeps 13 - 4 = 9 hours at night.

Answer: you need to do it on your own

Step-by-step explanation:

Answer:Hypothesis: A polygon has four equal sides and four right angles.

Conclusion: The polygon is a square.

Converse: If the angles are congruent, then the measure of 4] equals the measure of K.

Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.

Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.

Original statement: If a number is even, then it is divisible by two.

Inverse: If a number is not divisible by two, then it is not even.

Biconditional statement: This month is November if and only if next month is December.

Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.

Converse: If a triangle contains a right angle, then it is a right triangle.

The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).

Step-by-step explanation:

Hypothesis: A polygon has four equal sides and four right angles.

Conclusion: The polygon is a square.

Converse: If the angles are congruent, then the measure of 4] equals the measure of K.

Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.

Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.

Original statement: If a number is even, then it is divisible by two.

Inverse: If a number is not divisible by two, then it is not even.

Biconditional statement: This month is November if and only if next month is December.

Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.

Converse: If a triangle contains a right angle, then it is a right triangle.

The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).

To find the sum of the Xm'f column, we first need to calculate the midpoint (Xm) for each class interval and then multiply it by the frequency (f) for that interval. The midpoint of each class interval can be calculated as the average of the lower and upper bounds of the interval.

For the first class interval 50-52:

Xm = (50 + 52) / 2 = 51

Xm'f = Xm * f = 51 * 5 = 255

For the second class interval 53-55:

Xm = (53 + 55) / 2 = 54

Xm'f = Xm * f = 54 * 8 = 432

For the third class interval 56-58:

Xm = (56 + 58) / 2 = 57

Xm'f = Xm * f = 57 * 12 = 684

For the fourth class interval 59-61:

Xm = (59 + 61) / 2 = 60

Xm'f = Xm * f = 60 * 13 = 780

For the fifth class interval 62-64:

Xm = (62 + 64) / 2 = 63

Xm'f = Xm * f = 63 * 11 = 693

Finally, we can add up the Xm'f values for each interval to get the sum of the Xm'f column:

Sum of Xm'f = 255 + 432 + 684 + 780 + 693 = 2954

So the sum of the Xm'f column is 2954.

The similarity statement is competed as follows

The proportion is completed as below

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

KL / KJ and ML / KL

LJ / MJ and KJ / LJ

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The equation representing the total cost is 15x + 750 and the total cost of restringing 32 lacrosse sticks would be $1230.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Let, The number of lacrosse sticks be 'x' and the total cost is C(x).

Therefore, The equation representing the context is,

C(x) = 25x + 750.

The total cost of restringing 32 lacrosse sticks would be,

C(32) = 15×32 + 750.

C(32) = 480 + 750.

C(32) = 1230.

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Answer:

We have 10 digits to choose from (0-9), so the total number of 6-digit permutations is 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000.

Of these, the permutations that start with 0 can be eliminated, leaving 9 × 9 × 9 × 9 × 9 × 9 = 729,000.

Now, we need to figure out how many of these are odd. To do this, we note that odd numbers end in 1, 3, 5, 7, or 9. This means that the last digit of an odd 6-digit permutation is always one of these five digits. Since we are choosing the last digit from 5 options, there are 5 × 729,000 = 3,645,000 odd 6-digit permutations that do not start with 0.

Answer: no solution

Step-by-step explanation:

If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Mr. Olsen has a PC business wherein he sells everything at 44.5% above the wholesale price. On the off chance that he bought a printer for $80 wholesale.

Then the retail price is given as,

⇒ $80 x (1 + 0.445)

⇒ $80 x 1.445

⇒ $115.60

If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.

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The sample size if the probability that the mean life is less than 1120 hours is 0.92 is given as follows:

n = 24.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 1100, \sigma = 70, s = \frac{70}{\sqrt{n}}[/tex]

The p-value of Z when X = 1120 is of 0.92, hence Z = 1.405, and the sample size is obtained as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]1.405 = \frac{1120 - 1100}{\frac{70}{\sqrt{n}}}[/tex]

[tex]20\sqrt{n} = 70 \times 1.405[/tex]

[tex]n = \left(\frac{70 \times 1.405}{20}\right)^2[/tex]

n = 24.

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Answer:The range is all number greater than -10, so the values that are elements of the range of f(x) are c) -9, d) -6, and e) -2

Step-by-step explanation: