Suppose you can chose from 3 different shirts, 2 pairs of pants, and 5 pairs of shoes. Use the fundamental counting principle to find out how many different outfit combinations you can make.​

The cyclist's speed converts to 43.2 km/h. In 3 hours, she will travel a distance of 129.6 kilometers.

The rate of the cyclist in kilometers per hour can be calculated by converting meters per second to kilometers per hour. To do this, we multiply the speed in meters per second by 3.6 (since 1 m/s = 3.6 km/h). Thus, the cyclist's speed in km/h is 12 m/s * 3.6 = 43.2 km/h.

To calculate the distance she will travel in 3 hours, we multiply the speed (in km/h) by the time in hours. So, the distance is 43.2 km/h * 3 hours = 129.6 km.

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The cyclist's rate in kilometers per hour is 43.2 km/h, and she will travel 129.6 km in 3 hours.

To convert the rate from meters per second (m/s) to kilometers per hour (km/h), we need to use conversion factors.

Conversion factors:

1 m/s = 3.6 km/h

1 hour = 3600 seconds

Let's calculate:

Rate in km/h = (Rate in m/s) × (Conversion factor from m/s to km/h)

Rate in km/h = 12 m/s × 3.6 km/h

Rate in km/h = 43.2 km/h

To calculate the distance traveled in 3 hours, we can use the formula:

Distance traveled = Rate × Time

Distance traveled = 43.2 km/h × 3 hours

Distance traveled = 129.6 km

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The answer to Number 21 is A

Answer:

The equation of the axis of symmetry is x = 3

Step-by-step explanation:

Perform the indicated mult., obtaining:

y = 3(x² - 6x + 9) + 4.

Mult. each term inside parentheses by 3, we get:

y = 3x² - 18x + 27 + 4, or

y + 3x² - 18x + 31

Here the coefficients are a = 3, b = -18 and c = 31.

The axis of symmetry is x = -b / (2a), which here is:

      -(-18)

x = ----------- = 18/6 = 3

       2(3)

The equation of the axis of symmetry is x = 3

ANSWER

x=3

EXPLANATION

The given function is

[tex]y= -3(x-3)^2+4[/tex]

This function is of the form.

[tex]y= a(x-h)^2+k[/tex]

This is called the vertex form.

The axis of symmetry is given by

[tex]x = h[/tex]

By comparing to

[tex]y= -3(x-3)^2+4[/tex]

a=-3, h=3 and k=4

Hence the axis of symmetry is x=3

Answer:

So, if it is translated down 4 units, that puts point d at (-6,5). and after reflecting it over the y axis, that puts it at (6,5). Making the final answer (6,5).

Step-by-step explanation:

The coordinates of point D after being translated four units down and reflected across the Y-axis are (6, 5).

To find the coordinates of point D after the given translation and reflection, we need to perform each step in order.

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Answer:

400 thousand or 400,000

Step-by-step explanation:

just round 389 to the nearest hundred ------ 400

Answer:400,000

Step-by-step explanation:

389,935

the hundred thousand place is the 8 it is greater than 5 so you round up to 400,000

Answer:  D. A pentagon

According given statement Ragan drew pentagon. Therefore, option D is the correct answer.

A pentagon is a five-sided polygon with five straight sides and five angles. It is a regular polygon, meaning all of its sides are equal in length and all of its angles are equal in measure.

Given that, Ragan drew a polygon with more than a square and fewer vertices than a hexagon.

We know that, square has 4 sides and a hexagon has 6 sides.

According to statement, Ragan drew pentagon.

Therefore, option D is the correct answer.

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Answer:

Step-by-step explanation

round the numbers so it is easier to work with

10 * 7 = 70

70 * 7 = 490

20 * 7 = 140

140 *7 = 980

980 + 490 = 147.0

The total amount that Diego could have spent on lunch over the past seven weeks could be between $77 and $119.

To determine the total amount Diego could have spent on lunch over the past seven weeks, you should find the minimum and maximum amounts he could have spent. The minimum amount would be if he spent $11 each week, and the maximum if he spent $17 each week.

To find these amounts, you multiply the number of weeks by the respective cost. So, for the minimum, you multiply 7 weeks by $11, which gives a total of $77. Then, for the maximum, you multiply 7 weeks by $17, which gives a total of $119.

Therefore, the total amount that he spent on lunch for the past 7 weeks could be any amount between $77 and $119.

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Answer:

Answer:

Entonces Patricia necesitara 4 estampas de $3 dolares y 6 estampas de $1 dolar

Step-by-step explanation:

Cuatro estampas de tres dolares cada una es:

3 × 4 = 12

Ahora necesitamos encontrar  cuantas estampas mas Patricia puede comprar. Podemos hacer esto restando 12 a 18, que es el costo total de las estampas menos del valor encontrado

18 - 12 = 6

Ahora sabemos que Patricia necesita 6 dolares de estampas ($1 estampas) para acompletar las 10 estampas  dando un total de $18 dolares.

6 × 1 = 6 < sumar 6 de 12

12 + 6 = 18

Entonces Patricia necesitara 4 estampas de $3 dolares y 6 estampas de $1 dolar

To solve this problem using a system of equations, we can let x represent the number of stamps that Patricia bought for $3.00 and y represent the number of stamps she bought for $1.00.

To solve this problem using a system of equations, we can let x represent the number of stamps that Patricia bought for $3.00 and y represent the number of stamps she bought for $1.00. The problem tells us that Patricia bought a total of 10 stamps and paid a total of $18.00. Therefore, we can set up the following system of equations:

x + y = 10

3x + y = 18

To solve this system, we can use the substitution or elimination method. Let's use the substitution method. From the first equation, we can solve for x in terms of y: x = 10 - y. Now we can substitute this expression for x in the second equation:

3(10 - y) + y = 18

30 - 3y + y = 18

30 - 2y = 18

-2y = -12

y = 6

Substituting this value of y back into the first equation, we can find the value of x:

x + 6 = 10

x = 4

So Patricia bought 4 stamps for $3.00 each and 6 stamps for $1.00 each.

Answer:

[tex]P =0.857[/tex]

Step-by-step explanation:

We know that 60% of students have an iPad and a car and 70% have a car.

If we call A the event "have an iPad" and call the event B "have a car"

So

[tex]P (A\ and\ B) = 0.6\\\\P(B) = 0.7[/tex]

We look for the probability that a student with a car also has an iPad. This is

[tex]P (A | B) = \frac{P(A\ and\ B)}{P(B)}\\\\P (A | B) = \frac{0.6}{0.7}\\\\P (A | B) = 0.857[/tex]

Answer:

86%

Step-by-step explanation:

To solve this problem you need to use the formula for conditional probability.  

P(Ipod|Car) = P(Car and Ipod)P(Car).

P(a student with a car also has an iPod) = 0.6/0.7 = 0.857 = 86%

Answer:

[tex]\left\{x\ |-4<x<6\right\}[/tex]

Step-by-step explanation:

We need to write a compound inequality to represent all of the numbers between -4 and 6. Which should be done in set builder notation .

if x represents the required number then we can write x>-4 and x<6

or we can write -4<x<6

Hence required inequality in set builder notation will be given by :

[tex]\left\{x\ |-4<x<6\right\}[/tex]

the correct answer is d

Answer:

D

Step-by-step explanation:

all rational numbers where m ≥ 0

The number of hours it takes to hike through the jungle can be calculated from any fraction of a mile or miles.

Answer:

Answer: A.  Y= -10x -4.

Step-by-step explanation:

Steeper line : is a line which is closed to y-axis, or closed vertically.

Since, the standard form of a line is,

y = mx + c

Where m is the slope,

If the absolute value of the slope ( that is, |m| ) is maximum then it is called it has the steepest graph.

For,  y=-2x+6,

The absolute value of slope = 2,

For, y =8x-1,

The absolute value of slope = 8,

For, y=-10x-4,

The absolute value of slope = 10,

For, Y=7x+3,

The absolute value of slope = 7,

Since, 2< 7 < 8 < 10

Hence, the line y = -10 x - 4 is closest to y-axis,

⇒ Line y = -10 x - 4 has the steepest graph.

A steeper line is one with a greater absolute slope value. Among the provided equations, y = -10x - 4 has the steepest graph due to its absolute slope value of 10.

The correct answer is option A.

A steeper line in the context of linear equations can be understood as a line that is closer to the y-axis or one that has a more significant vertical incline. The steepness of a line is determined by its slope, represented as 'm' in the standard linear equation form, y = mx + c. The slope 'm' quantifies the rate at which the line rises or falls as it moves horizontally along the x-axis. The greater the absolute value of the slope (|m|), the steeper the line.

To identify the steepest line among several equations, one must calculate and compare the absolute values of their slopes. Let's evaluate a few examples:

For y = -2x + 6, the absolute value of the slope is |2|.

For y = 8x - 1, the absolute value of the slope is |8|.

For y = -10x - 4, the absolute value of the slope is |10|.

For y = 7x + 3, the absolute value of the slope is |7|.

Comparing these absolute values, we find that 2 < 7 < 8 < 10. Therefore, the line with the steepest graph is y = -10x - 4. This line is closest to the y-axis, indicating the most significant vertical incline among the given equations.

Therefore, from the given options the correct one is A.

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QUESTION 1

The point-slope form equation of a line is given by:

[tex]y-y_1=m(x-x_1)[/tex]

Given slope:

[tex]m = \frac{2}{3} [/tex]

and point:(-3,5)

The point-slope form equation is:

[tex]y-5= \frac{2}{3} (x- - 3)[/tex]

This simplifies to:

[tex]y-5= \frac{2}{3} (x + 3)[/tex]

The correct option is D.

QUESTION 2

We use any two points from the table to find the required equation.

(2,14) and (4,23)

The slope is given by the formula,

[tex]m = \frac{23 - 14}{4 - 2} = \frac{9}{2} [/tex]

The equation is given by;

[tex]y-y_1=m(x-x_1)[/tex]

We plug in values to get;

[tex]y-14= \frac{9}{2} (x-2)[/tex]

Expand:

[tex]y = \frac{9}{2} x - 9 + 14[/tex]

The slope-intercept form is:

[tex]y = \frac{9}{2} x + 5[/tex]

The correct choice is B

For reference,

[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]

a. [tex]\dbinom{52}5=2,598,960[/tex] - nothing special here, you're just choosing any 5 cards from the deck

b. [tex]\dbinom{13}4\dbinom{39}1=27,885[/tex] - 13 hearts to choose from, and 39 of any other suit

c. [tex]\dbinom{40}5=658,008[/tex] - there are 12 face cards to omit from the count

d. [tex]\dbinom{26}5=65,780[/tex] - half the deck contains spades/clubs

e. [tex]\dbinom{26}5=65,780[/tex] - essentially the same situtation as (d)

f. [tex]\dbinom{40}5\dbinom{12}0+\dbinom{40}4\dbinom{12}1+\dbinom{40}3\dbinom{12}2=2,406,768[/tex] - either 0, 1, or 2 face cards are allowed

g. [tex]\dbinom{13}2\dbinom{39}3+\dbinom{13}3\dbinom{39}2+\dbinom{13}4\dbinom{39}1+\dbinom{13}5\dbinom{39}0=953,940[/tex] - similar to (f)

A) Total Different Hands=2,598,960

B) Hands Containing 4 Hearts=27,885

C) Hands Containing No Face Cards=658,008

D) Hands Containing Only Spades or Only Clubs=2,574

E) Hands Containing Only Red Cards=65,780

F) Hands Containing No More Than 2 Face Cards= 915528

G) Hands Containing At Least 2 Hearts=1,894,929

This problem involves calculating the number of different hands possible when dealing five cards from a standard deck of 52 playing cards.

We also need to determine the count for various specific conditions.

A) Total Different Hands

To determine the number of different hands, we use the combination formula C(n, k) where n is the total number of items, and k is the number of items to choose.

For our case:

C(52, 5) = 52! / (5!(52-5)!) = 2,598,960

B) Hands Containing 4 Hearts

We select 4 hearts from the 13 available and the 5th card from the remaining 39 cards:

C(13, 4) * C(39, 1) = 715 * 39 = 27,885

C) Hands Containing No Face Cards

There are 40 non-face cards (4 suits each with A-10). Thus, the number of ways to select a 5-card hand with no face cards is:

C(40, 5) = 658,008

D) Hands Containing Only Spades or Only Clubs

Since we can't mix suits, we compute separately and add:

C(13, 5) * 2 (one for each suit) = 1,287 * 2 = 2,574

E) Hands Containing Only Red Cards

There are 26 red cards (hearts and diamonds), so we choose from these:

C(26, 5) = 65,780

F) Hands Containing No More Than 2 Face Cards

Calculating for 0, 1, and 2 face cards separately:

Total=C(40, 5) + C(12, 1) * C(40, 4) + C(12, 2) * C(40, 3) = 658,008 + 114,960 + 142,560 = 915528

G) Hands Containing At Least 2 Hearts

We use the complement rule: subtract the combinations with 0 or 1 heart from the total:

Total=C(52, 5) - (C(39, 5) + C(13, 1) * C(39, 4)) = 2,598,960 - (575,757 + 128,274) = 1,894,929

Seems like you had your minus signs backwards. Try y = 3 and y = -6

Answer:

Option B. [tex]26\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle EBD

we know that

[tex]m<EBD+m<CBD+m<ABE=180\°[/tex]

remember that

[tex]m<EBD=m<CBD[/tex]

[tex]m<ABE=52\°[/tex]

substitute the values

[tex]2m<EBD+52\°=180\°[/tex]

[tex]2m<EBD=180\°-52\°[/tex]

[tex]m<EBD=128\°/2=64\°[/tex]

step 2

Find the measure of the angle EDB

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

In the right triangle BED

[tex]m<EBD+m<BED+m<EDB=180\°[/tex]

we have

[tex]m<EBD=64\°[/tex]

[tex]m<BED=90\°[/tex]

substitute

[tex]64\°+90\°+m<EDB=180\°[/tex]

[tex]m<EDB=180\°-(64\°+90\°)=26\°[/tex]

Answer:

B.[tex]26^{\circ}[/tex]

Step-by-step explanation:

We are given that a triangle ABD, BE is perpendicular to AD and angle EBD is congruent to angle CBD.

[tex]\angleABE=52^{\circ}[/tex]

We have to find the measure of angle EDB.

Let [tex]\angle EBD=x[/tex]

Then, [tex]\angle CBD=x[/tex] because angle EBD is congruent to angle CBD.

[tex]\angle ABE+\angle EBD+\angle CBD=180^{\circ}[/tex] (linear sum)

[tex]52+x+x=180[/tex]

[tex]2x=180-52=128[/tex]

[tex]x=\frac{128}{2}=64^{\circ}[/tex]

In triangle EBD

[tex]\angle BED=90^{\circ}[/tex]

[tex]\angle EBD=64^{\circ][/tex]

[tex]\angle EBD+\angle BED+\angle EDB=180^{\circ}[/tex] (sum of angles of triangle )

Substitute the values then we get

[tex]64+90+\angle EDB=180[/tex]

[tex]154+\angle EDB=180[/tex]

[tex]\angle EDB=180-154=26^{\circ}[/tex]

Hence, [tex]m\angle EDB=26^{\circ}[/tex]

Answer: What's the question?

Step-by-step explanation:

Answer:

-  The lines of both functions have the same slope.

- The line of the first function intercepts the y-axis at the point (0,-6) and the  line of the new function intercepts the y-axis at the point (0,-8).

- The new graph is the graph of the first function but shifted 2 units down.

Step-by-step explanation:

The equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where the slope is "m" and the intersection of the line with the y-axis is "b".

Given the function in the form [tex]y=x-6[/tex], you can identify that:

[tex]m=1\\b=-6[/tex]

And from the new function in the form  [tex]y=x-8[/tex], you can identify that:

[tex]m=1\\b=-8[/tex]

This means that the lines of both functions have the same slope, but the line of the first function  [tex]y=x-6[/tex] intercepts the y-axis at the point (0,-6) and the  line of the new function  [tex]y=x-8[/tex] intercepts the y-axis at the point (0,-8).

Therefore, the graph of the new function is 2 units below of the function [tex]y=x-6[/tex], or, in other words, the new graph is the graph of the first function but shifted 2 units down.

Answer:

A,C, AND D

Step-by-step explanation:

A. 3+4>5 therefore a triangle

B. 1+7<10 therefore not a triangle

C. 1.5+1.5>2.5 therefore a triangle

D. 7+7>7 therefore a triangle

E. 6+6=12 therefore not a triangle

Answer: Option A

[tex]A=0.001[/tex]

Step-by-step explanation:

The sinusoidal functions have the following form

[tex]Y = Asin (bx)[/tex]

Where

[tex]\frac{2\pi}{b}[/tex] is the period of the function

A is the amplitude: Half the difference between the minimum value and the maximum value of the function.

In this case the function is:

[tex]y = 0.001sin(880\pi\phi)[/tex]

Therefore the amplitude of this equation is [tex]A=0.001[/tex]

Answer:

Step-by-step explanation:

From 1:45 to 4:00 is:

15 min to 2:00

from 2:00 to 4:00 is 2h

We know 1h = 60min, therefore 1min = 1/60 h

2h and 15min = 2h + 15/60 h = 2h + 1/4 h = 2 1/4h = 2.25h

it is a statistical question due to you having to collect data to answer this question, you'd have to collect data on how tall the giraffes are and i'm sure they all don't grow up to be the same height so there will be differentiations in heights of all.

Answer:

what the other person said

Step-by-step explanation:

Answer:

x=44

Step-by-step explanation:

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=8\\ h=4 \end{cases}\implies 8=\cfrac{1}{2}b(4)\implies 8=2b\implies \cfrac{8}{2}=b\implies 4=b[/tex]

To find the length of the base of a triangle with an area of 8 square feet and a height of 4 feet, you rearrange the formula for the area of a triangle and solve for the base, resulting in a base length of 4 feet.

The question asks for the length of the base of a triangle given that the area is 8 square feet and the height is 4 feet. To find the base of the triangle, we can rearrange the formula for the area of a triangle, which is A = (1/2) * base * height. Substituting in the given values and solving for the base, we get:

Base = (2 * Area) / Height

Next, we replace the values for Area and Height:

Base = (2 * 8 sq ft) / 4 ft

Base = 16 sq ft / 4 ft

Base = 4 feet

Therefore, the length of the base of the triangle is 4 feet.

Answer:

600 cocoa beans

Step-by-step explanation:

because pounds and lb is that same thing and for 3 pounds of chocolate, you need 600 cocoa beans

200 cocoa beans makes 1 pound of chocolate.

Since,

1 multiplied to 3 is 3.

So,

200x3 cocoa beans make 1 pound of chocolate.

=600 cocoa beans

Therefore 600 cocoa beans make 3 pounds of chocolate.

2⃣, -4⃣ = x; no radical necessary.

1/6 < 1/4 so 1/6 would equal 2/12 and 1/4 would equal 3/12 so which means if you take one from each it would be 5/12 but if you took 2 from the first one it would only be 2/12 which is why you need to read correctly because THE REASON MARK IS CORRECT IS BECAUSE 5/12 IS GREATER THAN 2/12

Answer:

[tex]\$189.50[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=2\ years\\ P=\$175\\ r=0.04\\n=4[/tex]  

substitute in the formula above  

[tex]A=\$175(1+\frac{0.04}{4})^{4*2}=\$189.50[/tex]  

5950 have been bullied in that particular school of 7000