Complete question :
Seven cards are drawn from an ordinary deck. In how mnat ways is it possible to draw (a) only 5s (b)only 8s, 9s, and 10s, (c) no 8s, 9s, and 10s (d) exactly 2 jacks or kings, (e) 5 spades and 2 hearts?
Answer:
0; 792 ; 100396 ; 30408224 ; 18643560 ;
Step-by-step explanation:
Number of cards in a deck = 52
Number of cards to be drawn = 7
Using combination:
nCr = n! ÷ (n-r)!r!
A.)
Number of 5's in a deck = 4
4C7 = 0
(B.)
only 8s, 9s, and 10s,
Number of 8, 9 and 10's = 4 *3 = 12
12C7 = 12! ÷ 5!7! = 792
(C)
no 8s, 9s, and 10s ;
Number of cards to select from = 52 - (3(4)) = 40C7 = 18643560
(D)
exactly 2 jacks or kings,
Number of jack or king in deck = 8 ; other 5 could be any of the rest : (52 - 8) = 44
8C2 * 44C5 = 28 * 1086008 = 30408224
(e) 5 spades and 2 hearts?
Number of spades = 13
Number of hearts = 13
13C5 * 13C2
1287 * 78 = 100396
calculate the number of sides of a regular polygon with sum interior angles of 2160°.
Answer:
14 sides
Step-by-step explanation:
The sum of all interior angles of a polygon = (n - 2)180°
2160° = (n - 2)180°
[tex]n - 2 = \frac{2160 \degree}{180 \degree} \\ \\ n - 2 = 12 \\ \\ n = 12 + 2 \\ \\ n = 14[/tex]
Hence, the polygon has 14 sides.
can someone please figure this out for me or at least explain this because im lost here
Let f(x)=3x+2, g(x)=x3−3x2+2x+11, and h(x)=x2−3. Perform the following operations.
a) g(-2)=
b) h(-1)=
c) g(x) - h(x)=__x^3 +__x^2+__x+__
d) -2f(x) * h(x)= __x^3+__x^2+__x+__
e) f(h(x)) = __x^2+__x+__
f) f(g(x)) =__x^3+__x^2+__x+__
Answer:
Step-by-step explanation:
the concepts are confusing of what a function is. f(x) seems mysterious , huh
it's just a way to give a label to some set of terms. Just think of it as a name of a person, but in a generic sense, like hey "guy" or hey "gal" you can address many people that way. f(x) is doing that same thing addressing by a name, a set of math terms.
a)
in a) we are addressing the g(x) function and we are also sending that function the number -2 as an input. so find the g(x) function and put in (-2) everywhere that there is an "x" , so
g(x)=[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11
g(-2) = [tex](-2)^{3}[/tex]-3[tex](-2)^{2}[/tex]+2(-2)+11
g(-2) = -8 -3(4) - 4 +11
g(-2) = -8 -12 -4 + 11
g(-2) = -24 + 11
g(-2) = -13
b)
h(-1) find the h(x) function and input a negative 1 where ever there is an x
h(x) =
h(-1) = [tex](-1)^{2}[/tex] - 3
h(-1) = 1 - 3
h(-1) = -2
c)
for c) just combine like terms of the two given functions
g(x) - h(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - ([tex]x^{2}[/tex] - 3)
g(x) - h(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - [tex]x^{2}[/tex] + 3
g(x) - h(x) = [tex]x^{3}[/tex]-4[tex]x^{2}[/tex]+2x + 14
d)
-2f(x) - h(x) = -2(3x + 2) - ([tex]x^{2}[/tex] - 3)
-2f(x) - h(x) = -6x - 4 - [tex]x^{2}[/tex] + 3
-2f(x) - h(x) = -6x - 1 - [tex]x^{2}[/tex]
-2f(x) - h(x) = - [tex]x^{2}[/tex] - 6x - 1
e)
f(h(x)) this gets a bit more confusing b/c it's a composition of functions, that's just a fancy way of saying the functions are nested. one inside the other.
f(x) = 3x + 2
h(x) = [tex]x^{2}[/tex] - 3
plug h(x) in to f(x) where ever there is an x in f(x) , luckily there is only one x in f(x) :)
f(h(x)) = 3([tex]x^{2}[/tex] - 3) + 2
f(h(x)) = 3[tex]x^{2}[/tex] - 9 + 2
f(h(x)) = 3[tex]x^{2}[/tex] - 7
f(h(x)) = 3[tex]x^{2}[/tex] + 0x + (-7)
f)
f(x) = 3x + 2
g(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11
f(g(x)) = 3([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11) + 2
f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 33 + 2
f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 35
Hope that helps :)
Question 30
What was the median annual earnings for all U.S. civilian workers in 2016?
O $51,980
O $49,630
O $41,778
O $46,230
V 153
Given tan A= - and that angle A is in Quadrant IV, find the exact value of
sec A in simplest radical form using a rational denominator.
4
The secant of the angle A is 13/4
How to determine the value of sec(A)?The given parameter is:
[tex]\tan(A) = -\frac{\sqrt{153}}{4}[/tex]
Using the trigonometry identity, we have:
[tex]\sec^2(A) = \tan^2(A) + 1[/tex]
This gives
[tex]\sec^2(A) = (-\frac{\sqrt{153}}{4})^2 + 1[/tex]
Evaluate the exponent
[tex]\sec^2(A) = \frac{153}{16} + 1[/tex]
Evaluate the sum
[tex]\sec^2(A) = \frac{169}{16}[/tex]
Take the square root of both sides
[tex]\sec(A) = \pm \frac{13}{4}[/tex]
Secant in quadrant IV is positive.
So, we have:
[tex]\sec(A) = \frac{13}{4}[/tex]
Hence, the secant of angle A is 13/4
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What best describes the distance between two points with coordinates (2,-3) and (-4,2)
Answer:
Option c (7.8) is the correct alternative.
Step-by-step explanation:
The given points are:
(x₁, y₁) = (2, -3)
(x₂, y₂) = (-4, 2)
As we know,
The distance between two points will be:
= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
On substituting the values, we get
= [tex]\sqrt{(-4-2)^2+(2-(-3))^2}[/tex]
= [tex]\sqrt{(-4-2)^2+(2+3)^2}[/tex]
= [tex]\sqrt{(6)^2+(5)^2}[/tex]
= [tex]\sqrt{36+25}[/tex]
= [tex]\sqrt{61}[/tex]
= [tex]7.8 \ units[/tex]
Please help ASAP
Please help
No links please
Answer:
base = 3 units
height = 5 units
area = 1/2 x 3 x 5 = 7.5 square units
Answer:
[tex]b[/tex] = 3 units
[tex]h[/tex] = 5 units
[tex]a[/tex] = 7.5 units
Step-by-step explanation:
We can find the base of the figure by counting the number of units from the left to the right of the triangle. So, we can find that the base is 3 units.
The height of the figure can be found by counting how many units the figure measures from the tip to the bottom. The height, then, is 5 units.
The easiest way to find the area of a right triangle is to imagine it as a rectangle, with the same [tex]l[/tex] (length) and [tex]w[/tex] (width) dimensions, and then divide the area of the rectangle by two.
So, to find the area of this rectangle, multiply the length and width, 3 and 5, together.
3 · 5 = 15
Then, we can divide this product by two.
[tex]\frac{15}{2}[/tex] = 7.5
The area is 7.5 units².
Hope this helped :] Good luck!
Three times Francis' age plus five times Earl's age is 230. Earl is also four times Francis age. How old is Earl?
Answer:
E = 40 years
Step-by-step explanation:
Let the age of Francis be F.
Let the age of Earl be E.
Translating the word problem into an algebraic expression, we have;
3F + 5E = 230 ......equation 1
E = 4F .......equation 2
To find the value of F;
Substituting eqn 2 into eqn 1, we have
3F + 5(4F) = 230
3F + 20F = 230
23F = 230
F = 230/23
F = 10 years
Now, to find the value of E;
From eqn 2;
E = 4F
Substituting the value of "F" we have;
E = 4*10
E = 40 years
Therefore, Earl is 40 years old.
NO WEBSITES ALLOWED (especially bitly)
Answer:
top right is an acute angle the top left is an obtuse angle and the bottom right is a right angle and I'm not to sure what the bottom right is
Answer:
Bottom right is a right
Step-by-step explanation:
and since it has no matching sides it would be a Isosceles
look at pic 10 pts will mark brainilest
someone please help me im timed
Answer:
C
Step-by-step explanation:
All sides of a square are equal.
Find the surface area of the solid figure represented by the given net. 10cm squared 10cm squared 10cm squared 10cm squared 25cm squared
Answer:
its actually 65
Step-by-step explanation:
If an object moves in uniform circular motion in a circle of radius R = 2.00 meters, and the object takes 5.00 seconds to complete ten revolutions, calculate the centripetal acceleration. ALWAYS use significant figure rules. Remember that these rules apply to all numbers that are measurements. a= _____ m/s2 39.4 m/s 2 100. m/s 2 158 m/s 2 50.2 m/s 2
Help pleaseee! Whats the answer
Answer:
The answer is 16 for the blue dot
I'm think it's 16
Step-by-step explanation:
This is because it seems that it jumps from 0 to 4. So you add four to the number 4...
I need help I already failed the first attempt
Step-by-step explanation:
Hi,
y - 1 = 2 - x has a negative slope.
x + y = 0 has a negative slope.
y = 4x - 3 has a positive slope.
y = 1 has a 0 slope.
x = 10 has an undefined slope.
I hope this helps :)
Please help! Needed ASAP!
Answer:
1 bagel $3.5
1muffin $1.25
1ticket$9
1snack$2
Step-by-step explanation:
miffin(y)
bagel(x)
x+3y=7.25
x+2y=6
since x is similar in both equations you cancel it out
subtract this
3y=7.25
2y=6
y=$1.25(price for 1 muffin)since we had 3 muffins it will be 1.25×3=7.25,where you do 7.25 to get 3.5 (price for 1 bagel)question 8:ticket(x)
snack(y)
2x+3y=24×3
3x+4y=35×2
×3 and ×2 so we can eliminate the x
6x+9y=72
6x+8y=70
eliminate x
y=2
so snack is $2
2x+(3×2)=24
24-6=18
18÷2x=9
so a ticket is $9
Help me!!!!!!!!!!!! And look at the picture plzzzz!!!!
Answer: 72
Step-by-step explanation:
Set it up as a ratio
[tex]\frac{12}{15} =\frac{x}{90} \\15x=1080\\x=72[/tex]
Hey guys!!! I forgot how to do this :/ lol
whats 10+4÷2?
Answer:
12
Step-by-step explanation:
how many outfits can you make out of 2 helmets, 6 shirts, and 2 pairs of shorts
Answer:
2 OUTFITS
Step-by-step explanation:
In an effort to test the hypothesis that the proportion of voters in the younger than 40 year old age bracket who will vote for a particular politician is different than the proportion voters in the above 40 age bracket, the following data was collected. Test hypothesis at 0.10 level of significance.
Population Number Who Will Vote for Politician Sample Size
Below 40 348 700
Above 40 290 650
Required:
a. Reject the Null Hypothesis and condlude that the proportion of voters in the younger than 40 year oid age bracket who will vote for a particular different than the proportion voters in the above 40 age bracket.
b. Do not reject the Null Hypothesis and conclude that the proportion of wotors in the younger than 40 year old age bracket who will vote for a particular politician is not different than the proportion voters in the above 40 age bracket.
Answer:
We reject H₀ we support the claim that the two proportion are different
Step-by-step explanation:
Younger than 40 years old
Sample size n₁ = 700
x₁ = 348
p₁ = 348 / 700 p₁ = 0,497 p₁ = 49,7 %
Above 40 years old
Sample size n₂ = 650
x₂ = 290
p₂ = 290/ 700 p₂ = 0,414 p₂ = 41,4 %
p = ( n₁*p₁ + n₂*p₂ ) / n₁ + n₂
p = 700 * 0,497 + 650 * 0,414 ) / 700 + 650
p = ( 347.9 + 269,1 ) / 1350
p = 0,457 p = 45,7 %
q = 1 - p q = 54,3 % q = 0,543
CI is 90 % significance level is 10 % α = 10 % α = 0,1 α/2 = 0,05
zscore for α/2 from z- table is : z(c) = 1,64
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
To calculate z(s) = ( p₁ - p₂ ) / √ pq/n₁ + pq/ n₂
p₁ - p₂ = 0,497 - 0,414 = 0,083
√ pq/n₁ + pq/ n₂ = √ 0,457*0,543/ 700 + 0,457*0,543/ 650
√ pq/n₁ + pq/ n₂ = √ 3,545*10⁻⁴ + 3,82 * 10⁻⁴
√ pq/n₁ + pq/ n₂ = 2,71 * 10⁻² = 0,0271
z(s) = 0,083/ 0,0271
z(s) = 3,06
Comparing z(s) and z(c)
|z(s)| > |z(c)|
Then z(s) is in the rejection region and we reject H₀
Elias purchases a home for $38,900. The value of the home, in thousands of dollars, since his purchase is shown in the table. A 2-column table with 6 rows. The first column is labeled years since purchase with entries 0, 5, 10, 15, 20, 25. The second column is labeled value (thousands of dollars) with entries 38.9, 62.4, 89.3, 145.2, 210.8, 326.5. Find an exponential function that models the data. Round numerical values to the nearest hundredth. Let x be the number of years since the purchase. The function f(x) = ( )x models the data. Use the model to predict the home’s value. After 12 years, the home’s value will be about $ thousand. After 35 years, the home’s value will be about $ thousand.
Answer:
f(x)=39.59 (1.09)
Use the model to predict the home’s value.
After 12 years, the home’s value will be about $
111 thousand.
After 35 years, the home’s value will be about $
808 thousand.
Step-by-step explanation:
Edge 2021 :)
A function assigns the values. After 35 years, the home’s value will be about $215.079.68 thousand.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A general exponential equation is given as,
y = A(1+b)ˣ
Now, if x is the number of years since the purchase. And we substitute the value of the x and y from the table. Then we can write,
38.9 = A(1+b)ˣ
A = 38.9
Therefore, the equation can now be written as,
y = 38.9(1+b)ˣ
Substitute the second point in the equation,
y = 38.9(1+b)ˣ
62.4 = 38.9(1+b)⁵
1.604113 = (1+b)⁵
1+b = 1.09912
b= 0.09
Hence, the function that can model the value of the house after x years is y=38.9(1.09)ˣ.
B.) Now the value of the house after 12 years,
y=38.9(1.09)ˣ
y=38.9(1.09)¹²
y = 109.41
The home’s value will be about $ 109.41 thousand.
C.) After 35 years, the home’s value will be,
y=38.9(1.09)ˣ
y=38.9(1.09)¹⁰⁰
y = 215.079.68
After 35 years, the home’s value will be about $215.079.68 thousand.
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Help help help help help help
Answer:
More than for the first box and less than for the second.
Sami opened an account with a deposit of $4,000.
• The bank pays 3.5% annual simple interest on this account
• Sami did not make any additional deposits or withdrawals.
How long will it take for Sami to earn $2,100 in interest on this
account?
835.71$
Step-by-step explanation:
is the answer just done it
In 2009 Zambrano's salary was 18,750,000. He pitched in 28 games in 2009. What was his salary per game in 2009? Round to the nearest cent.
Answer:
his salary per game is 669,643
Step-by-step explanation:
The computation of the salary per game in the year 2009 is shown below
Given that
His salary in the year 2009 is 18,750,000
And, he pitched 28 games in the year 2009
Based on the above information
His salary per game is
= 18,750,000 ÷ 28 games
= 669,643
hence, his salary per game is 669,643
The same is relevant
PLS HELP IMA GIVE BRAIN LISTTT!!!
Which model is 85% shaded?
Done
Answer:
First left
Step-by-step explanation:
17/20 = 0.85 = 85/100 = 85%
Compare areas: the side of a square is 14 m long. If all four size increased by 5, how my how much is the area increase?
The areas from _____ m^2 to _____ m^2, which is an increase of _____ m^2.
9514 1404 393
Answer:
196361165Step-by-step explanation:
The original side length is 14 m, so the area is (14 m)² = 196 m².
The longer side length is 14 m + 5m = 19 m, so the area is (19 m)² = 361 m².
The increase in area is ...
361 m² -196 m² = 165 m²
The area increases from 196 m² to 361 m², which is an increase of 165 m².
Answer:
The areas from 196 m² to 361 m², which is an increase of
165 m²
what is the area of the triangle? no links just the answer plz.
Answer:
A = 25
Step-by-step explanation:
Base = |-2-(-7)| = |-2+7| = 5
equation of the line that includes the base
x = 6 (because it is parallel to y axis)
the height passes to the point (-4,-4) and must be perpendicular to the base
the equation of the line of the base hasn’t the slope expressed, so the line of the height has a slope equal to 0
so the equation of the line is y= -4
the point (6,-4) is where the two lines intercept and it is the point where the height hit the base
height = |-4-6| = 10
A = (base x height)/2 = (5x10)/2 = 25
Katie worked 40.5 hours this week. She makes $8 per hour. How much money did she earn this week?
Answer:
$324
Step-by-step explanation:
if
=> 1hr = $8
then,
=> 40.5 x 8 = 324
=> 40.5 hr = $324
She earned $324 this week.
hope this helps and is right :)
Answer:
$324
Step-by-step explanation:
So, First we have to establish what we are solving for, in this equation we are solving for how much money Katie made this week after working 40.5 hours at a salary of $8 per hour.
To find how much Katie made we have to multiply 40.5 and 8!
Let's make it easier by splitting 40.5 into 40 and 0.5
40 × 8 = 320
0.5 × 8 = 4
320 + 4 = 324
Katie made $324 this week!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Evaluate the polynomial for x = -2.
x² - 9x+7
Answer:
Hi! The answer to your question is [tex]29[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Please help will give brainliest!
Answer:
Yes, Yes, No, Yes.
Step-by-step explanation:
2/5 as a decimal = 0.4
4 ÷ 0.4 = 10
1 is correct.
2 x 10 = 20
2 is correct.
6 x 10 = 60
3 is incorrect.
10 ÷ 2 = 5
4 is correct.
Bob has a bulb factory that produces two types of bulbs: white light (x) and color light (y). It is known that the standard deviation of service life for the population of white light bulbs is hours and hours for color bulbs, both are normally distributed. He tested the mean service life of those two types of bulbs by randomly drawing a sample of 20 bulbs from each type. The estimated mean service life are hours and hours. Assume that . What is the absolute value of the t-statistic if the null hypothesis is that both types of bulbs have the same service life?
Answer:
The answer is "3.51".
Step-by-step explanation:
[tex]\to t=\frac{\bar{x}-\bar{y}}{\sqrt{\frac{\sigma_x^2}{n_x}+\frac{\sigma_y^2}{n_y}}}\\\\[/tex]
[tex]=\frac{960-945}{\sqrt{\frac{14^2}{20}+\frac{13^2}{20}}}\\\\=\frac{15}{\sqrt{\frac{196}{20}+\frac{169}{20}}}\\\\=\frac{15}{\sqrt{\frac{196+169}{20}}}\\=\frac{15}{\sqrt{\frac{365}{20}}}\\\\=\frac{15}{\sqrt{18.25}}\\\\=\frac{15}{4.27}\\\\=3.51[/tex]