80 five-card hands (drawn from a standard deck) contain exactly two aces
What is permutation and combination ?Permutations and combinations are ways of representing groups of objects by selecting them and subsetting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.
CalculationIt's always helpful to try to visualize the problem and how to approach it.
Think of the card arrangements as an array of length 5 named A.
Lets get the total number of ways that 2 slots of the 5 can be selected (Number of possible arrangements of 2 elements in an array of size 5) in A. That's a simple combination. That is:
(5/2)
Now lets get the total number of ways the available Aces can be arranged at those 2 selected slots in A.
(4/2)
Multiplying both combinations given above gives us the number of ways 2 cards of a set of 4 cards can be placed at 5 slots:
(5/2)(4/2)
NOTE: This is not the numbers of 5-card hands that has exactly 2 Aces. This is the total number of arrangements of 2 Aces of the 4 in A.
We have yet to compute the number of arrangements of the remaining cards. We took out 4 cards (The Aces) of the 52 card deck so that leaves us with 48 remaining cards to be arranged at A and took 2 slots from A. So that gives us:
(48/3)
So the answer is:
(5/2)(4/2)(48/3) = 80 five-card hands (drawn from a standard deck) contain exactly two aces
learn more about permutation and combination here :
brainly.com/question/28720645
#SPJ4
Find the coordinates of triangle PQR with vertices P(-3, -2), Q(-1, 4), and R(2, -2) under the translation
(x,y) → (x+2y-4)
a. P'(-1, 2), Q'(1,8), R(4, 2)
b. P'(-5, -6), Q'(-3, 0), R(-4, -6)
c. P'(-1, -6), Q'(1, 0), R(4, -6)
d. P'(-5, 2), Q'(-3, 8), R(-4, 2)
The coordinates of triangle PQR under the translation (x,y) → (x+2,y-4) are P'(-1,-6), Q'(1,0), R'(4,-6).
Translation of coordinates is done by adding the horizontal translation at each vertex of the triangle. It is the process of shifting the location of the figure without changing the size and dimensions of the figure.
The coordinates of the triangle PQR are given as P(-3,-2), Q(-1,4), R(2,-2). The property under translation is given as (x,y) → (x+2,y-4). Now, let us apply this for all vertices.
P(-3,-2) → P'(-3+2,-2-4) → P'(-1,-6)
Q(-1,4) → Q'(-1+2,4-4) → Q'(1,0)
R(2,-2) → R'(2+2,-2-4) → R'(4,-6)
Thus, the vertices after translation are P'(-1,-6), Q'(1,0), R'(4,-6).
To know more about the translation:
https://brainly.com/question/8973543
#SPJ1
Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5 Ann paid a total of $49.10.
Write an equation to determine the distance in miles (x)(x)left parenthesis, x, right parenthesis between the airport and Ann's home.
Ella is working two summer jobs, making $22 per hour tutoring and making
$10 per hour clearing tables. In a given week, she can work a maximum of 9
total hours and must earn at least $130. If x represents the number of hours
tutoring and y represents the number of hours clearing tables, write and solve
a system of inequalities graphically and determine one possible solution.
The system of inequalities and a possible solution is by working 2 hours removing wires and 6 hours tutoring.
What is Inequalities?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
Here are the variables defined:
x is the quantity of tutoring hours worked.
Y = quantity of h
clearing cables is our job.
Since we know she can only work a maximum of 9 hours per week:
x + y ≤ 9
She also wants to earn at least $130 each week, so:
x*$22 + y*$10 ≥ $130
As a result, we have the inequality system listed below:
x + y ≤ 9
x*$22 + y*$10 ≥ $130
The graph of this system can be shown in the graphic below, where the intersection of the two shaded regions shows where the system's solutions are.
There are some solutions there, including:
y = 0, x = 8
y = 2, x = 6.
As a result, her situation might be resolved by working 2 hours removing wires and 6 hours tutoring.
To learn more about Inequalities click on the link
https://brainly.com/question/24372553
#SPJ13
[Will give Brainliest!]
Answer Needed ASAP!!
Write the Polynomial expression for the area of the shaded region of the figure
Answer:
4x^2+6x-49
Step-by-step explanation:
(3x-8)(2x+13)-(X+11)(2x-5)
(6x^2+39x-16x-104)-(2x^2-5x+22x-55)
(6x^2+23x-104)-2x^2-17x+55
4x^2+6x-49
Hopes this helps please mark brainliest
Identify the slope and y-intercept of the line with the given equation.
*do not enter the y-intercept as an ordered pair
m =
b=
y=-3x+8
Answer:
m = -3
b = 8
Step-by-step explanation:
y = -3x + 8 is in slope-intercept form, which is:
y = mx + b
so the slope is the m, the number right there beside the x. In your equation its -3. The b is the y-intercept, so its the last number tacked on the end of the equation there on the right. For your question, its the 8.
Slope is -3 and y-intercept is 8.
please help with this qn asap!! tyy!!
Answer:
i) AC = 6 - √3 cmii) BC² = 37 - 12√3 cm²----------------------
Given triangle withArea of 1/4(12 + 9√3),Side AB = √3 + 2,Angle BAC is 60°.Part iFind the side AC.
Use area formula:
A = ab sin∠C / 2, where a, b are adjacent sides and C is angle between a and b.Substitute and solve for AC:
1/4(12 + 9√3) = (√3 + 2) AC sin(60°) / 21/4(12 + 9√3) = AC (√3 + 2) (√3/2) / 2(12 + 9√3)/4 = AC √3(√3 + 2)/412 + 9√3 = AC√3(√3 + 2)AC = (12 + 9√3) /√3(√3 + 2)AC = (4√3 + 9) / (√3 + 2)AC = (4√3 + 9)(√3 - 2) / (√3 + 2)(√3 - 2)AC = (4√3√3 + 9√3 - 8√3 - 18) / (3 - 4) AC = (4*3 + √3 - 18) / ( - 1)AC = - (√3 - 6)AC = 6 - √3Part iiUse the law of cosines
BC² = AB² + AC² - 2 × AB × AC × cos ∠ABC² = (√3 + 2)² + (6 - √3)² - 2(√3 + 2)(6 - √3) cos 60°BC² = 3 + 4 + 4√3 + 36 + 3 - 12√3 - 2(6√3 - 3 + 12 - 2√3) / 2 BC² = 46 - 8√3 - (4√3 + 9)BC² = 46 - 8√3 - 4√3 - 9BC² = 37 - 12√3Answer:
[tex]\textsf{(i)} \quad \left(6-\sqrt{3} \right)\; \sf cm[/tex]
[tex]\textsf{(ii)} \quad \left(37-12\sqrt{3}\right)\; \sf cm^2[/tex]
Step-by-step explanation:
Part (i)[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}[/tex]
Given:
[tex]\textsf{Area}=\dfrac{1}{4}(12+9\sqrt{3})[/tex][tex]a=(\sqrt{3}+2)[/tex][tex]C=60^{\circ}[/tex]Substitute the given values into the formula to find AC (side b).
[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{2}ab \sin C\\\\\implies \dfrac{1}{4}(12+9\sqrt{3})&=\dfrac{1}{2}(\sqrt{3}+2)b \sin 60^{\circ}\\\\\dfrac{1}{4}(12+9\sqrt{3})&=\dfrac{1}{2}(\sqrt{3}+2) \dfrac{\sqrt{3}}{2}b\\\\\dfrac{1}{4}(12+9\sqrt{3})&=\dfrac{\sqrt{3}}{4}(\sqrt{3}+2)b\\\\12+9\sqrt{3}&=\sqrt{3}(\sqrt{3}+2)b\\\\12+9\sqrt{3}&=(3+2\sqrt{3})b\\\\b&=\dfrac{12+9\sqrt{3}}{3+2\sqrt{3}}\\\\b&=\dfrac{12+9\sqrt{3}}{3+2\sqrt{3}}\cdot \dfrac{3-2\sqrt{3}}{3-2\sqrt{3}}\end{aligned}[/tex]
[tex]\begin{aligned}b&=\dfrac{36-24\sqrt{3}+27\sqrt{3}-54}{9-6\sqrt{3}+6\sqrt{3}-12}\\\\b&=\dfrac{-18+3\sqrt{3}}{-3}\\\\b&=6-\sqrt{3}\end{aligned}[/tex]
Therefore, the length of AC is (6 - √3) cm.
Part (ii)[tex]\boxed{\begin{minipage}{6 cm}\underline{Cosine Rule} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
Given:
[tex]c = BC[/tex][tex]a = AB=(\sqrt{3}+2)[/tex][tex]b = AC=(6-\sqrt{3})[/tex][tex]C = \angle BAC=60^{\circ}[/tex]Substitute the given values into the formula to find BC²:
[tex]\begin{aligned}c^2&=a^2+b^2-2ab \cos C\\\\\implies BC^2&=AB^2+AC^2-2(AB)(AC) \cos C\\\\BC^2&=(\sqrt{3}+2)^2+(6-\sqrt{3})^2-2(\sqrt{3}+2)(6-\sqrt{3}) \cos 60^{\circ}\\\\BC^2&=7+4\sqrt{3}+39-12\sqrt{3}-2(9+4\sqrt{3}) \cdot \dfrac{1}{2}\\\\BC^2&=7+4\sqrt{3}+39-12\sqrt{3}-9-4\sqrt{3} \\\\BC^2&=37-12\sqrt{3}\end{aligned}[/tex]
Therefore, BC² is (37 - 12√3) cm².
Victoria needs an average of 90% to get an "a" in science class. so far her scores are 88. 86, and 92. what is the lowest score she can get to receive an "a" in science?
By solving a linear inequation, it is obtained that
Victoria should get a minimum marks of 94 to get 'a' in science
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, [tex]\geq[/tex], [tex]\leq[/tex]
A one degree inequation is known as linear inequation.
Here, an inequation needs to be solved
Suppose the full marks of Victoria in each subject is 100
Marks obtained by Victoria in Science = 88, 86, 92
Let the fourth marks be x,
Average marks = [tex]\frac{88 + 86 + 92 + x}{4}[/tex]
= [tex]\frac{266 +x}{4}[/tex]
By the Problem,
[tex]\frac{266 + x}{4} \geq 90\\266 +x \geq 90\times 4\\266 +x \geq 360\\x \geq 360-266\\x\geq 94[/tex]
Victoria should get a minimum marks of 94 to get 'a' in science
To learn more about linear inequation, refer to the link-
https://brainly.com/question/24372553
#SPJ4
I, III, and IV
I, II, and III
I and IV
All four quadrants
The location of the solutions of the inequality are quadrant in I, III, and IV
What is an inequality?An inequality is a non-equal comparison between quantities, variables or mathematical expressions.
The specified inequality is; [tex]y \leq\dfrac{2}{3} \cdot x-4[/tex]
The line of the inequality is a straight line that has a positive slope.
The y-intercept is at (0, -4)
The x-intercept is found as follows;
[tex]y=\dfrac{2}{3} \cdot x-4[/tex]
[tex]0 =\dfrac{2}{3} \cdot x-4[/tex]
[tex]4 =\dfrac{2}{3} \cdot x[/tex]
x = 6
The x-intercept = (0, 6)
The graph therefore from quadrant III enters quadrant IV at (0, -4), then enters into quadrant I at the x-intercept (0, 6)
The solution of the inequality, found by the coordinates of the intercepts and the path through of the line of the inequality are in I, III, and IV
Learn more about inequalities here:
https://brainly.com/question/22976364
#SPJ1
What is the diameter of a sphere with a volume of 78006\text{ in}^3,78006 in 3 , to the nearest tenth of an inch?.
The diameter of the sphere is 53.01 inches.
What is volume of sphere?
The volume of sphere is the amount of space occupied, within the sphere. The sphere is defined as the three-dimensional round solid figure in which every point on its surface is equidistant from its centre. The fixed distance is called the radius of the sphere and the fixed point is called the centre of the sphere.
Given, volume of the sphere = 4/3πr^3
Where r is the radius of the sphere.
Therefore,
( 4/3 ) πr³ = 78006 inch³
πr³ = 78006
r³ = 18622.56 inch³
r = 26.506
We know diameter = 2r
d = 53.01 inches.
To know more about volume of the sphere, visit:
https://brainly.com/question/21399448
#SPJ4
Determine whether each pair of triangles is congruent. If yes, include the theorem that applies.
Answer:
The triangles are congruent.
Step-by-step explanation:
The pair of triangles shown on the image are congruent triangles by ASA postulate.
ASA postulate is the postulate where two triangles are congruent by two Angles and a Side length.
The two triangles are congruent by RHS congruency property.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given are two right-angle triangles.
Also given the height of both the triangles are similar and the two angles are also congruent therefore sides opposite to the similar angles are also similar hence these two right-angled triangles are congruent
learn more about congruency here :
https://brainly.com/question/7888063
#SPJ1
a slice of cake is 20m due east and 10m due south. Another cake slice is 15m due west and 15m due north. Which slice is closer
The cake slice with 15m due west and 15m due north is closer
What is distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.Distance is how far apart objects are.Here , the slice of cake is 20m due east and then 10 m due south.
consider it as triangle ABC.
Required Displacement can be calculated by Pythagoras theorem -
AC = √ ( AB )² + ( BC )²
By substitution,
⇒ AC = √ ( 20 )² + ( 10 )²
⇒ AC = √ ( 400 + 100 )
Simplifying this equation, we get
⇒ AC = √500
⇒ AC = 10 √5
⇒ AC = 22.56
Thus , The cake slice is 22.56 m far away.
Here another slice of cake is 15m due west and 15m due north.
consider it as a triangle DEF.
Therefore,
⇒ DF = √ ( DE )² + ( EF )²
By substitution,
⇒ DF = √ ( 15 )² + ( 15 )²
Simplifying this equation, we get
⇒ DF = √ ( 225 + 225 )
⇒ DF = √ 450
⇒ DF = 15 √2
⇒ DF = 21.21
Thus the cake slice is 21.21 m far away.
Therefore this slice is closer.
To learn more about distance refer to;
https://brainly.com/question/26046491
#SPJ1
Solve for X
HELPPPPPPPPPPPPP
On saturdays, cars arrive at sami schmitt's scrub and shine car wash at the rate of 6 cars per fifteen minute interval. Using the poisson distribution, the probability that five cars will arrive during the next five minute interval is.
The probability that five cars will arrive during the next thirty minute interval is 0.0361
What is probability?
Probability is a way of calculating how likely something is to happen. Numerous things are difficult to forecast with absolute confidence.
Main Body:
Let X = number of cars arriving at Sami Schmitt's Scrub and Shine Car Wash.
The average number of cars arriving in 15 minutes is 6.
The average number of cars arriving in 1 minute is = 6/15 = 2/5
The average number of cars arriving in 5 minutes is, (2/5)*5 = 2
The random variable X follows a Poisson distribution with parameter λ = 2.
The probability mass function of X is:
P(X=[tex]x[/tex]) = [tex](e^{-2} 2^{x} )/x![/tex] , x = 0,1 ,2 ,3...
Compute the probability that 5 cars will arrive in 5 minutes as follows:
P(X=5) =[tex](e^{-2} 2^{5} )/5![/tex]
P (X= 5) = 0.0361
Hence probability is 0.0361
to learn more about probability , visit;
https://brainly.com/question/24756209
#SPJ4
Robert cuts a string that's 4 feet long into pieces that are each 2/6 foot long
Answer:
12 pieces
Step-by-step explanation:
Number of pieces Robert cuts
= 4 feet ÷ [tex]\frac{2}{6}[/tex] feet
= 12 pieces
a private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. how large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%?
By using the concept of confidence interval, it is obtained that the sample needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4% = 601
What is confidence interval?
Let the quantity which is to be estimated is [tex]\theta[/tex] . A confidence interval for the parameter θ, with confidence level is the interval (a, b), where
P(a < [tex]\theta[/tex] < b) = , P is the probability
Here,
the formula for sample size n = [tex]\frac{p(1-p)z^2}{e^2}[/tex]
p is the sample proportion,
z is the z score associated with the level of confidence
e is the margin of error
Now,
e = 0.04
p = [tex]\frac{1}{2}[/tex]
z = 1.96
n = [tex]\frac{0.5(1-0.5) \times 1.96^2}{0.04^2}[/tex]
n = 600.25
Sample size needed = 601
To To learn more about confidence interval, refer to the link
brainly.com/question/15712887
#SPJ4
during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of five free software packages. there are 9 different software packages from which to select. how many different groups of software packages can be selected?
The required group of software packages that can be selected is 28.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Examples of permutation and combination, Organizing people, numbers, numerals, alphabets, notes, and colors are examples of permutations. Choosing of menu, foodstuffs, dresses, matters, and the group are examples of combinations.
CalculationHere,
Choice of six free software packages. there are 8 different software packages from which to select.
n = 8, r = 6
Groups of software packages can be selected= 8C6
8C6 = n!/r!(n - r)!
8C6 = 8! / 4! 2!
8C6 = 8 * 7 / 2 / 1
8C6 = 28
Thus, the required group of software packages that can be selected is 28.
Learn more about permutations and combinations here: brainly.com/question/2295036
#SPJ4
To estimate the product 8.42 x 7.24, Marisa multiplied 9 x 8 to get 72. Complete the explanation for how
she can make a closer estimate.
Part 1 out of 2
8.42 is closer to
Check
15
and 7.24 is closer to
Next
The actual value is 8.42 x 7.24 = 59.6576.
as an estimate she has rounded the values up to the nearest whole number ;
i.e. 8.42 ≅ 9 and 7.24 ≅ 8
to obtain 9 x 8 to get 72.
What is rounded value?
Making a number simpler while maintaining a value that is close to what it was is known as rounding.
Although less accurate, the outcome is simpler to utilize.
For instance, 73 equals 70 when rounded to the closest 10, since 70 is closer to 73 than 80 is. However, 76 rises to 80.
What is whole number?
Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.
What is natural number?
Natural Numbers The numbers that we use when we are counting or ordering {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …} Whole Numbers The numbers that include natural numbers and zero. Not a fraction or decimal.
Learn about rounded values click on the link:
https://brainly.com/question/28676349
#SPJ13
my homework is due tomorrw and i its 10:30 but i cant get this question
please help
Answer: w= -18
Step-by-step explanation:
1.) 3(6t2+5t+-4)
2.) 12(-2)power of 2+15(-2)-12
3.) 24-30-12
4.) -6-12
5.) -18
(04.04 MC)
What is the 8th partial sum of 10,000 -2,000+400-80+...? Round your answer to the thousandths place.
12,499.970
O9,999.974
8,333.333
8,333.312
Answer:
C
Step-by-step explanation:
Answer:
8,333.312
Step-by-step explanation:
I did the test...
a pic to help u is below
(1) The slope of the function is 11.99.
(2) The y-intercept of the function is 7.
(3) The slope indicates the per-month subscription fee.
(4) The y-intercept indicates the one-time subscription fee.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given equation is c(m) = 11.99m+7.
Note that the equation is written in slope-intercept form.
The slope of the function is 11.99.
The y-intercept of the function is 7.
The slope indicates the value of the change in c(m) when there is a unit change in m.
Therefore, the slope of 11.99 indicates the per-month subscription fee.
The y-intercept indicates the value of c(m) when m is zero, therefore, the y-intercept to 7 represents that the one-time subscription is 7.
Hence,
(1) The slope of the function is 11.99.
(2) The y-intercept of the function is 7.
(3) The slope indicates the per-month subscription fee.
(4) The y-intercept indicates the one-time subscription fee.
To learn more about the slope-intercept form of a line, click here:
https://brainly.com/question/9682526
#SPJ1
Which of the following are common multiples of 60 and 1120?
Select all of the correct answers.
2³×3×7
2²×3×5
27×3×5²×7
2²x5
25×3×5×7
2³×3×5²x7
25×3×5×7²
25x5x7
The common multiple of 60 and 1120 is 2³×3×7.
What is the least common multiple?
The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, denoted by lcm in arithmetic and number theory, is the smallest positive integer that is divisible by both a and b.
The least common multiple of 60 and 1120 is 3360.
2³×3×7 = 168
2²×3×5 = 60 -----(This is the common multiple)
27×3×5²×7 = 14175
2²x5 = 20
25×3×5×7 = 2625
2³×3×5²x7 = 4200
25×3×5×7² = 18375
25x5x7 = 875
Hence, the common multiple of 60 and 1120 is 2³×3×7.
To learn more about the common multiple visit:
https://brainly.com/question/16054958
#SPJ9
Your plan for your t-shirt business calls for you to be able to produce 60,000 screen printed shirts in a month. If each screen press can handle 500 shirts per day, about how many presses do you need?.
Answer:
120 presses
Step-by-step explanation:
hope this helps :)
Answer:120 presses
Step-by-step explanation:
Mike is a new photographer. In order for his work to get exposure, Mike has decided to have a booth at an arts festival. He is
charging $21.49 for his color prints and $29.84 for his black and white prints. Which is a reasonable amount that Mike would make if
he sold 7 color prints and 4 black and white prints?
OA. $561.00
OB. $267.00
OC. $357.00
OD. -$27.00
Answer: The reasonable amount that Mike would make if he sold 7 color prints and 4 black and white prints is OB 267 dollar
What do three-variable linear equations mean?
A linear equation in three variables is ax + by + cz = r if a, b, c, and r are real integers (and if a, b, and c are not all equal to 0).
How can a system of three linear equations be solved?
Choose two equation pairs from the system. Use the addition/subtraction method to remove the same variable from each pair. then use the Addition/Subtraction method to solve the system of the two newly discovered equations.
Assume there are "x" number of touchdowns, "y" extra-point kicks, and "z" number of field goals.
Step-by-step explanation:
Given that
For color print he charge x = 21.49 dollar
For black and white print he charge y = 29.84 dollar
Equation of his money
[tex]21.49(x)+29.84(y)=z[/tex]
Z is the money he earn
Now putting the value of x and y we get value of z
[tex]21.49(7)+29.84(4)=z\\z= 269.79[/tex]
Which is closest to 267 dollar
Hence the answer is Option B $267.00
Visit the following websites to learn more about the linear equations:
brainly.com/question/26150814
#SPJ13
What is the angle for a ratio of 1 2?.
The acute angles in a right triangle have measures of 30 degrees and 60 degrees if the ratio of these angles is 1:2.
How is a right triangle formed?The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle. There are a few unique varieties of right triangles, including the 45°-45° and the 30°-60° varieties.
The ratio of the angular dimensions of the acute angles of a right triangle is 1:2.
Consider x
Sum of three angles is 180 degrees.
Now,
180=90 + x + 2x
180 - 90=3x
3x = 90
x = 30
here, x and 2x, are two angles 30 and 60 degrees.
To know more about Right Angle visit:
https://brainly.com/question/4364353
#SPJ4
Chris has a cell phone plan with a flat fee of $26.00 per month, plus a cost of $0.12 per minute of usage. Chris can only afford a monthly bill of $86.00.
Which statement is true?
The consumption of minutes should be less than or equal to 500 for each month.
A linear equation is a first-order (linear) term and a constant in an algebraic equation of the form y=mx+b.
The telephone bill of Chris can be written in the form of linear equation.
C(x)=$26.00+$0.12x
Here x is the number of minutes, for every one minute there is a charge of $0.12.
Chris can afford monthly bill of $86 or less not more. The linear inequality can be written as,
$26.00+$0.12x<=$86
$0.12x<=$86-$26.00
$0.12x<=$60
x<=$60/$0.12
x<=500.
The number of minutes that Chris should use should be less than or equal tp 500.
To learn more on linear equation here:
https://brainly.com/question/13738061#
#SPJ9
30 points if you get this right
look at image below
The intervals where the graph is decreasing are given as follows:
-1 < x < 0.0 < x < 1.How to identify where the function is increasing and where it is decreasing?The behavior of the function regarding increase or decrease depends on the orientation of the graph, as follows:
Increasing function: moving along to the right on the graph, the line of the function is moving up.Decreasing function: moving along to the right on the graph, the line of the function is moving down.Hence the intervals describing the behavior of the function are given as follows:
Left of x = -1: increasing.Between x = -1 and x = 1: decreasing.Right of x = 1: increasing.The decreasing interval can be divided into two intervals, as follows:
-1 < x < 0.0 < x < 1.More can be learned about decreasing functions at https://brainly.com/question/1503051
#SPJ1
If you were given $1000.00 what would you do with it and why?
help me please!!!!!! im in rushhh
Answer: Help my parents pay
bills and buy myself some shoes
PLEASE ANSWER QUICK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which expression represents "2 less than the product of 5 and a number"?
Responses
5+n−2
5 plus n minus 2
5n−2
5 over n end fraction minus 2
2−5n
2 minus 5 n
5n−2
help meeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(a) in 2001: 150.4 thousand
(b) in 2018: 467.5 thousand
Step-by-step explanation:
You want the value of the expression modeling the number of students abroad for different values of x. That expression is 123.1(1.069^x).
(a) 2001The value of x is the difference between the year (2001) and the reference year (1998). In the attachment, we let the calculator find that difference. It tells us, for x = 2001 -1998 = 3, the number of students is about ...
y = 123.1(1.069^3) ≈ 150.4 . . . . thousand
(b) 2018In 2018, the value of x is 2008 -1998 = 10, and the number of students studying abroad is ...
y = 123.1(1.069^10) ≈ 467.4 . . . . thousand
Haley got a 93% on her first math test and an 86% on her second test. What is her percent decrease from test 1 to test 2 to the nearest tenth?.
Haley’s Percentage Decrease from Test 1 to Test 2 to the nearest tenth is 7.5%
Nearest tenth can be defined as , Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5
Given that,
Haley’s Percent score in Test 1 = 93 %
Haley’s Percent score in Test 2 = 86%
Formula For calculating the Percentage Decrease is :
(Beginning Percentage – Final Percentage) / Beginning Percentage * 100
So, by using this formula we can calculate the percentage decrease of Haley’s Test
Percentage Decrease = (93% - 86%)/93% * 100
= 7.5%
To know more about Percentage Decrease, Click here :
https://brainly.com/question/14808025
#SPJ4
