An indoor running track is 200 meters in length. During a 3,000-meter race, runners must complete 15 laps of the track. An electronic timing device records the amount of time it takes each runner to complete a lap for every lap in the race. These are called lap times. The histograms below display the lap times for both Stefano and Alex, runners in the 3,000-meter race.

2 histograms. A histogram titled Alex apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 35 to 36, 1; 36 to 37, 5; 37 to 38, 4; 38 to 39, 4; 39 to 40, 1. A histogram titled Stefano apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 32 to 33, 1; 34 to 35, 1; 36 to 37, 1; 37 to 38, 4; 38 to 39, 5; 39 to 40, 1; 40 to 41, 2.

Using the histograms, which of the following is a correct comparison?

Neither runner had a lap time between 35 and 36 seconds.
Alex’s lap times show less variability than Stefano’s lap times.
The median lap time for both runners is in the 38–39 interval.
Both runners’ highest number of lap times in the 37–38 interval.

Answer:

I think it's 1.17 - -3.85

Answer:

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x ( x + 7 ) -3 ( x + 7 ) = 0

( x - 3 ) ( x + 7 ) = 0

∴ x - 3 = 0              or              x + 7 = 0

  x = 0 + 3                               x = 0 - 7

  x = 3                                      x = -7

Using a linear function, it is found that 80 picnic tables can be produced for a total daily cost of 4,800.

A linear function is modeled by:

y = mx + b

In which:

Considering the daily fixed cost of 1200 as the y-intercept, and the variable cost of 45 as the slope, the linear function for the cost of producing n picnic tables is given by:

C(n) = 1200 + 45n.

Now, we have to solve for n when C(n) = 4800, hence:

1200 + 45n = 4800

45n = 3600

n = 3600/45

n = 80.

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Answer:

5

Step-by-step explanation:

Given expression:

[tex]\dfrac{6^{n+2}-6^n}{6^{n+1}+6^n}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]

[tex]\implies \dfrac{6^n6^2-6^n}{6^n6^1+6^n}[/tex]

Factor:

[tex]\implies \dfrac{6^n(6^2-1)}{6^n(6^1+1)}[/tex]

Cancel [tex]6^n[/tex] :

[tex]\implies \dfrac{(6^2-1)}{(6^1+1)}[/tex]

Simplify:

[tex]\implies \dfrac{36-1}{6+1}[/tex]

[tex]\implies \dfrac{35}{7}[/tex]

[tex]\implies 5[/tex]

Answer:

3d²

Step-by-step explanation:

Hello!

To simplify, we combine the like terms by adding them.

Like terms are terms with the same variable and degree. A degree is a power to which the term is raised. Like terms can have numerical coefficients. For example, a coefficient of 4 to x² would mean 4 times x².

We can see that the variable d² is common throughout the three terms, meaning they are like terms. We can simply add and subtract them.

The simplified form is 3d².

Answer:

Amount in Blank total = $160

Amount of money Daniel’s agent made = $40

Amount of money Daniel and the agent made

from the show  = $160

Step-by-step explanation:

this question is based on the calculation of percentages

so,

it is is given in the question that -

Daniel is a singer, and he promises his agent that he will give him a 25% commission based on what he makes from a show.

After paying the agent, Daniel takes home =  $120

so,

let 'x' is the total amount of money that Daniel earned form the show

it is also given that Daniel promised to give 25 % to his agent from what he earned from the show

so, percentage of money left to the Daniel is

100-25 = 75%

therefore according to the question,

75percent of the x = $120

75/100×(x)   =  120

  3/4×(x)   =  120

     3x   =   120×4

     3x  =  480

       x  =  $160

so the total amount of money Daniel earned from the show is $160

Now we know that Daniel’s agent made 25% of the total amount of money earned from the show

therefore

25percent of 160 = Daniel’s agent made

     25/100 ×160  = Daniel’s agent made

             $40 =  Daniel’s agent made

so the amount of money earned by Daniel’s agent made is $40

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Answer: Daniel’s agent made

✔ $40

Daniel and the agent made a total of

✔ $160

from the show.

.

Step-by-step explanation:

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

As per the law of cosine, the measure of angle x can be written as,

[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]

Hence, the value of x is 117.8°. thus, the correct option is A.

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Answer:

(x+6)(y+3)

Step-by-step explanation:

Definition:

[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]

also

[tex]a^1=a\\\\a^0=1[/tex]

[tex]6^1=6\\\\3^2=3\cdot3=9\\\\2^3=2\cdot2\cdot2=8\\\\1^7=1[/tex]

therefore

Answer:

x=67.4

Step-by-step explanation:

well sin30:1/2

So y is not 30 since 5/13 doesn’t equal 1/2

So it’s either the the third or fourth option

And x>y

So option 4 is correct

Answer: [tex]\left(\frac{4}{3}, -\frac{5}{3} \right)[/tex]

Step-by-step explanation:

Setting the equations equal to each other.

[tex]x-3=-2x+1\\\\3x=4\\\\x=\frac{4}{3}\\\\\implies y=\frac{4}{3}-3=-\frac{5}{3}[/tex]

Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

For the given inequalities, the graph can be plotted as shown below. Now when the coordinates have been plotted the point that will satisfy both the inequalities is (-2,2).

Hence, the correct option is B.

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Functions which are polynomials are y=[tex]5x^{4} +x^{2} -8[/tex] ,y=[tex]7x^{3}[/tex] and y=[tex]6^{x}[/tex]

Given Functions : 1) y=[tex]-x^{2} +1/1-2x[/tex] 2)y=[tex]5x^{4} +x^{2} -8[/tex]. 3) y=[tex]7x^{3}[/tex]and g(x)=[tex]6^{x}[/tex].

We need to find which functions are polynomials. We know that polynomials is an expression consisting of indeterminates and coefficients that involves only the operations of addition, subtraction, multiplication and non negative integers .

First function is y=[tex]-x^{2} +1/1-2x[/tex]

The above function is not a polynomial because it has not a variable containing power in whole number and it is in fraction form. Two different polynomials can form numerator and denominator in a fraction.

Second function is y=[tex]5x^{4} +x^{2} -8[/tex]

The above function is a polynomial as it has a variable having power and it is not in fraction also.

Third function is  y=[tex]7x^{3}[/tex]

The above function is also a polynomial for the same reason.

Fourth function is g(x)=[tex]6^{x}[/tex].

The above function is also a polynomial.

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Answer: 484/5

Step-by-step explanation:

For this word problem, it seems confusing with the wording but the equation would just be:

968÷10=x

solving for x, we get 484/5.

The correct answer for the given expression is 99.22.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

The expression will be solved as:-

E = [tex]({5 -\dfrac{10}{27}})^3[/tex]

E = [tex](\dfrac{135-10}{27})^3[/tex]

E =[tex]\dfrac{125}{27}^3[/tex]

E = 99.22

Therefore the correct answer for the given expression is 99.22.

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The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³

The volume of the air space surrounding the cone inside the cylinder is as follows:

volume of the air space = volume of cylinder - volume of a cone

volume of cylinder = πr²h

volume of cylinder = π16 × 5²

volume of cylinder = 400π

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × π × 12 × 4²

volume of the cone = 64π

Therefore,

volume of the air space = 400π - 64π

volume of the air space = 336π

volume of the air space = 1055.04 cm³

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Answer:

35+3I

Step-by-step explanation:

35+3I

Usando proporciones, en conjunto con multiplicación cruzada, encontra-se que el valor de p es de 6.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

En este problema, relación es dada por:

[tex]\frac{p}{p+2} = \frac{6}{8}[/tex]

Aplicando multiplicación cruzada:

8p = 6(p + 2)

8p = 6p + 12

2p = 12

p = 12/2

p = 6.

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The system of equation can be used to find the root of the equation is y= x³-4x² +2x and y=0 , y=4x² and y= x³+2x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

y=-4x²

y= x³+2x

By equating the above equation we have

-4x²=x³+2x

Now, y= x³-4x² +2x

and y=0

By equating the above equation we have

x³-4x² +2x=0

y=4x²

y= -x³-2x

By equating the above equation we have

4x²=-x³-2x

Lastly,

y=4x²

y= x³+2x

By equating the above equation we have

4x²=x³+2x

Hence, the equation can be used is y= x³-4x² +2x and y=0 ,

y=4x² and y= x³+2x

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The probability that a red ace is drawn first and then a black ace is mathematically given as

x=1/4

Where

Sample mean=(x,y)\, x, y \in \{h,d,c,s\}

If we want a player to draw two cards of the same color from their deck, the following combinations of cards are appropriate choices:

[tex](h,h),\ (h,d),\ (d,h),\ (d,d),\ (c,c),\ (c,s),\ (s,c),\ (s,s)[/tex]

Generally, 8 possible pairings above 16. This indicates that the likelihood of a player drawing two cards of the same color is 8/16, which is equivalent to a probability of half.

In conclusion, In a similar vein, the following pairs of cards illustrate the likelihood of obtaining a black ace after having drawn a red ace in the previous round:

[tex](h,c),\ (h,s),\ (d,c),\ (d,s)[/tex]

Giving

x=4/16

x=1/4

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Answer:

1/4

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

the inverse of

y=1/2x + 10

is

x=1/2y+10

from here you just solve for y

x-10 = 1/2y

2(x-10) = y

2x-20 = y

The question was incomplete. Below you will find the missing content.
The square root function f(x) is x <= 7

Options are :

A. 7 is subtracted from the x-term inside the radical.
B. The radical is multiplied by a negative number.
C. 7 is added to the radical term.
D. The x-term inside the radical has a negative coefficient.

Option D is correct, which is : The x-term inside the radical has a negative coefficient.

Given, the domain of the square root function f(x) is x <= 7
Consider the function y = √x.
The domain of this function is x ≥ 0 and the range is y ≥ 0.
The expression inside the radical must be greater than or equal to zero.
Now, if x ≤ 7
x - 7 ≤ 0
7 - x ≥ 0
And the function y = √(7-x) will have the domain x ≤ 7.
This implies that the x-term inside the radical has a negative coefficient.
Therefore, the statement that the x-term inside the radical has a negative coefficient must be true.

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Answer:

a

Step-by-step explanation:

Answer: See Attachment

Step-by-step explanation: I wasn’t sure if you meant -2 < x, but that’s the work I did to get the answer. If you can, send a picture of the question itself in case you didn’t mean -2 < x.