Solve for t
3t-15 < -3 and -4t < 12

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

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

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]

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:

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:

Option A is correct.

Step-by-step explanation:

A complex number is that which has imaginary number i.e i in it.

We know √-1 = i

So, any term containing √-1 can be complex number.

In our question option A is only number having √-1 so, Option A i.e

[tex]\frac{2}{3} + \sqrt{-\frac{7}{3} }[/tex] is complex number.

Option: A is the correct answer.

The one which is a complex number is:

              A.   [tex]\dfrac{8}{3}+\sqrt{-\dfrac{7}{3}}[/tex]

We know that the complex number is one which is expressed in the form of :

                 a+ib

where a and b belongs to the set of real numbers.

and i is known as a imaginary number which is represented by:

            [tex]i=\sqrt{-1}[/tex]

A)

[tex]\dfrac{8}{3}+\sqrt{-\dfrac{7}{3}}[/tex]

This could also be written in the form of:

[tex]\dfrac{8}{3}+\sqrt{\dfrac{7}{3}\times -1}\\\\i.e.\\\\=\dfrac{8}{3}+\sqrt{\dfrac{7}{3}}\cdot \sqrt{-1}\\\\i.e.\\\\=\dfrac{8}{3}+i\cdot \sqrt{\dfrac{7}{3}}[/tex]

Hence, the number is in the form of:

              a+ib

where

[tex]a=\dfrac{8}{3}[/tex] which is a rational number and hence belong to real number

and

[tex]b=\sqrt{\dfrac{7}{3}}[/tex] which is a irrational number and hence belong to a real number.

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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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:

net 2 is the anwser to the solid figure

The answer is Net 2. I think so.

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:

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.

For more such information on: absolute slope value

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5950 have been bullied in that particular school of 7000

Answer:

Answer:

I believe the answer is 90.6

Step-by-step explanation:

I added 200+900+240+70+855 and got 2,265.  If I divide that by 25 I get 90.6.  

Hope this helps!

Answer with Step-by-step explanation:

A class of 25 students took a spelling test.

Number of students                  Marks obtained

2                                                       100

9                                                        95

10                                                       90

3                                                         80

1                                                          70

Average marks=sum of marks/number of students

Sum of marks=100×2+9×95+10×90+3×80+70×1

                     =2265

Number of students=25

Average=2265/25

             =90.6

Hence, average score of the spelling test rounded to one decimal place is:

90.6

The answer to Number 21 is A

Answer:

x=44

Step-by-step explanation:

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:

[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]  

2⃣, -4⃣ = x; no radical necessary.

Answer:

7z + 17

Step-by-step explanation:

15 and 2 are the only alike terms.

Please mark brainliest!

Answer:

19958400

10

8

1814400

Step-by-step explanation:

* Lets explain how to solve the problem

- Permutation is the act of arranging the members into order

- The number of permutations of n members taken r at a time is

  denoted by nPr

- nPr = n!/(n - r)! , where n! means n(n - 1)(n - 2)(n - 3) ......... × 1

* Lets solve the problem

- There are eleven people on a softball team

∴ n = 11

- There are nine different positions

∴ r = 9

∴ The number of ways can be made = 11P9

∵ 11P9 = 11!/(11 - 9)! = 11!/2! = 19958400

* The number of total arrangements of the player is 19958400

- If Amy does not want to play pitcher

∵ They are 11 players

∴ The number of players can be pitch = 11 - 1 = 10

* If Amy does not want to play pitcher, then there are now 10 people

 available to pitch

- Assuming the pitcher has already be chosen

∴ There are 10 remaining players

∵ The positions are 9

∴ The remaining positions = 9 - 1 = 8

* There are 8 remaining positions

- Lets find how many ways to arrange the remaining positions

∵ n = 10

∵ r = 8

∴ 10P8 = 10!/(10 - 8)! = 10!/2! = 1814400

* The number of ways to arrange the remaining players is 1814400

Answer:

19958400

10

8

Step-by-step explanation:

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.

The answer is:

The ball will hit the ground in 7.69 seconds.

To solve this problem, we need to apply the following projectile motion equation:

[tex]y=vo*sin(\alpha)*t-\frac{1}{2}gt^{2}[/tex]

To calculate when the ball wil hit the ground, in other words the time of flight, we need to make "y" equal to 0, and considerate the initial height, so, we have:

[tex]0=initialheight+vo*sin(\alpha)*t-\frac{1}{2}gt^{2}[/tex]

Then, we are given the following information:

[tex]InitialHeight=4.5feet\\\alpha =54\°\\vo=\frac{152ft}{s}[/tex]

Now, substituting and solving, we have:

[tex]-(\frac{1}{2})*\frac{32.15ft}{s^{2}}*t^{2}+\frac{152ft}{s}*sin(54\°)+4.5ft\\\\-16.07\frac{ft}{s^{2} }*t^{2}+122.97\frac{ft}{s}*t +4.5ft=0[/tex]

We have a quadratic equation, where:

[tex]a=-16.07\\b=122.97\\c=4.5[/tex]

Now, using the quadratic equation to find the values of "t" , we have:

[tex]\frac{-b+-\sqrt{b^{2}-4ac} }{2a}[/tex]

Substituting we have:

[tex]\frac{-122.97+-\sqrt{(122.97)^{2}-4*(-16.0)*(4.5)} }{2*(-16.07)}\\\\\frac{-122.97+-\sqrt{(122.97)^{2}-4*(-16.07)*(4.5)} }{2*(-16.07)}=\frac{-122.97+-\sqrt{15121.62+289.26}}{-32.14}\\\\\frac{-122.97+-\sqrt{15121.62+289.26}}{-32.14}=\frac{-122.97+-(124.14)}{-32.14}[/tex]

[tex]t_1=\frac{-122.97+124.14}{-32.14}=-0.04\\\\t_2=\frac{-122.97-124.14}{-32.14}=7.69[/tex]

Therefore, since the time cannot be negative, we have to discard "t1", so, the answer is: 7.69 seconds

Hence, the ball will hit the ground in 7.69 seconds.

Have a nice day!

Answer:

7.72 s

Step-by-step explanation:

I got the question wrong when I put 7.69 and saw that this was the correct answer.

An ordered pair is a solution to the equation y = 4x + 15 if when its elements are substituted into the equation, both sides of the equation hold equal. For instance, the ordered pair (2,23) is a solution to this equation.

The question is asking which ordered pair is a solution to the linear equation y = 4x + 15. An ordered pair consists of values of x and y that make this equation true. Therefore, we plug in the values of the ordered pair into the equation.

For example, if we have the ordered pair (2,23), we substitute the x value (2) and y value (23) into the equation: y = 4x + 15 becomes 23 = 4*2 + 15. By doing the calculation, we find that the left side of the equation equals the right side, therefore, (2,23) is a solution for the equation y= 4x+15.

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The ordered pair (2, 23) is a solution to the equation y = 4x + 15. By substituting x = 2, the corresponding y value is 23, validating the solution in the linear relationship.

To find an ordered pair that is a solution to the equation y = 4x + 15, we can choose values for x and compute the corresponding y value.

Let's try x = 2:

y = 4(2) + 15 = 8 + 15 = 23

So, the ordered pair (2, 23) is a solution to the equation.

In this context, for any chosen x, plugging it into the equation and calculating y will yield a valid solution. The equation represents a linear relationship where y is four times x plus 15. Therefore, any pair of x and y that satisfies this relationship is a solution to the equation. The solution set consists of an infinite number of ordered pairs, each representing a point on the graph of the linear equation.

The probable question may be:

What ordered pair is a solution to the equation

y= 4x+15

Answer:

Second answer choice

Step-by-step explanation:

Since -10 is outside t you multiple every number inside the parenthesis by -10

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]

To find the average add all the scores together, then divide that by the number of quizzes.

77 + 71 + 82 + 79 + 76 + 78 + 85 + 83 = 631

8 quizzes

Average = 631 / 8 = 78.875  = 79

Answer:

78.875

Step-by-step explanation:

the average = sum of the scores/ number of scores

average = (77 + 71+ 82+79+ 76+78+85+83)/8

average = 631/8 = 78.875

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

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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