Blake mows the neighbors' lawns to earn money. He earns $50 for 4 hours of mowing.
a. At what unit rate (dollars/hour) does Blake get paid?

Answer:

Let represent the number of minutes until Cassie’s distance to Ben is twice that of Abby’s distance to Ben. In minutes Abby will walk m and Cassie will walk m. The following diagram contains the information showing Abby’s position, , Ben’s position, , and Cassie’s position, , at time .

A right-angled triangle is formed by joining Abby's initial position to points A and B. Its hypotenuse is A B and its other sides are of length 100 and 20 times t. Another right-angled triangle is formed by joining Cassie's initial position to points C and B. Its hypotenuse is B C and its other sides are of length 160 and 41 time. Represent Abby, Ben and Cassie’s respective positions at noon as points on the -axis so that Ben is positioned at the origin , Abby is positioned units left of Ben at and Cassie is positioned units right of Ben at .

solution 2

Let represent the number of minutes until Cassie’s distance to Ben is twice that of Abby’s distance to Ben.

In minutes Abby will walk south m to the point . In minutes Cassie will walk north m to the pointTherefore, in

minutes ( minutes seconds), Cassie’s distance to Ben will be twice that of Abby’s distance to Ben. .

The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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Answer:

\(\sqrt{1000\times 1000}\)

\(=\sqrt{1000^2}\)

\(=1000\)

-------------------------

Thanks!

Have a great day!!

The 6.005 g of carbon contains 0.5000 moles of C. option  C

The mole is a unit of measurement in chemistry used to quantify the amount of a substance. One mole of a substance contains Avogadro's number of entities of that substance. Avogadro's number is defined as 6.022 x 10^23 entities per mole and is a fundamental constant in chemistry.

The mole is used to convert the amount of a substance in mass or volume to the number of entities (such as atoms, molecules, or ions) of that substance. The mole is useful in chemical reactions, where it provides a convenient way to express the amounts of reactants and products involved in a reaction.

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Answer:

110 women, see below for explanation. (hope this helps)

Step-by-step explanation:

3 to 5

3x + 5x = 176

8x = 176

x = 176/8

x = 22

3*22 = 66 men

5*22 = 110 women

Answer:

y < 106

Step-by-step explanation:

Step 1: Add 21 to both sides.

Therefore, the solution is y < 106.

To graph it on a graph:

Answer:

$1.22 per song

Answer:

5 binders

Step-by-step explanation:

(244.94 -199.99) / 8.99

Answer:

D

Step-by-step explanation:

Because the slope of two of the guys' climb was 0(∆h/∆t) for 2 mins

Answer: The answer is 0

Step-by-step explanation:

You can put it into an online calculator and it makes 0

The angle that the vector  \(\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}\)  makes with the y-axis is (B) tan⁻¹ 2/3.

To find the angle of the given vector:

Given: \(\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}\)

So,

\(\begin{aligned}&\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}} \\&\overrightarrow{\mathrm{A}} \cdot \hat{\mathrm{j}}=\sqrt{13} \cos \theta \\&3=\sqrt{13} \cos \theta \\&\theta=\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\end{aligned}\)

Using the formula \(\tan \left(\cos ^{-1} x\right)=\frac{\sqrt{1-x^2}}{x}\), we obtain:

\(\begin{aligned}&\theta=\tan ^{-1} \frac{\sqrt{1-\frac{9}{13}}}{\frac{3}{\sqrt{13}}} \\&\theta=\tan ^{-1}\left(\frac{2}{3}\right)\end{aligned}\)

Therefore, the angle that the vector  \(\overrightarrow{\mathrm{A}}=22_1^{\mathrm{A}}+3 \hat{\mathrm{j}}\)  makes with the y-axis is (B) tan⁻¹ 2/3.

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The correct question is given below:

The angle that the vector  \(\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}\)  makes with the y-axis is:

(A) tan⁻¹ 3/2

(B) tan⁻¹ 2/3

(C) sin⁻¹ 2/3

(D) cos⁻¹ 3/2

Using Exponential Smoothing ,

if the smoothing factor is higher that means more weight placed on recent

observations.

The weight , 1.2 is applied to the observations four periods ago.

Exponential Smoothing:

Exponential smoothing is a type of forecasting method that generates a forecast as a weighted average of the observed value and forecasted value. The weight is determined by the value of the smoothing parameter.

The exponential smoothing formula could be written as follows:

sₜ = α × xₜ + (1−α)sₜ₋₁

sₜ--> smoothed stati, xₜ--> current observations

sₜ₋₁--> previous Smooth statistic

α--> the smoothing factor

Thus the higher the smoothing factor, the more weight is placed on recent observations, and less weight is placed on past observations.

The weight placed on observations t periods before is α x t

Applying the formula, given a smoothing parameter of 0.3, the weight placed on observations four periods before is:

0.3×4 = 1.2

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Answer:

The answer is

The first choice

False. Consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices.

The highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices.The definition of a minimum spanning tree states that it is a subset of edges of a graph that connect all of the vertices without forming any cycles, and with the minimum total weight. If a graph contains an edge with the highest weight, it may still be included in the MST if it is the only connection between two vertices. To illustrate this, consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices. In this case, the highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices, and thus the minimum total weight is achieved.

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a) The function is one-to-one, but not onto. b) The function is not one-to-one, but it is onto. c) The function is neither one-to-one nor onto. d) The function is one-to-one and onto.

a. f(x)=−3x+4

This function is one-to-one, but not onto. It is one-to-one because for every input x, there is a unique output f(x). However, it is not onto because there are some outputs in R that are not the image of any input x. For example, the output 3 is not the image of any input x.

b. f(x)=−3\(x^2\)+7

This function is not one-to-one, but it is onto. It is not one-to-one because there are two inputs, x=1 and x=-1, that have the same output f(x)=4. However, it is onto because for every output y in R, there is an input x such that f(x)=y. For example, if y=4, then x=1 or x=-1 will both work.

c. f(x)=(x+1)/(x+2)

This function is neither one-to-one nor onto. It is not one-to-one because there are two inputs, x=0 and x=-2, that have the same output f(x)=1. It is also not onto because there are some outputs in R that are not the image of any input x. For example, the output 0 is not the image of any input x.

d. f(x)=\(x^5\)+1

This function is one-to-one and onto. It is one-to-one because for every input x, there is a unique output f(x). It is also onto because for every output y in R, there is an input x such that f(x)=y. This can be shown by using the Intermediate Value Theorem.

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The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:

-51.136

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. For Joshua's triangle; the distance of the green side of the triangle d₃ is 5.

2. For Murney's triangle, the perimeter of the triangle is 12.

3. For Grace, Abby and Chris's triangle, the perimeter of the triangle is 5 + √17 +  4√2.

4. For Chloe's triangle, the perimeter of the triangle is 11 + √65.

The distance of the triangles is calculated as follows;

For Joshua's triangle;

The length of d₁, d₂, and d₃ is calculated as follows;

d₁ = √ [(3 - 2)² + (2 - 0)²] = √5

d₂ = √ [(-1 - 3)² + (4 - 2)²] = 2√5

d₃ = √ [(-1 - 2)² + (4 - 0)²] = 5

The distance of the green side of the triangle d₃ = 5

For Murney's triangle, the perimeter of the triangle is calculated as;

BC = √ [(4 - 4)² + (6 - 2)²] = 4

AC = √ [(1 - 4)² + (2 - 2)²] = 3

AB = √ [(4 - 1)² + (6 - 2)²] = 5

Perimeter = 4 + 3 + 5 = 12

For Grace, Abby and Chris's triangle, the perimeter of the triangle is calculated as;

AC = √ [(-3 - 2)² + (2-2)²] = 5

BC = √ [(1 - 2)² + (2 + 2)²] = √17

AB = √ [(1 + 3)² + (2 + 2)²] = 4√2

Perimeter = 5 + √17 +  4√2

For Chloe's triangle, the perimeter of the triangle is calculated as;

AC =  √ [(-3 - 4)² + (2-2)²] = 7

BC =  √ [(4 - 4)² + (6-2)²] = 4

AB =  √ [(4 + 3)² + (6-2)²] = √65

Perimeter = 7 + 4 + √65 = 11 + √65

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Answer:

252

Step-by-step explanation:

t50 = t1 + (n - 1)(d)

= 7 + (50 - 1) (5)

= 7 + (49)(5)

= 7 + 245

= 252

Answer:

The 50ᵗʰ term of this sequence is 252

Step-by-step explanation:

Here,

First Term = a₁ = 7

Common Difference = (d) = 5

Now, For 50ᵗʰ term, n = 50

aₙ = a + (n - 1)d

a₅₀ = 7 + (50 - 1) × 5

a₅₀ = 7 + 49 × 5

a₅₀ = 7 + 245

a₅₀ = 252

Thus, The 50ᵗʰ term of this sequence is 252

-TheUnknownScientist

Answer:

27

Step-by-step explanation:

(3,18), (4,21)

M = (21-18)/(4-3) = 3

Y = mx + c

18 = 3(3) + c

C = 18 - 9 = 9

Y = 3x + 9

6 hours implies x=6

Y = 3(6) + 9 = 18 + 9 = 27

Num of pages = 27

The value of the ratio a:b is 2:1

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b\(\sqrt{3}\) = \(\frac{1}{2 - \sqrt{3} }\)

Rationalizing the right hand side by the conjugate surd which is 2 + \(\sqrt{3}\)

\(\frac{1}{2 - \sqrt{3} }\)  x \(\frac{2 + \sqrt{3} }{2 +\sqrt{3} }\) = \(\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}\) = \(\frac{2 + \sqrt{3} }{1}\) = 2 + \(\sqrt{3}\)

Equating,

a + b\(\sqrt{3}\) = 2 + \(\sqrt{3}\)

Comparing the variables,

a = 2,   b\(\sqrt{3}\) = \(\sqrt{3}\), b = 1

The ratio, a: b = 2:1

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Answer:

the answer is A

To determine the number of ways Samantha can arrange her mathematics books and computer science books on the shelf, we can use the concept of permutations.

1. First, we'll arrange the 3 mathematics books in the first 3 positions. Since Samantha has 7 mathematics books to choose from, she can arrange them in 7P3 ways:
7P3 = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210 ways

2. Next, we'll arrange the 2 computer science books in the last 2 positions. Since Samantha has 5 computer science books to choose from, she can arrange them in 5P2 ways:
5P2 = 5! / (5-2)! = 5! / 3! = 5 x 4 = 20 ways

3. Now, we need to multiply the number of ways to arrange the mathematics books by the number of ways to arrange the computer science books since these are independent events:
Total ways = 210 (mathematics books) x 20 (computer science books) = 4200 ways

So, Samantha can arrange her 7 mathematics books and 5 computer science books in 4200 different ways, with the first 3 positions occupied by math books and the last 2 by computer science books.

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The first graph is the exponential function.

The exponential function serves as the  positive-valued function with respect to real variable. and  the values denoted as X which is exponential is  all real numbers.

Analyzing the first graph, moving down the graph, we can see that  x value increases.

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Answer:

First Graph

Step-by-step explanation:

Edge

False
While it is true that the general solution of a 2nd-order ODE of the form y''=c is given by y(t)=c/2*t^2 +bt+1, not all solutions are parabolas. Parabolas are a specific type of quadratic function with a constant value of a, which determines the curvature. In this general solution, 'a' is represented by c/2, and it can take any real value. So, although the solutions are quadratic functions, they are not necessarily parabolas.

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Answer:

the answer you are looking for is C

Answer:

Given information:

To obtain the equation of the regression line for the given data.

The equation of regression line of y on x is given by:

y

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y

y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy

The calculations for the equation of regression line is tabulated below:

The regression coefficient of y on x is given by:

b

y

x

=

∑

x

y

−

1

n

∑

x

∑

y

∑

x

2

−

1

n

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=

1944

−

1

5

×

98

×

69

2580

−

1

5

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98

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2

=

591.6

659.2

=

0.898

byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898

Mean of x is calculated as:

¯

x

=

1

n

∑

x

=

1

5

×

98

=

19.6

x¯=1n∑x=15×98=19.6

Mean of y is calculated as:

¯

y

=

1

n

∑

y

=

1

5

×

69

=

13.8

y¯=1n∑y=15×69=13.8

The equation of regression line is given as:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

y

−

13.8

=

0.898

(

x

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19.6

)

y

=

0.898

x

−

3.8

y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8

Therefore, the required equation of regression line is y = 0.898x - 3.8.

f(x) = 16x - x² is the given quantity expressed as a function f(x)

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

Given that: the product of two numbers x and y whose sum is 16. Thus:

f(x) = x × y  ---- (1)

x + y = 16   ---- (2)

=> y = 16-x  ---- (3)

Put (3) in (1):

f(x) = x × (16-x )

f(x) = 16x - x²

Therefore, the given quantity expressed as a function f(x) is f(x) = 16x - x²

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Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)