Answer:
b = -a
Step-by-step explanation:
Since a and b are equally distant to zero but in opposite directions, a and b are opposites, or additive inverses.
The sum of additive inverses is zero.
a + b = 0
b = -a
A research team collects both quantitative and qualitative data. They code the qualitative data and examine how variations in the themes are related to the quantitative data. What type of mixing is this
Its related to the mixing in the Analysis.
Quantitative data:
They are used when a researcher is trying to quantify a problem, or address the "what" or "how many" aspects of a research question. It is data that can either be counted or compared on a numeric scale.
Qualitative data :
It describes qualities or characteristics. It is collected using questionnaires, interviews, or observation, and frequently appears in narrative form. For example, it could be notes taken during a focus group on the quality of the food at Cafe Mac, or responses from an open-ended questionnaire.
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This is the graph of f(x). What is the value of f(3)?
10+
2
-5
C
A. 5
B. 3
C. 6
D. 8
5
X
The value of f(3) is 8
To make lemonade, I use a ratio of $7$ parts water to $1$ part lemon juice. If I want to make a gallon of lemonade, and there are four quarts in a gallon, how many quarts of water do I need
Answer:
3 1/2 quarts
Step-by-step explanation:
The fraction of the lemonade that is water can be determined from the ratio of water to lemon juice. That fraction of a gallon is the quantity of interest.
Water fractionOf the 7+1 = 8 parts that make up the lemonade, 7 of those are water. That is, water is 7/8 of the lemonade.
Water quantityOf the 4 quarts of lemonade, the quantity that is water will be ...
(7/8)(4 quarts) = 7/2 quarts = 3 1/2 quarts . . . of water
the width of a rectangle is 9 inches less than its length and the area is 36 square inches. what are the length and width of the rectangle
Answer:
12 and 3
Step-by-step explanation:
Let x= length
If you draw a rectangle. two sides would be the length x. The other two sides would be (x-9).
(length)(width) = Area
(x)(x-9) = 36
x^2 - 9x = 36 Substitute in x and x-9 for the length and width
x^2 - 9x - 36 =0 Subtract 36 from both sides
(x-12)(x+3) = 0 We are looking for 2 number that add to -9 and mult. to -36
x-12=0 and x+3=0 Set both factors to 0 and solve
x = 12 and x =-3. It does not make sense that a length could be -3 so we reject that answer. If the length is 12, then the width is 3
The average weight of 3 men a, b and c is 84 kg. another man d joins the group and the average now becomes 80 kg. if another man e whose weight is 3 kg more than that of d, replaces a then the average weight of b, c, d and e becomes 79 kg. what is the weight of a?
The weight of A is 75kg.
How to calculate the weight?Total weight of A + B + C = 84 x 3 = 252kg
Total weight of A + B + C + D = 80 x 4 =.320 kg
Weight of D = 320 - 252 = 68 kg
Given, E = D + 3 = (68 + 3) kg = 71 kg
Total weight of B + C + D + E = (79 x 4) = 316 kg
Weight of B + C = 316 kg - 71 kg - 68 kg = 177 kg
Weight of A only will be:
= 320 kg - 177 kg - 68 kg
= 75 kg
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Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
77 m (nearest metre)
Step-by-step explanation:
Angle of Elevation
If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.
To find how tall the flagpole is, model as a right triangle and solve using the tan trigonometric ratio.
Tan trigonometric ratio
[tex]\sf \\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven information:
Person height = 1.6 mHorizontal distance (from person to flagpole) = 35 mAngle of elevation = 65°Therefore:
[tex]\theta[/tex] = 65°O = height of flagpole less height of personA = 35 mAs the person is 1.6 m tall, we model the line of sight as 1.6 m above ground level. Therefore, when calculating the height of the flagpole, we will need to add the height of the person to the value found using the trig ratio.
Substitute the given values into the formula and solve for O:
[tex]\implies \sf \tan(65^{\circ})=\dfrac{O}{35}[/tex]
[tex]\implies \sf O=35\tan(65^{\circ})[/tex]
Therefore the height of the flagpole is:
[tex]\implies \sf 35\tan(65^{\circ})+1.6=76.65774222...[/tex]
[tex]\implies \sf Height\:of\:flagpole=77\:m\:(nearest\:metre)[/tex]
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Suppose that E and F are two events and that P(E)=0.3 and P(F|E)=0.5. What is P(E and F)?
P(E and F)=
(Simplify your answer.)
E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15
Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.
P(F|E)=P(E and F)÷P(E)
It is given that P(E)=0.3,P(F|E)=0.5
Using Bayes' formula,
P(F|E)=P(E and F)÷P(E)
Rearranging the formula,
⇒P(E and F)=P(F|E)×P(E)
Substituting the given values in the formula, we get
⇒P(E and F)=0.5×0.3
⇒P(E and F)=0.15
∴The correct answer is 0.15.
If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.
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12.5% of a number is 25, find the number
Answer:
200
Step-by-step explanation:
Let's call the number x :
12.5% of x = 25
Changing 12.5% into decimal would be 0.125
Now we have the equation :
0.125x = 25
Divide both sides by 0.125 to make x the subject :
x = 25 ÷ 0.125
x = 200
To check we can substitute this value into the question :
12.5% of 200 = 25
Hope this helped and have a good day
the central angle of the arc of 75
Answer:
75 degrees.
Step-by-step explanation:
Central angle = subtending arc.
honestly don’t know this ?
1 ) 6
2) 6
3) -2
4) 2
5) -2
6) 2
x+2/3 - x+1/5 = x-3/4 - 1
Answer:
x = 157/60
Step-by-step explanation:
x + 2/3 - x + 1/5 = x - 3/4 - 1
x - x - x = -2/3 - 1/5 - 3/4 - 1
-60x/60 = -40/60 - 12/60 - 45/60 - 60/0
-60x = -40 - 12 - 45 - 60
-60x = -157
x = -157/-60
x = 157/60
157/60 + 2/3 - 157/60 + 1/5 = 157/60 - 3/4 - 1
2/3 + 1/5 = 157/60 - 3/4 - 1
40/60 + 12/60 = 157-60 - 45/60 - 60/60
40 + 12 = 157 - 45 - 60
52 = 157 - 105
If t is the midpoint of segment rs then, segment rt is congruent to segment ts..
help please!!!!
It is the definition of Midpoint
Disclaimer!!!
The question is incomplete and the correct question is shown below
What definition would justify the following statement?
If T is the midpoint of segment RS then, Segment RT is congruent to segment TS..
Definition of Angle BisectorDefinition of CongruenceDefinition of MidpointDefinition of Segment BisectorIf t is the midpoint of segment rs then, segment rt is congruent to segment ts. is the definition of the midpoint
The line segment of a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.
Hence It is the definition of the midpoint
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Answer: C: Definition of Midpoint
Step-by-step explanation: Hope that helped!
A student found the MAD of the data shown. What was the student’s error?
A.When calculating the mean, the student divided the sum by the wrong number.
B.When calculating the MAD, the student divided the sum by the wrong number.
C.When calculating the distances to the mean, the student forgot to take the absolute values.
D.When calculating the MAD, the student forgot to take the absolute value of the result.
The error made while find the mean absolute deviation was: C. When calculating the distances to the mean, the student forgot to take the absolute values.
What is the Mean Absolute Deviation?The mean absolute deviation is simply the average of the sum of the "absolute difference" of the mean and each data point.
In the calculation of the student, after getting the difference of the mean and each data point, the student failed to take the absolute value, and still kept the minus sign included.
Therefore, the error was: C. When calculating the distances to the mean, the student forgot to take the absolute values.
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WILL MARK BRAINLIEST!!!
1. Describe three different ways to solve a quadratic equation. Describe the strengths and limitations of each method, and explain how you would decide which one to use to solve a particular problem.
2. Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
Divide all terms in the equation by a.
Subtract the constant (the term without an x) from both sides.
Add a constant (in terms of a and b) that will complete the square.
Take the square root of both sides of the equation.
Solve for x.
3. Write a linear equation that intersects y = x2 at two points. Then write a second linear equation that intersects y = x2 at just one point, and a third linear equation that does not intersect y = x2. Explain how you found the linear equations.
Thank You!!
The ways that can be used to solve a quadratic equation include:
Factorization
Using the quadratic formula.
Completing the squares.
What is a quadratic equation?It should be noted that a quadratic equation simply means an algebraic equation of the second degree in x.
Here, the factorization, using the quadratic formula, and completing the squares method can be used.
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Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.
Subsets with bit strings:
001110000010100100010111001110What are subsets?A set A is a subset of a set B if all of its items are also elements of B; B is, therefore, a superset of A. A and B can be equal; if they are unequal, then A is a legitimate subset of B. Inclusion refers to the relationship of one set being a subset of another.To find the subsets with bit strings:
We need to express a) b) and c) into bit strings.
Firstly, a number of elements in the universal set represent the number of bits in the bit string.
Secondly, 1 = yes element is present in both universal sets as well as in subset.
0 = No, the element is not present in the subset but present in the universal set.
Hence, we have:
a) Subset {3,4,5} = 0011100000 (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.
Similarly,
b) Subset {1, 3, 6, 10} = 1010010001
c) Subset {2, 3, 4, 7, 8, 9} = 0111001110
Therefore, Subsets with bit strings:
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Complete question:
Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.
a) {3, 4, 5}
b) {1, 3, 6, 10}
c) {2, 3, 4, 7, 8, 9}.
Louis is very hungry when he spots a hot dog stand. The stand sells soft drinks for $1.25 each and hot dogs for $2.50 each. Louis has $21 in his pocket and he really wants to buy one soft drink and as many hot dogs as he can purchase. How many hot dogs can he buy?
Answer:
7 hot dogs
Step-by-step explanation:
Set up an equation:
2.5x + 1.25 = 21
2.5x = 19.75
x = 7.9
You cannot buy .9 of a hot dog, so the answer is 7
David is currently 3 times as old as his son. If David’s son’s current age is x years, how old will David be after 3 years?
Dave is 18 years old.
What is algebraic expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11
Given
Let x be Dave’s age today. Then:
x=3(x+3)-3(x-3)
x=3x+9–3x+9
x=18
Dave is 18 years old.
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PLLLLLLLLEASEEEEEEEEE
Answer:
[tex]x^2+8x+8+\frac{-9}{x+4}[/tex]
Step-by-step explanation:
it would be simpler to do synthetic division by removing the variables and using the coefficients:
i hope this helped!
Could someone please help me and show work
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
and the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with a, b, c being the sides opposite of their associated angles (A, B, C).
1)
17/sin(26) = 12/sin(C)
sin(C) = 12×sin(26)/17 = 0.309438457...
C = 18.02539254...° ≈ 18°
3)
180 = 27 + 115 + C
C = 38°
19/sin(38) = AC/sin(27)
AC = 19×sin(27)/sin(38) = 14.01065332... in ≈ 14 in
In first triangle side angle m∠C is 18° and in first triangle side AC is 14 in. This can be obtained by using the law of sine.
Find the required angle and side:We know the law of sine which is,
If in a triangle, Δ ABC,
[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex], where a is the side opposite to the angle m∠A, b is the side opposite to the angle m∠B and c is the side opposite to the angle m∠C.
sine of the angle scan be found using calculator.
From the question,
1) In first triangle side,
AB = 12ft, BC = 17 ft and m∠A=26°
⇒By using the law of sine,
[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]
sin 26°/17 = sin B/AC = sin C/12
sin 26°/17 = sin C/12
12×sin 26° = 17×sin C
sin C = 5.26/17 = 0.3091
C = 18.023° ≈ 18°
3) In second triangle side,
m∠B = 27°, AB = 19 in and m∠A = 115°
m∠A + m∠B +m∠C = 180°
115° + 27° + m∠C = 180°
142° + m∠C = 180°
m∠C = 38°
⇒By using the law of sine,
[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]
sin 115°/BC = sin 27°/AC = sin 38°/19
sin 27°/AC = sin 38°/19
sin 27° × 19 = sin 38° × AC
8.63 = 0.62 × AC
AC = 13.91 in ≈ 14 in.
Hence in first triangle side angle m∠C is 18° and in first triangle side AC is 14 in.
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Find a polynomial function of lowest degree with
rational coefficients that has the given numbers
as some of its zeros.
- 5i, 4
Answer:
x^3-4x^2+25x-100
Step-by-step explanation:
We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root
Combining the roots into a polynomial gives us:
(x+5i)(x-5i)(x-4)
Expand:
(x^2 + 25)(x-4)
x^3-4x^2+25x-100
Identify the sets of congruent angles. Explain your conclusions.
Answer:CB,CH,AE,AB
Step-by-step explanation:
equivalent to -8.2 - 5−8.2
The equivalent value of the given expression is -21.4
Difference of decimalsDecimals are values that include decimal points. Given the expression below
-8.2 - 5−8.2
Collect like terms
-8.2 −8.2 - 5
Convert to fractions
-82/10- 82/10 - 5
-164/10 - 5
-16.4 - 5
Take the sum
-21.4
Hence the equivalent value of the given expression is -21.4
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The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = a sine (b (t minus h)) k. what is the height of the ball at its equilibrium?
Based on the height of the ball suspended from a spring, the height of the ball at equilibrium is K feet.
What is the ball's height at equilibrium?The model for the height of the ball when it is suspended from a spring is shown as:
= aSin(b ( t - h)) + k
Given this, we can infer the value of h by looking at the general form of the Sin function which is:
y = Asin(Bx) + c
In the above:
A = amplitude
B = (2 x pi) / Period
C = midline
Comparing the function and the general Sin function, we notice that:
C = K
If C = K then it means that K is the height of the ball at its equilibrium because C as the midline represents the equilibrium height.
In conclusion, the height of the ball at equilibrium is K feet.
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Year: %Households:
1999 12.3
2000 18.2
2001 24.4
2002 25.7
2003 27.9
Estimate the instantaneous rate of change in percent of households that played games over the internet in the year 2000. Use the method of averaging a preceding and following interval AND the method of choosing a surrounding interval.
Based on the table showing the percentage of households playing games over the net, the average rate of change from 1999 to 2003 is 3.9% per year.
What is average rate of change?This can be found as:
= (27.9 - 12.3) / 4 years
= 3.9% per year
In 2000, the instantaneous rate of change would be:
= (Rate in 2001 - Rate in 1999) / difference in years
= (24.4 - 12.3) / (2001 - 1999)
= 6.05%
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The equation represents an ellipse. which point is the center of the ellipse? (−9, 5) (−5, 9) (5, −9) (9, −5)
The point which is the center of the ellipse whose equation is; (y+5)²/121+(x-9)²/49=1 s in the task content is; (-5, 9).
Which point represents the center of the ellipse whose equation is given as; (y+5)²/121+(x-9)²/49=1?It follows from convention that the equation of an ellipse usually takes the form;
(y-h)²/a²+(x-k)²/b²=1 in which case, the center of the ellipse is given by the point; (h, k).
On this note, By comparison of the actual equation and the standard equation, it follows that;
+5 = -h and consequently, h = -5,
-9 = -k and consequently, k = 9.
Ultimately, the point which is the center of the
ellipse is; (-5, 9).
Remark: The equation of the ellipse which is missing in the task content is; (y+5)²/121+(x-9)²/49=1
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Answer: D. (9, −5)
Not (-5, 9)
Step-by-step explanation:
Question If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0
Answer: If the product of any two numbers in the list is equal to 0, you can't conclude that the list is composed only by zeroes. In fact, suppose that you have a list of N numbers which are all zeroes except one. Whenever you multiply two elements of this list, you either multiplies two zeroes, or you multiply the non-zero element by a zero element, and so the result is zero, but the list is not composed by zeroes only.
Step-by-step explanation:
The monthly income of a government servant is Rs 77,280 and he gets the festival expense of one month's salary, what is his taxable income?
I don't think this question is complete but here's ur answer
In a mathematics test, Jack scored 17 marks more than Yazid while Susan scored twice Yazid's score. If their total score is 161, what is Jack's score?
Answer:
53
Step-by-step explanation:
Let yazid's score be x
x + x + 17 + 2x = 161
4x + 17 = 161
4x = 144
x = 36
jack = x + 17
jack = 53
Answer:
Jack: 36
Bonus: Yazid: 53 and Susan: 72
Step-by-step explanation:
Let J, Y, and K stand for Jack, Yazin, Susan's scores.
We are told that:
J = Y + 17 [Jack scored 17 marks more than Yazid]
S = 2Y [Susan scored twice Yazid's score]
J + Y + S = 161 [total score is 161]
Substitute the first two expressions into the last equation:
J + Y + S = 161
(Y+17) + Y + (2Y) = 161
4Y = 144
Y = 36
Use Y = 36 to find the other scores:
J = Y + 17
J = 36 + 17
J = 53
S = 2Y
S = 2*(36)
S = 72
CHECK:
Does 36+53+72 = 161?
YES
Volume=
Help me please thanks so much :)
The volume of the oblique cylinder is 6867.18 cubic units
How to determine the volume?The given parameters are:
Height = 27
Radius = 9
The volume is calculated as:
[tex]V = \pi r^2 h[/tex]
So, we have:
[tex]V = 3.14 * 9^2 * 27[/tex]
Evaluate
V = 6867.18
Hence, the volume of the oblique cylinder is 6867.18 cubic units
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Which could be the missing data item for the given set of data if the median of the complete data set is 14?
10 11 10 19 16 14 12 12 15 11 18 19
A. 10
B. 11
C. 12
D. 18
The missing data item for the given set of data if the median is 14 is 18.
How to find the median of a data sets?The Median is the "middle" of a sorted list of numbers.
Therefore, the missing data item for the given set of data if the median is 14 can be calculated as follows:
10 10, 11, 11, 12, 12, 14, 15, 16, 18, 19, 19,
Therefore, if you add 18 the middle number of the sorted numbers will be 14.
10 10, 11, 11, 12, 12, 14, 15, 16, 18, 18, 19, 19,
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