500 +126 200 + 129 129+100 123+34 123+123 1000+12 2013+1200 123+120 100+304 123+103 104+1200

Hello, the solution of the problem is in this photo.

If the graph of the line falls from left to right, then the slope is negative.

Answer:

No

Step-by-step explanation:

Lets simplify both expressions:

We will start with Gloria's first expression:

[tex]1/4 (12x + 24) -9x[/tex]

Apply distributive property:

[tex](3x + 6) -9x[/tex]

Combine like terms, we are then left with:

[tex]6-6x[/tex]

Now lets simplify the second expression

[tex]-6(x+1)[/tex]

Apply distributive property

[tex]-6x-6[/tex]

Rearrange:

[tex]-6-6x[/tex]

Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.

Answer:426.6

Step-by-step explanation:

.138 x =.088(x - 69.7) + .394(69.7)

.138 x -  .088x = 69.7(.394 - .088)

.05x = 21.3282

/

x = 426.564

This rounds to x = 426.6

The midpoint of point A and point B is (5, -2.5)

The coordinates are given as:

A = (3, -8)

B = (7, -3)

The midpoint is calculated as:

(x, y) = 0.5 * (x1 + x2, y1 + y2)

So, we have:

(x, y) = 0.5 * (3 + 7, -8 + 3)

This gives

(x, y) = 0.5 * (10, -5)

Evaluate

(x, y) = (5, -2.5)

Hence, the midpoint of point A and point B is (5, -2.5)

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The number of students with heights less than 163 cm should be expected is 12.

According to the statement

The mean of height is 175 cm

and  the standard deviation of height is 6 cm.

We use normal distribution here with formula

Z= X - μ /σ

Here X is 167.5 and μ is 175 and σ is 6 cm.

Substitute the values in it then

Z = 167.5 - 175 / 6

Z = -1.25

-1.25 have a p value 0.012

Out of 1000 students:

0.012 x 1000 = 12.

So, The number of students with heights less than 163 cm should be expected is 12.

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The example on direct variation is illustrated below based on the information given.

An example will be:

When x = 2, y = 10. Find the value of y when x is 6.

In this case, this will be calculated thus:

y = kx

10 = 2k

k = 10/2

k = 5

Since y = kx.

y = 5 × 6

y = 30

The value of y is 30.

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Answer:

  A.  The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.

Step-by-step explanation:

Reflection is a rigid transformation. It preserves both angles and side lengths. Dilation preserves angles, but changes all lengths by the same scale factor.

The described triangle was subject to reflection, which preserves angles and lengths. It was also subject to dilation, which preserves angles, but not lengths.

The appropriate description is that of choice A.

An equation which is equivalent to the equation bsin(A) = asin(B) is: B. [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]

The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.

Mathematically, the law of sines is given by this equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]

In this context, we can infer and logically deduce that an equation which is equivalent to the equation bsin(A) = asin(B) is [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex].

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Answer: B

Explanation: sin(A)/a=sin(B)/b

The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The point A = (1 - 4, -3 - 2) = (-3, -5)

The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)

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The formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]

What are series?

In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount.

We will find the formula as shown as below:

Let [tex]S=1+2^2+3^2+4^2+................+n^2[/tex]

We know [tex](n+1)^3=n^3+3n^2+3n+1[/tex]

[tex](1+1)^3=1^3+3(1)^2+3(1)+1[/tex]

[tex](2+1)^3=2^3+3(2)^2+3(2)+1[/tex]

[tex](3+1)^3=3^3+3(3)^2+3(3)+1[/tex]

.

.

[tex](n+1)^3=n^3+3(n)^2+3(n)+1[/tex]

On adding

[tex]2^3+3^3+4^3......(n+1)^3=(1^3+2^3+3^3+.....+n^3)+3(1^2+2^2+.....+n^2)+3(1+2+3....n)+(1+1+1+....+1)[/tex]

[tex]2^3+3^3+4^3......(n+1)^3-(1^3+2^3+3^3+.....+n^3)=3S+\frac{3n(n+1)}{2}+(1+1+1+....+1)[/tex]

[tex](n+1)^3-1^3=3S+\frac{3n(n+1)}{2} +n[/tex]

[tex]n^3+3(n)^2+3(n)+1-1=3S+\frac{3n(n+1)}{2} +n[/tex]

[tex]2n^3+6n^2+6n=6S+3n^2+3n+2n[/tex]

[tex]6S=2n^3+3n^2+n[/tex]

[tex]6S=2n^2(n+1)+n(n+1)[/tex]

[tex]6S=(n+1)(2n^2+n)[/tex]

[tex]6S=n(n+1)(2n+1)[/tex]

[tex]S=\frac{n(n+1)(2n+1)}{6}[/tex]

Hence, the formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]

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Answer:

-3

Step-by-step explanation:

look at the hint: slope (most call it gradient) = change in y/change in x

so you take 2 x and y variables and subtract

15 - 9 = 6   ← change in y

0 - 2 = -2   ← change in x

slope (gradient) = 6/-2

slope (gradient) = -3

Answer:

Step-by-step explanation:

The function with the greatest rate of change over the interval [0, 2] is: D. a

Answer:

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

Step-by-step explanation:

A -----------------------z------------B

          Left      Speed(km/h)      Time

Car:   12PM            X  

Van:   12PM           60

Car/Van

DistanceCar        AB + z

DistanceVan       Az

Ratio:                  (AB+z)/Az  = 7/5

Time until both meet = T (in hours)

Distance Car:            xT

Distance Van:           60T

====

  xT = AB + z

  60T = Az

---

(xT/60T)= (7/5)

x = 60(7/5)

x = 84 km/h

=====

Time for car to reach B is:    time (hr) = 108 km/(84 km/h)

                                                 time = 1.286 hours

Distance for at 1.289 hours is:    distance (km) = (60 km/h)*(1.286 h)

                                                   distance = 77.14 km

At 1.286 hours, the car reverses direction.  The van is (108 km - 77.14 km) or 30.86 km away.

Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours.  The sum will be 30.86 km when they meet, at time of T.

Car Distance + Van Distance = 30.86 km

T(84 km/h) + t(60 km)

They meet when they are 0 km apart, which can be modeled with the following equation:

Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.

Let t be the time after 1.286 hours that both vehicles meet/collide.

t*(60 km/h)  +  t(84 km/h) = 30.86 km

t(60+84) = 30.86 km

t(144 km/h) = 30.86 km

t = 0.2143 hr

Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.

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

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

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

CHECK

Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?

Car distance is (1.5 hr)(84 km/h) = 126 km

Van distance is (1.5 hr)(60 km/h) = 90.0 km

Ratio is 126/90 or 1.4

Ratio of 7/5 is 1.4

YES

Answer:

Step-by-step explanation:

Write it out in expanded form and you will see why Connor is correct.

3^5 means 3x3x3x3x3

6^8 means 6x6x6x6x6x6x6x6

3^9 means 3x3x3x3x3x3x3x3x3

6^10 means 6x6x6x6x6x6x6x6x6x6

These numbers are all multiplied together, so how many of each number do we have?

3x3x3x3x3x6x6x6x6x6x6x6x6x3x3x3x3x3x3x3x3x3x6x6x6x6x6x6x6x6x6x6

3^14 6^18

Answer:

2.5

Step-by-step explanation:

v = u + at is one of the kinematics equations.

Given v = 10, t = 2, u = 5, we will substitute these values into the equation to find a.

[tex]v = u + at\\10=5+2a\\2a=10-5\\2a = 5\\a = \frac{5}{2} \\= 2.5[/tex]

The exact value of sin 5π/4 is 0. 0677

It is important to note that π = 3. 142

Let's find sin 5π

Substitute the value

sin 5π = sin (5 × 3. 142) = sin 15. 71

= [tex]\frac{sin 15. 71}{4}[/tex]

Find the sine of the number

= [tex]\frac{0. 27076}{4}[/tex]

= [tex]0. 0677[/tex]

Thus, the exact value of sin 5π/4 is 0. 0677

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Answer:

-  sqrt2/2

Step-by-step explanation:

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 3, 4 )

m = [tex]\frac{4-2}{-3-3}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]

[tex]\small\mathbb\green{slope=M= \frac{y2 - y1}{x2 - x1} = \frac{4 - ( - 2)}{3 - 3} \: = \frac{6}{0} \: = ∞} [/tex]

A) Sample size of compound event = 25

B) New Sample size = 36

What is Compound event?

A compound event is one that has more than one sample point. Simple events are less complicated than compound events. These occurrences entail the possibility of multiple occurrences. One is the probability of all possible outcomes of a compound event.

An event that consists of two or more simple events is called a compound event. Simple events are those that can only have one result, whereas complex events can have a variety of distinct results. Compound events can consist of several independent or dependent occurrences, where the result of one event has no bearing on the likelihood of the other.

Given,

Number of buttons in a container = 5

Lucas picks one button, replaces it and then picks another.

Therefore,

Sample size of the compound event

                 n = 5[tex]\times[/tex]5

                 n  = 25

Now, one more button is added in the container and in total there are 6 buttons.

Lucas repeats the same process again and hence,

Sample size of the new compound event will be,

                  n = 6[tex]\times[/tex]6

                  n = 36

Full Question is - Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is  ___  Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be ____

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Answer:

167

Hope this helps you out

Answer:

167

Step-by-step explanation:

Break it into steps.

2+2+5 = 9

69 + 9 = 78

78 + 89 = 167

Hope this helps.

The probability of rolling an even number first and an odd number second is; One Fourth

As two cubes are 6 sided, the total number of possibilities as seen in the attached table are;

6 * 6 = 36 possible numbers

Now in those possibilities, the first number will be even and the second number will be odd.  From the the table, such possible pairs are,  

(2,1), (2,3), (2,5), (4,1), (4,3), (4,5), (6,1), (6,3), (6,5)

Therefore, we can see we have a total of 9 sets with the combination of first number even and second number odd.  So, the probability of rolling with this combination will be; 9/36 = 1/4

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Using a linear function, the inequality is given by: 69.5 + 5x < 90.

The solution is: x < 4.1.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we have that:

Hence the cost of using x gigabytes is:

C(x) = 69.5 + 5x.

The cost has to be under 90, hence the inequality is:

C(x) < 90

69.5 + 5x < 90.

Then the solution is:

5x < 90 - 69.5.

x < 20.5/5

x < 4.1.

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Answer:

Inequality: 5x+35<50

Answer: x<3

Step-by-step explanation:

The true statements are (b), (d) and (e)

From the function, we have the following piecewise function and the domains

D(t) = 300t + 125, 0 ≤ t < 2.5

D(t) = 875, 2.5 ≤ t ≤ 3.5

D(t) = 75t + 612.5, 3.5 < t ≤ 6

When t = 2, we use the domain 0 ≤ t < 2.5

So, we have

D(2) = 300 * 2 + 125

Evaluate the product

D(2) = 600 + 125

Evaluate the sum

D(2) = 725 --- this is true

When t = 3, we use the domain 2.5 ≤ t ≤ 3.5

So, we have

D(t) = 875

This gives

D(3) = 875 -- this is true

When t = 6, we use the domain 3.5 < t ≤ 6

So, we have

D(t) = 75t + 612.5

This gives

D(6) = 75* 6 + 612.5

Evaluate the product

D(6) = 450 + 612.5

Evaluate the sum

D(6) = 1062.5 --- this is true

Hence, the true statements are (b), (d) and (e)

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Complete question

Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.

Answer:

At 2 hours, the traveler is 725 miles from home.

At 3 hours, the distance is constant, at 875 miles.

The total distance from home after 6 hours is 1,062.5 miles.

Step-by-step explanation:

2b^3 -5 b^2 +b+2. R 9/ b-4

Use synthetic division

Domain refers to the term which best describes the set of all possible input values for a function and is therefore denoted as option C.

These are all the values which go into a function which is defined and is denoted as the sign below:

dom · ( f ).

They are also among the values which form the independent variables in this type of context while on the other hand, the output is referred to as the range.

These set of values are usually inputted into the function to check its acceptability and also retrieve the output gotten from the type of operation given. It is also used to identify the independent variable which are present thereby making it the most appropriate choice.

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There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],

Now,

Substituting values,

We get,

[tex]^5N_5 = \frac{5!}{(5-5)!}[/tex]

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

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Answer:

1/2

Step-by-step explanation:

There is a couple ways of thinking about this.  Probably the fastest way is the rule, but the rule is not intuitive.  The rule is when you divide fraction, you keep the first fraction the same and then multiple and flip the second fraction.

2/8 x 18/9 = 36/72  To reduce the fraction, could keep dividing the top and the bottom by the same number until it is no longer possible, I could use: 2, 4 3, 9, 18, or 36.  If I used 36, I would only have to divide once.  36/16 is 1 and 72/36 is 2 so my answer would be 1/2.

I could have divided the top and bottom by 2 and got 18/36 and then divide by 2 again and get 9/18 and then by 9 and get 1/2.  As you can, see there are a lot of option.  

The second method is in the picture that I sent you, it is a little more work, but it makes sense.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{2}{8}\div\frac{9}{18} }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Simplify \ \frac{2}{8} \ to \ \frac{1}{4}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\div\frac{18}{9} }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: a\div \frac{b}{c}=a\times \frac{c}{b}a \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\times\frac{18}{9} }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: \frac{a}{b} \times \frac{c}d{}=\frac{ac}{bd}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1\times18}{4\times9} \ \to \ \ Multiply }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ \frac{18}{36}= }}\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{2} }} \end{gathered}$}} \end{gathered}$}[/tex]

The expansion of the expression (x + 2y)² is x² + 4xy + 4y².

The given expression is (x + 2y)². The expansion of the expression will be:

(x + 2y)²

= (x + 2y)(x + 2y)

= x² + 2xy + 2xy + 4y².

= x² + 4xy + 4y²

The expansion is x² + 4xy + 4y².

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Step-by-step explanation:

M=2G

M=J+10

G=J-8

2G=J+10

G=J-8

2(J-8)=J+10

2J-16=J+10

J=26

Considering the given stem-and-leaf plot, the outlier is given by:

A - 40

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

Outliers are usually the lowest or the highest value in the data-set. In this problem:

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