Answers
Answer:
10/13
Step-by-step explanation:
There are 52 cards in a standard deck. There are 4 queens (queen of spades, clubs, hearts, diamonds) and 36 (2 - 10 of four suites) number cards. Therefore the probability of drawing a queen or a number card is (4 + 36)/52 = 40/52 = 10/13.
Related Questions
How do you solve this?
Answers
Step-by-step explanation:
g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.
so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.
now, we look at the graphic.
for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.
but we are looking for a c that has only one solution (one value of x to create that result).
c = 1 ?
let's imagine a horizontal line through y = 1.
we see, it cuts the function also 3 times. 3 solutions.
c = -1 ?
a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions
but c = 3 !
a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !
and that is therefore our answer.
Oscar corporation is planning to construct an elliptical gate at its headquarters. the width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. the company wants to place two bright spots at the foci of the ellipse. how far from the center of the ellipse will the spots be located?
Answers
The distance from the center of the ellipse to where the spots are located will be 2 feet.
What is Distance?
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.The distance from the center of the ellipse to where the spots are located will be -
= 5 - 3
= 2 feet.
Therefore, the distance from the center of the ellipse is 2 feet.
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The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
Answers
The y-intercept of the linear equation that models the data indicates that:
There was 1 inch of water on the tub when the water was turned on.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, when x changes by 1, y changes by 2, hence the slope is of 2. Hence, since when x = 1, y = 3, when x = 0, y = 3 - 2 = 1, which means that the y-intercept is of 1, and the correct interpretation is:
There was 1 inch of water on the tub when the water was turned on.
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How does the mean absolute deviation (mad) of the data in set 1 compare to the mean absolute deviation of the data in set 2? set 1: 12, 8, 10, 50 set 2: 13, 9, 8 the mad of set 1 is 13 less than the mad of set 2. the mad of set 1 is 13 more than the mad of set 2. the mad of set 1 is 2 more than the mad of set 2. the mad of set 1 is 2 less than the mad of set 2.
Answers
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
How to estimate the Mean Absolute Deviation from the given data?Set 1: 12, 8, 10, 50
Set 2: 13, 9,8
To determine the mean for each set
Mean = totality of elements/number of elements
Mean of Set 1:
[tex]$=\frac{12+8+10+50}{4}[/tex]
[tex]$=\frac{80}{4}=20$[/tex]
Mean of Set 2:
[tex]$=\frac{13+9+8}{3}[/tex]
[tex]$=\frac{30}{3}=10$[/tex]
To determine the mean absolute deviation (MAD) of the data in each set.
M.A.D of Set 1:
[tex]$=\frac{|12-20|+|8-20|+|10-20|+|50-20|}{4}[/tex]
[tex]$=\frac{8+12+10+30}{4}=\frac{60}{4}=15$$[/tex]
M.A.D of Set 2:
[tex]$=\frac{|13-10|+|9-10|+|8-10|}{3}[/tex]
[tex]$=\frac{3+1+2}{3}=\frac{6}{3}=2$[/tex]
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
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pllllllllllllllllllllleasee one guys i neeed ur help one
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Calculate discriminant :
[tex]\qquad \sf \dashrightarrow \: 3 {x}^{2} + 6x - 1[/tex]
a = 3b = 6c = 1[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 36 - 12[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} [/tex]
Now, let's calculate it's roots ( x - intercepts )
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} [/tex]
So, the intercepts are :
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} [/tex]
and
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} [/tex]
Answer:
[tex]\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)[/tex]
Explanation:
Given expression:
f(x) = 3x² + 6x - 1
To find x intercepts, set f(x) = 0Use quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0[/tex]
Here after finding coefficients:
a = 3, b = 6, c = -1Applying formula:
[tex]x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}[/tex]
[tex]x = \dfrac{ -6 \pm \sqrt{48}}{6}[/tex]
[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{6}[/tex]
[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}[/tex]
[tex]x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}[/tex]
[tex]x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}[/tex]
Solve the equation the square root of the quantity x plus 4 minus 3 equals 1 for the variable.
Answers
Answer:
x = 12
Step-by-step explanation:
sqrt(x+4) - 3 = 1
First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.
sqrt(x+4) = 1 + 3
sqrt(x+4) = 4
To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.
(sqrt(x+4))^2 = 4^2
x + 4 = 16
subtract 4 to finish up.
x = 12
Check:
sqrt(12 + 4) - 3 = 1
sqrt16 - 3 = 1
4 - 3 = 1
1 = 1 Check!
Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
Prove: △HKJ ~ △LNP
Triangles H K J and L N P are shown. Triangle L N P is smaller and to the right of triangle H K J.
Statement Reason
1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given
2. m∠H + m∠J + m∠K = 180° 2. ?
3. 30° + 50° + m∠K = 180° 3. substitution property
4. 80° + m∠K = 180° 4. addition
5. m∠K = 100° 5. subtraction property of equality
6. m∠J = m∠P; m∠K = m∠N 6. substitution
7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent
8. △HKJ ~ △LNP 8. AA similarity theorem
Which reason is missing in step 2?
CPCTC
definition of supplementary angles
triangle parts relationship theorem
triangle angle sum theorem
Answers
Answer:
triangle angle sum theorem
Step-by-step explanation:
The missing statement is one that justifies the sum of the angles in a triangle being 180°.
That justification is provided by the ...
triangle angle sum theorem
Which of these expressions demonstrates the identity property? 25(0) = 25 25(1) = 25 25 + 0 = 25 25 + 1 = 25
Answers
The expressions which demonstrates the identity property of multiplication is; 25(1) = 25 option B
Identity Property
Identity Property of Multiplication states that any number multiplied by 1 does not change, that is, it is constant or remains the same
Check all options
25(0) = 25
0 = 25
Not true
25(1) = 25
25 = 25
True (identity property of multiplication holds)
25 + 0 = 25
25 = 25
True (Not identity property of multiplication)
25 + 1 = 25
26 = 25
Not true
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There are different types of correlation one can use based on the types of variables being examined. When conducting an analysis, when do you need to use spearman’s rho instead of pearson’s r ?.
Answers
The correct option is A.
When the data are nominal or ordinal.
What are the Types of correlation?There are three types of correlation:
1. Positive and negative correlation
2. Linear and non-linear correlation
3. Simple, multiple, and partial correlation
According to the information:There are different types of correlation one can use based on the types of variables being examined.
Spearman’s rho is a superb choice when you have nominal or ordinal data because Pearson’s isn't appropriate. Ordinal data have a minimum of three categories and the categories have a natural order. for instance , first, second, and third during a race are ordinal data.
Briefing:Two variables can have some quite relationship, i.e., change in one may cause a change within the other.
If a change within the value of one variable causes a simultaneous change in the other variable in the same or opposite direction, then it’s termed as correlation, or these variables are said to be correlated. Keeping these in mind the answer to this question is When the data are nominal or ordinal
When the data are nominal or ordinal.
So the option no A is correct.
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I understand that the question you are looking for is:
There are different types of correlation one can use based on the types of variables being examined. When conducting an analysis, when do you need to use spearman’s rho instead of Pearson's r ?
A. When the data are nominal or ordinal.
B. When the data are ratio or interval.
C. When the data are random.
D. Spearman's rho should never be used for correlations.
Find the distance in nm between two slits that produces the first minimum for 405-nm violet light at an angle of 57. 5°
Answers
The distance between two slits is d =2.89*10^-7 m
Distance between slits, d=2.89*10^-7 m
It is given that,
Wavelength, λ = 410nm= 410*10^-9 m
Angle, θ =45
We need to find the distance between two slits that produces first minimum. The equation for the destructive interference is given by :
dsinθ =(n+1/2) λ
For first minimum, n = 0
dsinθ =(1/2) λ
So, d is the distance between slits
d ={1/2 λ}sinθ
=2.89*10^-7 m
So, the distance between two slits is d =2.89*10^-7 m. Hence, this is the required solution.
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On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from the same corner post on the nearest adjacent side of the field. What is the distance from Sang to Jazmin?
A. 119
B. 101
C. 10,201
D. 1,980
Answers
The distance from Sang to Jazmin is 101 yards.
What is the distance from Sang to Jazmin?
From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.
The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.
From;
c^2 = a^2 + b^2
c = √a^2 + b^2
c = √(20)^2 + (99)^2
c = 101 yards.
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can someone help me with this?
Answers
Answer:
Step-by-step explanation:
Beatrice's conclusion is wrong
All of these points are not on the same line, because are different parallel lines
The slope between (-2,-1) and (1,0) is equal to 1/2
Answer:
Beatrice is incorrect. All of these points are not on the same line because the slope between (-2,-1) and (1,0) which are coordinates fr each of the pairs above, are equal to 1/2
Step-by-step explanation:
Let m1 be first slope
[tex]m1 \: = \frac{y2 - y1}{x2 - x1}= \frac{0 - ( - 2)}{4 - ( - 2)}= \frac{0 + 2}{4 + 2} \\ = \frac{2}{4} = \frac{1}{2} [/tex]
Let m2 be second slope
m2 = (y2 - y1)/ (x2 - x1)
= (2-(-1)) / (4-(-2)
= (2+1) / (4+2)
= 3/6 =1/2
Thus, the slopes are different parallel lines because m1 =m2
The table can be used to determine the solution to the system of equations, 2y − x = 8, and y − 2x = −5.
A table with 6 columns and 2 rows. The first column, Original System has 2 y minus x equals 8 and y minus 2 x equals negative 5. The second column, Equivalent System, has 2 y minus x equals 8 and negative y plus 4 x equals 10. The third column, Sum of equations in Equivalent System, has 3 x equals 18. The fourth column, Solution to System, is blank. The fifth column, New System Using Sum, has2 y minus x equals 8 and 3 x equals 18. The sixth column, Solution to New System is blank.
Which solution can be used to fill in both blanks in the table?
Answers
The solution to the system and the solution that fills the blank space is (6, 1)
System of equationsThis are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions
Given the following system of equations
2y − x = 8, and
y − 2x = −5.
From equation 2;
y = -5 + 2x ............. 3
Substitute equation 2 into equation 1 to have:
2(-5+2x) - x = 8
Expand to have:
-10 +4x -x = 8
-10 + 3x = 8
3x = 8 + 10
3x = 18
Divide both sides
by 3
3x/3 = 18/3
x = 6
Substitute x = 6 into equation 3
y = -5 + 2x
y = -5 + 2(3)
y = -5 + 6
y = 1
Hence the solution to the system and the solution that fills the blank space is (6, 1)
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Answer:
Its D (6,7)
Step-by-step explanation:
Brass is an alloy made by melting and mixing copper and zinc. A metallurgist has two brass
alloys, one that is 65% copper and one that is 90% copper. He would like to combine a
portion of each alloy to produce 500 g of a new alloy that is 75% copper.
Write a system of equations for this problem
Answers
Answer:
x +y = 5000.65x +0.95y = 0.75(500)solution: (x, y) = (300, 200)Step-by-step explanation:
A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.
SetupLet x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.
x + y = 500 . . . . . . quantity of new alloy needed
0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy
These are the desired system of equations.
SolutionThis problem does not ask for the solution, but it is easily found using substitution for x.
x = 500 -y
0.65(500 -y) +0.90y = 0.75(500)
(0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)
y = 500(0.10/0.25) = 200
x = 500 -200 = 300
300 grams of 65% copper and 200 grams of 90% copper are needed.
Consider the expressions shown below.
A. -8x^2 - 3x + 4
B. 8x^2 - 3x + 8
C. 8x^2 + 3x - 4
Complete each of the following statements with the letter that represents the expression.
(3x^2 - 7x + 14) + (5x^2 + 4x - 6) is equivalent to expression
(2x^2 - 5x - 3) + (-10x^2 + 2x + 7) is equivalent to expression
(12x^2 - 2x - 13) + (-4x^2 + 5x +9) is equivalent to expression
Answers
(3x² - 7x + 14) + (5x² + 4x - 6)
Match 3x² and 5x² to get 8x².
8x² - 7x + 14 + 4x - 6Combine −7x and 4x to get −3x.
8x² −3x + 14 − 6Subtract 6 from 14 to get 8.
8x² - 3x + 8Therefore, the expression (3x² - 7x + 14) + (5x² + 4x - 6), is equivalent to the expression "B".
===> Exercise 2
(2x² - 5x -3) + (-10x² + 2x + 7)
Combine 2x² and -10x² to get −8x².
−8x² −5x − 3 + 2x + 7Combine −5x and 2x to get −3x.
-8x² − 3x − 3 + 7Add −3 and 7 to get 4.
-8x² - 3x + 4Therefore, the expression (2x² - 5x -3) + (-10x² + 2x + 7), is equivalent to the expression "A".
===> Exercise 3
(12x² - 2x - 13) + (-4x² + 5x +9)
Combine 12x² and -4x² to get 8x².
8x² − 2x −13 + 5x + 9Combine −2x and 5x to get 3x.
8x² + 3x − 13 + 9Add −13 and 9 to get −4.
8x² + 3x - 4Therefore, the expression (12x² - 2x - 13) + (-4x² + 5x +9), is equivalent to the expression "C".
Solve for d.
5+d > 5−d
Answers
Answer:
d>0
Step by Step Explanation:
Let's solve your inequality step-by-step.
5+d>5−d
Step 1: Simplify both sides of the inequality.
d+5>−d+5
Step 2: Add d to both sides.
d+5+d>−d+5+d
2d+5>5
Step 3: Subtract 5 from both sides.
2d+5−5>5−5
2d>0
Step 4: Divide both sides by 2.
2d/2>0/2
d>0
Answer:
3
Step-by-step explanation:
You could put 3 because 5+3 is greater than 5-3.
Which is a recursive formula for the sequence 99.4, 0, –99.4, –198.8, where f(1) = 99.4? f(n 1) = f(n) 99.4, n ≥ 1 f(n 1) = f(n) – 99.4, n ≥ 1 f(n 1) = 99.4f(n), n ≥ 1 f(n 1) = –99.4f(n), n ≥ 1
Answers
The recursive formula for the given sequence is [tex]f(n+1)=f(n)-99.4[/tex]
What is recursive formula?Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula [tex]a_n = a_{n-1} + d[/tex]. [tex]a_n = a_{n-1}r[/tex] is the recursive formula for a geometric sequence.
We are given a sequence as:
99.4,0,-99.4,-198.8, and so on
We can see that the sequence is constantly getting decreased by -99.4
i.e. f(1)=99.4
Then, f(2)=f(1)-99.4
=99.4-99.4
=0
f(3)=f(2)-99.4
=0-99.4
=-99.4
Therefore, the recursive formula of the given series is [tex]f(n+1)=f(n)-99.4[/tex]
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Which of the following scatter plots does not have a zero correlation?
Answers
The first scatter plot does not have a zero correlation.
Option(a) is correct.
A statistic called correlation gauges how much two variables change in connection to one another.
Correlation quantifies correlation but cannot determine whether x causes y or vice versa, or whether a third component is responsible for the association.
A scatterplot may make it easier to spot correlation, particularly when the variables have a non-linear but nevertheless significant association.
Zero means there is no correlation between the two variables under comparison.
A 0 correlation indicates that there is no relationship between the two variables according to the correlation statistic. This merely indicates that there isn't a linear relationship, not that there isn't any link at all. The first scatter plot does not represent a linear relationship, thus, it has zero correlation.
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A locker combination consists of two non-zero digits. the digits in a combination are not repeated and range from 2 through 9. event a = the first digit is less than 5 event b = the second digit is less than 5 if a combination is picked at random, with each possible locker combination being equally likely, what is p(b|a) expressed in simplest form?
Answers
Answer:
1/3.
Step-by-step explanation:
P(event a occurs) = 3/9 = 1/3
P(event b occurs) = 3/9 = 1/3
P(a) ∩ P(b) = 1/3 * 1/3 = 1/9
P(b|a) = P(a) ∩ P(b) / P(a)
= 1/9 / 1/3
= 1/3.
math help pleasee!!!!
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Since this is an algebraic problem
⇒let's solve it like one
[tex]2*3^{x+5} < 14\\3^{x+5} < 7\\ x+5 < log_37\\x < -5 + log_37\\x < -3.2288[/tex]
Answer: x < -3.2288
Hope that helps!
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Write the equation of straight line passing through (3,4). Does the point (4,3) lie on
your line
Answers
Answer:
Is there more information? There is not enough to find the slope of a line. I'll answer with an equation that works, but I suspect it won't be correct.
Step-by-step explanation:
If the only requirement is to have a line that goes through (4,3). Then one could simply say:
y = 4
This is a horizonal line that goes through (3,4), and will always produce a y value of 4 regardless of x. No, it will not pass through (4,3) since y is aleways 4, regardless of x.
If you wanted to get fancier, we could write a needlessly more complex equation:
y = (4/3)x
When x = 3, y = 4, so (3,4) is on this line. But (4,3) is not. y = (4/3)(4) means y = (16/3), not 4.
Geometry: Use this illustration to calculate these values, ASAP!!!
Answers
Applying the same-side interior angles theorem,
7. m∠4 = 50°; m∠5 = 130°
8. m∠2 = 15°; m∠8 = 15°.
What is the Same-Side Interior Angles Theorem?The same-side interior angles theorem holds that, two interior angles on a side of a transversal are supplementary, that is they add up to 180 degrees.
What is the Alternate Exterior Angles Theorem?According to the alternate exterior angles theorem, exterior angles that alternate each other along a transversal are congruent, that is they have equal measures.
7. m∠4 + m∠5 = 180 [same-side interior angles theorem]
Substitute
y + 2y + 30 = 180
3y + 30 = 180
3y = 180 - 30
3y = 150
y = 50
m∠4 = y = 50°
m∠5 = 2y + 30 = 2(50) + 30
m∠5 = 130°
8. m∠2 = m∠8 [alternate exterior angles theorem]
Substitute
x - 30 = 3x - 120
x - 3x = 30 - 120
-2x = -90
x = 45
m∠2 = x - 30 = 45 - 30 = 15°
m∠8 = 3x - 120 = 3(45) - 120 = 15°
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[tex]\frac{12}{20} =_____% = _____ hundredths
Answers
The percentage form of given fraction is 60% and the hundredths form is 0.60
According to the statement
we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.
So, For this purpose,
The given fraction is 12/20.
Then the definition of the percentage is that
The Percentage, a relative value indicating hundredth parts of any quantity.
so, the percentage of given fraction is :
Percentage fraction = 12/20 * 100
After solving it, The percentage fraction will become:
Percentage fraction = 60%
and Now convert into the hundredths form then
In the hundredths form it will become
from 60% to 0.60.
So, The percentage form of given fraction is 60% and the hundredths form is 0.60
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Russ is solving an equation where both sides are linear expressions. he sets the expressions equal to y and graphs the system finding that they are the same line. how should russ interpret this outcome?
Answers
The correct option (D).
There are infinitely many intersection points.
What is liner equation?a two-variable equation that, when plotted on a graph, results in a straight line.
What does intersection point mean?The term "point of intersection" refers to the intersection of two lines.
According to the given information:Russ is attempting to solve an equation whose two sides are both linear expressions.
He graphs the system and finds that they are on the same line after setting the expressions to y.
Since both lines are the same, there are an endless number of junction places.
Russ should therefore consider the outcome to be option (D) There are a limitless number of intersections.
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I understand that the question you are looking for is:
Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome? There are no intersection points. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points.Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?
A. There are no intersection points.
B. There is exactly one intersection point.
C. There are exactly two intersection points.
D. There are infinitely many intersection points
In triangle r s t, angle r = 63 degrees, angle t = 90 degrees, side r s = 23 and side s t = 10.4. which ratios are correct?
Answers
The correct ratios are: cos 27=23/RT, sec 27= 23/10.4 and cot 63 = RT/10.4
What is trigonometry ratio in tringle?
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.In triangle RST, angle T= 90° and angle R= 63°
As the total of all angle in any triangle is 180°, so the measure of the angle S = 180°- (90°+63°)
S= 180°- 153°
S= 27°
According to the rule of trigonometric ratios,
cos(θ) = [tex]\frac{hypotenuse}{opposite}[/tex]
sec(θ) = [tex]\frac{hypotenuse}{adjacent}[/tex]
cot(θ) = [tex]\frac{adjacent}{opposite}[/tex]
In respect of angle R (63°), side RS(23) is hypotenuse , ST(10.4) is opposite and RT is adjacent.
cos(63°) = [tex]\frac{23}{10.4}[/tex]
sec(63°) = [tex]\frac{23}{RT}[/tex]
cot(63°) = [tex]\frac{RT}{10.4}[/tex]
Now, in respect of angle S(27°), hypotenuse is RS(23), adjacent is ST(10.4) and opposite is RT.
So, cos(27°) = [tex]\frac{23}{RT}[/tex]
sec(27°) = [tex]\frac{23}{10.4}[/tex]
cot(27°) = [tex]\frac{10.4}{RT}[/tex]
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please give the right answer and i will mark you brainlyist
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Considering the given box plots, we have that:
Class A has the higher IQR.Class A has the highest test score.Class B has the higher median.Class B has the smaller range.What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.Hence, for class A, we have that:
The smallest value is 62.The first quartile is 65.The median is of 70.The third quartile is 79.The highest value is of 86.Then:
The IQR is of 79 - 65 = 14.The range is of 86 - 62 = 24.Hence, for class B, we have that:
The smallest value is 68.The first quartile is 70.The median is of 74.The third quartile is 77.The highest value is of 79.Then:
The IQR is of 77 - 70 = 7.The range is of 79 - 68 = 11.Hence the correct options are given as follows:
Class A has the higher IQR.Class A has the highest test score.Class B has the higher median.Class B has the smaller range.More can be learned about box plots at https://brainly.com/question/27721471
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Using the digits below form the smallest number which is a multiple of 3
9,4,5
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This would be the least common multiple of 3, 4, 5, and 9. We can start by listing the multiples of the biggest number, 9, and seeing if each of the numbers can be divisible by the smaller numbers.
9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180
180 would be the answer because it is the first number in our list that is divisible by 3, 4, 5, and 9.
QUICK!!!HELP!!!!!!!!!!!!!!!!!!
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Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:
Z = (X - mu)/sigma
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
mu = 400, sigma = 50
The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:
X = 550:
Z = (X - mu)/sigma
Z = (550 - 400)/50
Z = 3
Z = 3 has a p-value of 0.9987.
X = 500:
Z = (X - mu)/sigma
Z = (500 - 400)/50
Z = 2
Z = 2 has a p-value of 0.9772.
0.9987 - 0.9772 = 0.0215 = 2.15% probability.
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What number is the height changing by each minute?
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The height is changing by 0.5 units per minute as evident in the given table.
By what number is the height changing?It follows from the task content that the table given indicates that at, 0min, the height was 150.
While at 1 min, the height is 150.5. On this note, it follows that the height increases by 0.5 units for after every minute.
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9 The cost of a mobile phone call is 30 cents plus 20 cents per minute.
a Find the possible cost of a call if it is:
i shorter than 5 minutes ii longer than 10 minutes
b For how many minutes can the phone be used if the cost per call is:
i less than $2.10 ii greater than or equal to $3.50
Answers
Using a linear function, we have that:
a) The costs are:
i. C(x) < $1.3.
ii. C(x) > $2.3.
b) The times are:
i. Less than 9 minutes.
ii. At least 16 minutes.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the y-intercept is of 0.3, while the slope is of 0.2, hence the cost for a call of x minutes is:
C(x) = 0.3 + 0.2x.
For calls shorter than 5 minutes, the costs are:
C(x) < 0.3 + 0.2 x 5
C(x) < $1.3.
For calls longer than 10 minutes, the costs are:
C(x) > 0.3 + 0.2 x 10
C(x) > $2.3.
The cost is less than $2.10 for calls of less than x minutes, found as follows:
0.3 + 0.2x < 2.1
0.2x < 1.8
x < 9.
The cost is greater or equal to $3.50 for calls of at least x minutes, found as follows:
0.3 + 0.2x >= 3.5
0.2x >= 3.2
x >= 16.
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