Answer: Come up with questions that make sence. That are good solvablequestions. Make sure that you are able to take data off of it to see how people result in it.
Step-by-step explanation:
B={x|x is an integer and -4
The resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
What is roster form?In the set-builder form, a short, statement, or formula is written inside a pair of curly braces, as opposed to the roster form, where the listed items are enclosed in a pair of curly braces and separated by commas.
Roster or tabular form: In roster form, all of the components of a set are listed, with commas used to divide them and braces used to enclose them.
For instance, Z = the set of all integers = {…,−3,−2,−1,0,1,2,3,…}.
So, we have:
B = {x:x is an integer and -4 < x < 6}
B has numbers from -4 and 6.
Now, write B in roster form as:
B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}
Therefore, the resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
Know more about the roster form here:
https://brainly.com/question/24130735
#SPJ1
Complete question:
Write the following sets in roster form:
B = {x:x is an integer and -4 < x < 6}
suppose that functions p and q are defined as follows
p(x) = 2x
q(x) = x^2-2
find the following :
(q•p) (-3)=
(p•q) (-3)
For triangle ABC, tell what information is given (i.e. SAS, SSS, ASA, etc.) in Column A. Solve for the indicated angle or side in Column B. If there are two solutions, give both. Express answers to the nearest tenth.
1. A=52°, b=120, c = 160, find a
2. a=13.7, A=2543°, B=78°, find b
3. A=38°, B=63°, c=15, find b
4. a=1.5, b=2.3, c=1.9, find B
5. b=795.1, c=775.6, B=51.85°, find C
6. b=40, c=45, A=51°, find a
7. b=50, a=33, A=132°, find B
8. a=20, b=12, c=28, find C
9. a=125, A=25°, b=150, find B
10. b=15.2, A=12.5°, C=57.5°, find c
Using the laws of sines and cosines, answers to the questions are as follows,
1. A=52°, b=120, c = 160,
SAS property, a=128
2. a=13.7, A=25.43°, B=78°,
AAS property, b=31.21
3. A=38°, B=63°, c=15,
ASA property, b=14
4. a=1.5, b=2.3, c=1.9,
SSS property, B=84
5. b=795.1, c=775.6, B=51.85°,
SAS property, C=50
6. b=40, c=45, A=51°,
SAS property, a=37
8. a=20, b=12, c=28
SAS property, C=120
9. a=125, A=25°, b=150
SAS property, 2 solutions are there, B1=149, B2=30.4
10. b=15.2, A=12.5°, C=57.5°
SAS property, c=14
What are the laws of sine and cosine?
We can determine a triangle's one side's length or one of its angles' measurements using the laws of sine and cosine.
In most cases, the unknown sides or angles of an oblique triangle are calculated using the law of sines formula.
The equation that connects the lengths of the triangle's sides and the cosines of its angles is known as the law of cosine or cosine rule.
1. Given A=52°, b=120, c = 160.
If we construct the triangle, we see that it is satisfying the SAS property
By using the law of cosine we get,
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{120^{2}+160^{2}-2.120.160.\cos 52}\\a=127.9[/tex]
2. Given, a=13.7, A=25.43°, B=78°
From angle A, angle B, and side a, we calculate side b, by using the Law of Sines,
[tex]\frac{b}{a}=\frac{\sin B}{\sin A}\\b=a.\frac{\sin B}{\sin A}\\b=13.7. \frac{\sin 78}{\sin 25.43}\\b=31.21[/tex]
3. A=38°, B=63°, c=15
From angle A and angle B, we calculate angle C,
[tex]A+B+C=180\\C=180-A-B\\C=180-38-63\\C=79[/tex]
Next, From angle A, angle C, and side c, we calculate side a, by using the Law of Sines
[tex]\frac{a}{c}=\frac{\sin A}{\sin C}\\a=c.\frac{\sin A}{\sin C}\\a=15. \frac{\sin 38}{\sin 79}\\a=9.41[/tex]
Calculation of the third side b of the triangle using a Law of Cosines,
[tex]b^{2}=a^{2} +c^{2}-2.a.c.\cos B\\b=\sqrt{a^{2}+c^{2}-2.a.c.\cos B}\\b=\sqrt{9.1^{2}+15^{2}-2.9.41.15.\cos 63}\\b=13.68[/tex]
4. a=1.5, b=2.3, c=1.9
Calculation of the inner angles of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{1.5^{2}+1.9^{2}-2.3^{2} }{2 . 1.5.1.9}\\B=84.15[/tex]
5. b=795.1, c=775.6, B=51.85°
From angle B, side c, and side b, we calculate side a. by using the Law of Cosines and quadratic equation:
[tex]b^2 = c^2 + a^2 - 2.c. a. {\cos B} \\ 795.1^2 = 775.6^2+a^2-2. 775.6. a . \cos 51\ \\ a > 0 \\ a = 989.175[/tex]
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{989.175^{2}+795.1^{2}-775.6^{2} }{2 . 989.795}\\C=50.5[/tex]
6. b=40, c=45, A=51°
Calculation of the third side a of the triangle using a Law of Cosines
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{40^{2}+45^{2}-2.0.45.\cos 51}\\a=36.87[/tex]
8. a=20, b=12, c=28
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{20^{2}+12^{2}-28^{2} }{2 . 20.12}\\C=120[/tex]
9. a=125, A=25°, b=150
2 solutions are possible for this,
solution for B1:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 28.21[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+28.21^{2}-150^{2} }{2 . 125.28}\\B=149[/tex]
solution for B2:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 243.679[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+243^{2}-150^{2} }{2 . 125.243}\\B=30.28[/tex]
10. b=15.2, A=12.5°, C=57.5°
From angle A and angle C, we calculate angle B:
[tex]A+B+C=180\\B=180-A-C\\B=180-12.5-57.5\\B=110[/tex]
From the angle A, angle B, and side b, we calculate side a, by using the Law of Sines.
[tex]\ \\ \dfrac{ a }{ b } = \dfrac{ \sin A }{ \sin B } \\ a = b \cdot \ \dfrac{ \sin A }{ \sin B } \\ a = 15.2 \cdot \ \dfrac{ \sin 12.30 }{ \sin 110\degree } = 3.5[/tex]
Calculation of the third side c of the triangle using a Law of Cosines
[tex]c^{2}=a^{2} +b^{2}-2.a.b.\cos C\\c=\sqrt{a^{2}+b^{2}-2.a.b.\cos C}\\c=\sqrt{15.2^{2}+3.5^{2}-2.15.4.\cos 57.30}\\c=13.64[/tex]
Therefore, we have found the solutions of all of the above bits using the law of sine and cosine.
To learn more about the laws of sine and cosine, visit the following page:
https://brainly.com/question/16231938
#SPJ4
The function c(r) = 0.47x + 20 represents the cost (in dollars) of a one-day truck rental when the truck is
driven x miles.
a. What is the truck rental cost when you drive 80 miles?
b. How many miles did you drive when your cost is $35.51?
Answer: the cost is $35.51, That must mean it would be driven 33.0 miles.
Step-by-step explanation: The given function c(r) represents the cost of a one-day truck rental when the truck is driven x miles. This means that the cost in dollars is a linear function of the number of miles driven.
To answer the first part of the question, we can plug in x = 80 into the function to find the truck rental cost when we drive 80 miles:
$$c(r) = 0.47x + 20 = 0.47(80) + 20 = \boxed{35.6}$$
To answer the second part of the question, we can solve the equation $c(r) = 0.47x + 20 = 35.51$ for x to find the number of miles driven when the cost is $35.51:
$$35.51 = 0.47x + 20 \Rightarrow 15.51 = 0.47x \Rightarrow x = \boxed{33.0}$$
Therefore, when the cost is $35.51, we must have driven 33.0 miles.
40 POINTS Use photo
Find BA.
There were 169 tickets for a major league baseball game. The lower box tickets cost $12.50 and the upper box tickets cost $10.00. The total amount of money spent was $1795.00. How many of each kind of ticket were purchased?
Answer:
42 lower box127 upper boxStep-by-step explanation:
You want the number of tickets of each kind sold if 169 tickets were sold for $1795, and lower box tickets were $12.50 while upper box tickets were $10.
SetupLet x represent the number of lower box tickets sold. Then 169 -x is the number of upper box tickets sold. The total revenue is ...
12.50(x) + 10.00(169 -x) = 1795.00
SolutionSimplifying, we get
2.50x +1690 = 1795
2.5x = 105 . . . . . . . . . . . subtract 1690
x = 42 . . . . . . . . . . . . divide by 2.5; the number of lower box ticket sold
169 -42 = 127 . . . . . . the number of upper box tickets sold
42 lower box and 127 upper box tickets were purchased.
The graph above shows the distance a tow truck is away from the company's base.
What is the rate of change of change from hour 4 to hour $7 ?
Solve for x: log(x) - log(3) = 2 log(6)
Answer:
Below
Step-by-step explanation:
log x = 2 log 6 + log 3 using properties of logs, this becomes
log x = log 6^2 + log 3
= log (6^2 * 3 ) = log (108)
x = 108
5) if the 4 digit number 7,2d2 is divisible by 6, then what is the largest possible value of digit d?
Write the systems of equations from the table below and find the solution?
The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)
How to determine the system of equations?From the question, we have the table of values as the parameters that can be used in our computation:
From the table, we have
Table 1
(x, y) = (0, -3) and (4, 13)
A linear equation is represented as
y = mx + c
Where
Slope = m
c = y when x = 0
This means that
c = -3
So, we have
y = mx - 3
The point (4, 13) implies that
13 = m * 4 - 3
So, we have
4m = 16
m = 4
So, the equation is
y = 4x - 3
Table 2
(x, y) = (0, 4) and (4, 6)
A linear equation is represented as
y = mx + c
This means that
c = 4
So, we have
y = mx + 4
The point (4, 6) implies that
6 = m * 4 + 4
So, we have
4m = -2
m = -1/3
So, the equation is
y = -1/3x + 4
Substitute y = -1/3x + 4 in y = 4x - 3
-1/3x + 4 = 4x - 3
So, we have
-x + 12 = 12x - 9
Evaluate the like terms
13x = 21
Divide
x = 21/13
y = -1/3x + 4 implies that
y = -1/3 x 21/13 + 4
So, we have
y = -7/13 + 4
Evaluate
y = 45/13
So, the solution is (21/13, 45/13)
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
I need help with this
Step-by-step explanation:
If M is the midpoint of AB then,
AM = BB so we can write the following equation:
4x + 13 = 3x + 17
transfer like terms to the same side of the equation4x - 3x = 17 - 13
add/subtractx = 4
Now on to the length of BM, we can replace x with 4 to find it.
3*4 + 17 = 29
Suppose the company desires to make a profit of shs. 195,000, what should be the output in units?
A) The break-even sales level in shillings XYZ Company needs to achieve is Shs.1,096,443.
B) The break-even sales level in units XYZ Company needs to achieve is 27,444 units to make a profit of Shs.195,000.
What is the break-even point?The break-even point is the sales level when total revenue equals total costs (fixed and variable).
At the break-even point, there is no profit or loss.
Selling price per unit = Shs.66
Variable production cost per unit = Shs.44
Variable selling cost per unit = Shs.4
Total variable cost per unit = Shs.48 (Shs.44 + Shs.4)'
Contribution margin per unit = Shs.18 (Shs.66 - Shs.48)
Contribution margin ratio = 27.27% (Shs.18/Shs.66 x 100)
Fixed production cost (total) = Shs.200,000
Fixed selling and administrative cost (total) Shs.99,000
Total fixed costs = Shs. 299,000 (Shs.200,000 + Shs.99,000)
Target profit = Shs.195,000
a) Break-even sales in shillings = Fixed costs/Contribution margin ratio
= Shs.1,096,443 (Shs.299,000/27.27%)
b) Break-even sales in units to achieve target profit = (Fixed costs + Target profit)/Contribution margin per unit
= (Shs.299,000 + Shs.195,000/Shs.18)
= Shs.494,000/Shs.18
= 27,444 units
Learn more about the break-even point at https://brainly.com/question/24233845 and https://brainly.com/question/15281855
#SPJ1
Question Completion:XYZ Company manufactures a product called "PERMA". Pertinent cost and revenue data relating to the manufacture of this product are given below:
Selling price per unit = Shs.66
Variable production cost per unit = Shs.44
Variable selling cost per unit = Shs.4
Fixed production cost (total) = Shs.200,000
Fixed selling and administrative cost (total) Shs.99,000
Required:
a) Calculate the break-even sales level in shillings;
b) Suppose the company desires to make a profit of shs.195,000, what should be the output in units?
5. Solve each equation using a function machine. The first one is started for you.
a. 3 x+4=25
c. 4 b-10=30
e. 5 n+2=37
g. 3 k+4=28
b. 3 x-4=11
d. 4 b+10=30
f. 2 w+10=2
h. 6 h-7=11
The solutions to the equations using function machine are x = 7, x = 5, b = 10, b = 5, n = 7, w = -4, k = 8 and h = 3
How to determine the solutions to the equations using function machineFrom the question, we have the following equations that can be used in our computation:
a. 3x+4=25 b. 3x-4=11c. 4b-10=30 d. 4b+10=30e. 5n+2=37 f. 2w+10=2g. 3k+4=28 h. 6h-7=11Using a function machine, we have:
Equation (a)
3x + 4=25
This becomes
x ⇒ [ ] ⇒ [ ] = [ ]
So, we have
x ⇒ [ 21 ] ⇒ [ +4 ] = [ 25 ]
This means that
x = 21/3
x = 7
Equation (b)
3x - 4 = 11
This becomes
x ⇒ [ ] ⇒ [ ] = [ ]
So, we have
x ⇒ [ 15 ] ⇒ [ -4 ] = [ 11 ]
This means that
x = 15/3
x = 5
Equation (c)
4b - 10 = 30
This becomes
b ⇒ [ ] ⇒ [ ] = [ ]
So, we have
b ⇒ [ 40 ] ⇒ [ -10 ] = [30]
This means that
b = 40/4
b = 10
Equation (d)
4b + 10 = 30
This becomes
b ⇒ [ ] ⇒ [ ] = [ ]
So, we have
b ⇒ [ 20 ] ⇒ [ +10 ] = [30]
This means that
b = 20/4
b = 5
Equation (e)
5n + 2 = 37
This becomes
n ⇒ [ ] ⇒ [ ] = [ ]
So, we have
n ⇒ [ 35 ] ⇒ [ +2 ] = [37]
This means that
n = 35/5
n = 7
Equation (f)
2w + 10 = 2
This becomes
w ⇒ [ ] ⇒ [ ] = [ ]
So, we have
w ⇒ [ -8 ] ⇒ [ +10 ] = [2]
This means that
w = -8/2
w = -4
Equation (g)
3k + 4 = 28
This becomes
k ⇒ [ ] ⇒ [ ] = [ ]
So, we have
k ⇒ [ 24 ] ⇒ [ +4 ] = [28]
This means that
k = 24/3
k = 8
Equation (h)
6h - 7 = 11
This becomes
h ⇒ [ ] ⇒ [ ] = [ ]
So, we have
h ⇒ [ 18 ] ⇒ [ -7 ] = [11]
This means that
h = 18/6
h = 3
Hence, the value of h is 3
Read more about equations at
https://brainly.com/question/2476251
#SPJ1
The plane is perpendicular to the axis but does not go through the vertex.
The plane intersects the double cone at only the vertex.
The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone.
The plane is tangent to both of the cones.
answers:
line
point
circle
elipse
match these
The plane is perpendicular to the axis but does not go through the vertex. The plane intersects the double cone at only the vertex is ellipse.
What is an ellipse ?A planar curve with two focal points is called an ellipse if at every point on the curve the sum of the two distances from the focal points is constant. It generalises the shape of a circle, a unique variety of ellipse in which the two focus points coincide.The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone is circle.A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.To learn more about ellipse refer :
https://brainly.com/question/16904744
#SPJ1
Hannah invested $2,500 in an account earning 3.4% annual interest that is compounded semi-annually. How long will it take the investment to triple?
(Round your answer to the nearest hundredth.)
Based on the fact that Hannah's investment will triple in 10 years and 10 months when compounding occurs every six months.
What is compounding?The process through which interest is added to the existing principal sum and the interest that has previously been paid is known as compounding.
As a result, compounding, sometimes known as the "magic of compounding," can be thought of as interest on interest, which has the effect of making returns on interest larger over time.
The amount of time required to triple the investment is as follows:
$2500 was invested.
3.4% interest rate.
Compounding: Every 6 months (Semiannually)
Now think about a time frame of two years:
3.4 * 6/12 = 1.7%
The effective interest rate will be 1.7%.
The current value of the 1.7% compounded rate over 65 factors is equivalent to 2.9913.
The value will therefore be $2,500 2.9913 = 7,478.25.
Six years divided by 65 months yields a total of 10.833 years.
10 months make up a year, or 0.833 * 12.
Therefore, based on the fact that Hannah's investment will triple in 10 years and 10 months when compounding occurs every six months.
Know more about compounding here:
brainly.com/question/29523718
#SPJ1
Find the missing length in the triangle below. Round to the nearest
tenth if necessary. Show all your work for credit.
0:05
9 ft
X
4 ft
The missing length in the triangle
is approximately
feet.
If a box of chocolate costs $8.00 and weighs 1 lb.
what is the cost per ounce?
Answer:
$0.50 per ounce
Step-by-step explanation:
To find the cost per ounce of the chocolate, you will need to divide the price of the box by the weight of the box in ounces. Since there are 16 ounces in a pound, the weight of the box in ounces is 1 * 16 = <<1*16=16>>16 ounces.
To find the cost per ounce, divide the price of the box by the weight of the box in ounces: $8.00 / 16 ounces = $0.50 per ounce.
Therefore, the cost per ounce of the chocolate is $0.50.
A phone company offers two monthly plans. plan A cost $19 plus an additional $0.11 for each minute of calls. plan B has no initial fee but costs $0.15 for each minute of calls.
Answer: 475 minutes.
Step-by-step explanation: To compare the cost of these two plans, you need to find how many minutes of calls are needed for the cost of each plan to be the same. Let's call this number of minutes x.
For plan A, the total cost will be $19 plus $0.11 for each minute of calls, or a total of 19 + 0.11x dollars.
For plan B, the total cost will be $0.15 for each minute of calls, or a total of 0.15x dollars.
Since the cost of the two plans is equal, we can set these expressions equal to each other and solve for x:
19 + 0.11x = 0.15x
Subtracting 0.11x from both sides, we get:
19 = 0.04x
Dividing both sides by 0.04, we get:
475 = x
Therefore, the number of minutes of calls needed for the cost of the two plans to be the same is 475 minutes.
Which data set could be represented by the box plot shown below?
A horizontal boxplot is plotted along a horizontal axis marked from 20 to 36, in increments of 1. A left whisker extends from 24 to 27. The box extends from 27 to 33 and is divided into 2 parts by a vertical line segment at 31. The right whisker extends from 33 to 34. All values estimated.
Choose 1 answer:
(Choice A)
A
24, 25, 29, 30, 31, 31, 32, 34, 34
(Choice B)
B
24, 27, 29, 30, 30, 31, 32, 34, 34
(Choice C)
C
24, 25, 29, 31, 31, 31, 32, 34, 35
(Choice D)
D
24, 25, 29, 30, 30, 31, 34, 34, 34
Answer:
A
Step-by-step explanation:
A box plot shows the five-number summary of a set of data.
Five-number summary:
Minimum value = The value at the end of the left whisker.Lower quartile (Q₁) = The left side of the box.Median (Q₂) = The vertical line inside the box.Upper quartile (Q₃) = The right side of the boxMaximum = The value at the end of the right whisker.Therefore, from inspection of the given box plot:
Minimum value = 24Lower quartile (Q₁) = 27Median (Q₂) = 31Upper quartile (Q₃) = 33Maximum = 34The median of a set of data is the middle value when all data values are placed in order of size.
Therefore, the only answer option that has a maximum value of 34 and a median of 31 is answer option A.
What is the remainder when 3x^3-5x^2-23x+24 is divided by x-3?
The remainder you got when 3x³ - 5x² - 23x + 24 is divided by x - 3 is -9.
What is Polynomials?Polynomials are expressions in algebra which consist of both variables and coefficients. Sometimes, variables are also known as indeterminates. Polynomials are classified as monomials, binomials, and trinomials based on the degree of the variables in the expression.
Variables in the monomials, binomials and trinomials have the highest degree equals 1, 2 and 3 respectively.
By doing the long division method, we will bet the quotient as 3x² + 4x - 11 and the remainder equals -9.
Let's check this using division algorithm.
Dividend = 3x³ - 5x² - 23x + 24
Divisor = x - 3
Quotient = 3x² + 4x - 11
Remainder = -9
By division algorithm,
Dividend = (Divisor × Quotient) + Remainder
3x³ - 5x² - 23x + 24 = [(x - 3) (3x² + 4x - 11)] + -9
= [3x³ + 4x² - 11x - 9x² - 12x + 33] + -9
= 3x³ + 4x² - 9x² - 11x - 12x + 33 - 9
= 3x³ - 5x² - 23x + 24
Hence -9 is the remainder of this division process.
To learn more about Polynomials, click on the link given below:
https://brainly.com/question/11536910
#SPJ1
(2k^3)^2
answer should contain only positive exponents
bro i need help so bad
its congruent angles and whatever
GEOMETRY 50 POINTSS
Answer:
x = 20°y = 70°Step-by-step explanation:
How many four-digit odd numbers less than 5000 can be formed using the digits 2, 3, 4, 5, 6, and 9?
Answer: 6.
Step-by-step explanation: We can solve this problem by using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, n is the number of choices (the digits 2, 3, 4, 5, 6, and 9) and r is the number of items in each combination (4 digits).
Plugging in the values, we get:
C(6, 4) = 6! / (4! * 2!) = (6 * 5 * 4 * 3) / (4 * 3 * 2) = 30
Therefore, there are 30 four-digit odd numbers that can be formed using the digits 2, 3, 4, 5, 6, and 9. However, not all of these numbers will be less than 5000, so we need to further filter the list to only include those that meet this requirement.
The four-digit odd numbers that can be formed using these digits are:
2359, 2395, 2539, 2593, 2935, 2953, 3259, 3295, 3529, 3592,
3925, 3952, 5239, 5293, 5329, 5392, 5923, 5932, 9235, 9253,
9352, 9523, 9532
Out of these numbers, only 2359, 2539, 2935, 3925, 5239, and 9523 are less than 5000. Therefore, there are 6 four-digit odd numbers less than 5000 that can be formed using the digits 2, 3, 4, 5, 6, and 9.
Therefore, the final answer is 6.
what is the simplified form of 89 ∛9
The expression given as 89 ∛9 cannot be further simplified
How to determine the simplified form of the expression?From the question, we have the following parameters that can be used in our computation:
89 ∛9
The above expression is a radical expression
And the radicand is ∛9
The radicand ∛9 implies that the cube root of 9
The cube root of 9 is a decimal number
So, it is better to leave the expression without changing its form
Hence. 89 ∛9 cannot be further simplified
Read more about expressions at
https://brainly.com/question/15775046
#SPJ1
Kara has five exam scores of 89, 82, 69, 79, and 70 in her biology class. What score does she need on the final exam to have a mean grade of 80? Round your answer to two decimal places, if necessary. (All exams have a maximum of 100 points.
Answer:
91
Step-by-step explanation:
[tex]\frac{89+82+69+79+70+x}{6}[/tex] = 80 Combine like terms
[tex]\frac{389+ x}{6}[/tex] = 80 Multiple by sides by 6
380 + x = 480 Subtract 389 from both sides.
x = 91
Suppose the scores x on a college entrance examination are normally distributed with a mean of 550 and a
standard deviation of 100. A certain prestigious university will consider for admission only those applicants
whose scores exceed the 90ℎ percentile of the distribution. Find the minimum score an applicant must
achieve to receive consideration for admission to the university.
Application acceptance requires a minimum score of 392, which is required.
How to calculated the minimal score for admission?Make "x" the required minimum score.
Given:
The average score is 500.
Standard deviation () is equal to 100
Admission percentage, P > 86 percent, or 0.86
Thus, the area under the normal distribution curve to the right of the z-score, which is 86%, is provided.
The portion of the score left over is displayed in the z-score table. As a result, we will calculate the z-score value for area as 100 - 86 = 14% or 0.14.
The z-score is therefore equal to -1.08 for value of 0.1401.
P(x>x0) = P(z > -1.08)
= -1.08 = x0 - 500 /100
x0 - 500 = -1.08 × 100
x0 = -1.08 + 500 = 392.
As a result, 392 is the minimal score needed for admission.
To Learn more About minimal score, refer To:
https://brainly.com/question/11014015
#SPJ1
which is faster
A. 4 miles in 1/3 hour
B. 1.3 mile in 4hours
C. 1/2 mile in hours
The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
4 miles in 1/3 hour ⇒ 4 x3/1 = 21 miles/hour
1.3 miles in 4 hours ⇒ 1.4/4 mile/hour
1/2 mile in hours ⇒ 0.5 miles/hour
Hence "The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster".
To learn more about the rate of change here,
brainly.com/question/12786410
#SPJ1
Find dy, dx if f(x) = (x + 1)2x.
Options:
A. 2xln(x + 1)
B. 2 times the natural log of the quantity x plus 1 plus 2 times x divided by the quantity x plus 1
C. 2x(x + 1)(2x - 1)
D. the product of the quantity 2 times the natural log of the quantity x plus 1 plus 2 times x divided by the quantity x plus 1, and the quantity x plus 1 raised to the 2x power
Answer:
D, I've taken the test already!
Step-by-step explanation:
there
7/9 - 1/4 please please please please
Answer: 19/36
Step-by-step explanation:
First the LCM (Least Common Denominater) must be found, the LCM of 9 and 4 is 36
Since 9 x 4 is 36, the numerator and denominator of 7/9 will be multiplied by 4 making it 28/36
Since 4 x 9 equals 36, the numerator and denominator of 1/4 will be multiplied by 4 making it 9/36
Now that they have common denominators the numerators can be subtracted from each other as well as the denominators
28/36 - 9/36 = 19/36
19/36 cannot be simplified therefore 7/9 - 1/4 = 19/36
Identify the quadratic function that is in standard form and has zeros -11 and 6. f(x) = x² + 5x + 66
f(x) = x² - 5x + 66
f(x)= x2 + 5x - 66
F(x)=x2-5x - 66
The standard quadratic equation is (c) y = x² + 5x - 66
How to determine the quadratic equation?From the question, we have the following parameters that can be used in our computation:
Zeros -11 and 6
This means that
x = -11 and x = 6
The quadratic equation can then be calculated as
y = (x - 6) * (x + 11)
Evaluate the products
y = x² - 6x + 11x - 66
Evaluae the like terms
y = x² + 5x - 66
Hence, the equation is y = x² + 5x - 66
Read more about quadratic equation at
https://brainly.com/question/1214333
#SPJ1