Answer:
Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
Step-by-step explanation:
We are given the following in the question:
The distribution of systolic blood pressure of other women is a bell shaped distribution that is a normal distribution.
z-score = 1.50
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Let x be the Gina's systolic blood pressure.
Thus, we can write:
[tex]1.50 = \displaystyle\frac{x-\mu}{\sigma}\\\\x = 1.5\sigma + \mu \\\text{where }\sigma \text{ is the standard deviation and }\\\mu \text{ is the mean for the given distribution of blood pressure.}[/tex]
Thus, we can write Gina's blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
Gina's z-score of 1.50 indicates that her systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
Explanation:The best interpretation of Gina's standardized score (z-score) of 1.50 is option B: Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age. Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.
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Which of the following is an estimating technique that uses a statistical relationship between historical data and other variables to calculate an estimate for activity parameters such as duration and cost?A. Bottom-up estimatesB. Influence diagramsC. SWOT analysisD. Analogous estimatingE. Parametric estimating
Answer: E. Parametric estimating
Step-by-step explanation:
A parametric estimate is the estimating process that uses a statistical relationship between past project's data and other variables to give an estimation for the parameters such as duration ,cost and budget.
It is based on parameters that summarize the risk , costs of algorithm , project , process , complexity and service.
It can create a greater level of accuracy.
Therefore , Parametric estimating is an estimating technique that uses a statistical relationship between historical data and other variables to calculate an estimate for activity parameters such as duration and cost.
Hence , the correct answer is E. Parametric estimating.
A small radio transmitter broadcasts in a 46 mile radius. If you drive along a straight line from a city 60 miles north of the transmitter to a second city 51 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answer:
The signal will not be picked up if he drives from the first city to the second city as far as he drives along a straight line.
Step-by-step explanation:
The attachment to the answer clearly explains why no signal will be picked up
Answer:
The answer is 38.5 miles
Step-by-step explanation:
From the attached diagram
AC represents the distance needed to be traveled before picking the signal.
Using Pythagoras'rule to solve for AC from triangle ACO
(AO)^2 = (AC)^2 + (CO)^2
(60)^2 = (AC)^ + (46)^2
(AC) = ✓[(60)^2 - (46)^2]
AC = 38.5 miles
Use the table above to determine how long it will take the Spirit Club to wax 60 cars
Answer:
22 1/2 hours
Step-by-step explanation:
There are several ways you can get there. One way is to use table values to form a sum of 60:
cars = 32×2 - 8×(1/2) = 64 -4 = 60
Then the corresponding hours are ...
hours = 12×2 - 3×(1/2) = 24 -1.5 = 22.5
It will take 22.5 hours to wax 60 cars.
__
Another way to get there is to use proportions:
hours/cars = 3/8 = ??/60
Multiply by 60 to find ??
(60)(3/8) = ?? = 180/8 = 22.5 . . . . hours
_____
We can do these things because we have determined the relationship between hours and cars is proportional: 8/3 = 16/6 = 32/12. If it weren't proportional, some other strategy would be needed to answer the question.
hello again I need to find an equation to find the long side of the triangle. but this time only the hypotenuse is given. brainliest if you get it right :)))
Answer:
The answer to your question is Long = 10.39
Step-by-step explanation:
Data
hypotenuse = 12
long = ?
Process
1.- To find Long, we must use the trigonometric functions sine or cosine.
If we use sine, we use the 60° angle
If we use cosine, we use the 30° angle
a) sin 60 = long / hypotenuse
Long = hypotenuse x sin 60
Long = 12 x sin 60
Long = 10.39
b) cos 30 = Long / hypotenuse
Long = hypotenuse x cos 30
Long = 12 x cos 30
Long = 10.39
Answer:
Long = 6√3Step-by-step explanation:
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : 2 : √3.
(short : hypotenuse : long)
We have hypotenuse = 12.
Therefore
short = 12/2 = 6
long = 6√3
QUESTION 3
Match each question to the right answer.
1. What can you conclude is necessary for an "and"
statement (P and Q) to be true?
2. What can you conclude is necessary for an “P or Q” statement to be true?
3. What can you conclude is necessary for an “if P, then Q” statement to be true?
4. What can you conclude is necessary for an “P if and only if Q” statement to be true?
A. Q is true when P is true.
B. Both P and Q are true or both P and Q are false.
C. Both P and Q are true.
D. At least one of the truth values of them (P, Q) is true.
PLEASE PROVIDE EACH QUESTION WITH ANSWERS! (Example: Question 1. is B.)
Answer:
.
Step-by-step explanation:
In a family of 10 children, where both parents are heterozygous for albinism, what mathematical equation predicts the probability that 9 are normal and 1 are albino?
Answer:
10:9:1
Step-by-step explanation:
A 15-foot ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall. How far up the wall does the ladder touch?
Answer: Using Pythagoras Rule the ladder touches 13.75ft ~ 14ft up the wall.
Step-by-step explanation: Using the Pythagoras Rule the Hypothenus is the leaning hieght of the ladder 15ft
And the base is 6ft. Now let's find the height of the wall h¹
h¹ = √{15² - 6²}
h¹ =√{225 - 36}
h¹ = √189
= 13.74ft
The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, what range of IQ scores do many (68%) people have
Answer:
Step-by-step explanation:
The Standard Deviation Rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15.
Therefore, the range of IQ scores that many (68%) people have is between
100 - 15 and 100 + 15
It becomes
85 to 115
The range of IQ scores for 68% of the people varies from 85 to 115
Given that the distribution of IQ (Intelligence Quotient) is approximately normal in shape
[tex]\rm Mean\; IQ =\mu = 100 \\Standard\; deviation = \sigma = 15[/tex]
According to the empirical relation for normal curve 68% of the data lies in the range
[tex]\rm \mu + \sigma\; to \; \mu - \sigma[/tex]
So the lower limit of the range of the normal distribution of IQ score = 100 -15 = 85
The upper limit of the range of the normal distribution of IQ score = 100 + 15 = 115
So we can conclude that the range of IQ scores for 68% of the people varies from 85 to 115
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2x – 6y = 5
x – 3y = -12
show all the steps to solve the system of equations below using substitution.
You can use any of the available methods for solving system of linear equations like method of elimination or method of substitution etc.
There are no solutions to the given system of equations.
How to find the solution to the given system of equation?For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.
If there comes a = a situation for any a, then there are infinite solutions.
If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.
Using the above method to solve the given system of equationsThe given system of equations is
[tex]2x - 6y = 5\\x - 3y = -12[/tex]
Using second equation to get x in terms of y
[tex]x - 3y - 12\\x = 3y - 12[/tex]
Substituting this expression for x in place of x in first equation,
[tex]2x - 6y = 5\\2( 3y - 12) - 6y = 5\\6y - 24 - 6y = 5\\-24 = 5[/tex]
The last statement we got is incorrect.
That conclusion above shows that the given system of equation has no solution.
We could've detected it from the fact that
[tex]2x - 6y = 5\\\text{dividing both sides by 2}\\x - 3y = 2.5[/tex]
Converting both equations to slope intercept form, we get:
[tex]x - 3y = 0.5\\\\y = \dfrac{1}{3}x - \dfrac{1}{6}[/tex]
and
[tex]x - 3y = -12\\\\y = \dfrac{1}{3}x + 4[/tex]
We see that both lines have same slope but different y intercept, which tells that both lines are parallel but not coincident, thus, not intersecting and thus, no common point(common points are solutions).
The graph of this system of linear equation is given below where lines represented by both linear equations are plotted.
Thus,
There are no solutions to the given system of equations.
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Final answer:
To solve the system of equations using substitution, rearrange one of the equations to solve for a variable and substitute that expression into the other equation. In this case, the system of equations is inconsistent and has no solutions.
Explanation:
To solve the system of equations using substitution, we rearrange one of the equations to solve for a variable, then substitute that expression into the other equation. Let's solve the system of equations:
Equation 1: 2x - 6y = 5
Equation 2: x - 3y = -12
In Equation 2, solve for x: x = 3y - 12Substitute this expression for x into Equation 1:2(3y - 12) - 6y = 56y - 24 - 6y = 5-24 = 5This is a contradiction, which means there is no consistent solution for x and y in this system of equations.Therefore, the system of equations is inconsistent, and there are no solutions.
If g(1)= -5 identify a point on the graph of g
Answer:
(1,-5)
Step-by-step explanation:
recall that for any function g(x), we can equate the function to y,
i.e y = g(x), where any point (x,y) that satisfies the equation is considered a point on the graph
in our case we are given, that g(1) = -5, rearranging:
-5 = g(1)
if we compare this with the the equation above y = g(x),
we can see clearly that y = -5 and x = 1.
and from our reasoning given in the paragraph above, we can say that (1,-5) is a point on the graph.
Caleb is putting tile down in his bathroom and needs to know the perimeter of the floor. Two sides rectangular floor are 5 1/3 feet, and the other two sides are 4 3/4 feet. What is the perimeter of calebs bathroom floor?
Answer:
20 1/6 ft
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides:
2×(5 1/3 ft) + 2×(4 3/4 ft) = 10 2/3 ft + 8 6/4 ft
= 10 2/3 ft + 9 2/4 ft . . . . change 6/4 ft to 1 1/2 ft
= 10 8/12 ft + 9 6/12 ft = 19 14/12 ft . . . . . use common denominator of 1/12 ft
= 20 2/12 ft . . . . . . change 14/12 ft to 1 2/12 ft; next reduce that fraction
= 20 1/6 ft . . . . perimeter of Caleb's bathroom
Distribution of data can be considered __________ or __________. A Skewed distribution shows data that is ____________ in one direction or the other.
Answer:
b
Step-by-step explanation:
for sure
Exactly 20% of the students in a school wear glasses. Sixty-five students are randomly selected to determine the probability that exactly 10 students wear glasses. Should a binomial probability density function or a cumulative distribution function be used? Explain.
A binomial cumulative distribution function should be used because the question asks for determining the probability that exactly 10 students wear glasses.
A binomial probability density function should be used because the question asks for determining the probability that exactly 10 students wear glasses.
A binomial cumulative distribution function should be used because the question states exactly 20% of students wear glasses.
A binomial probability density function should be used because the question states exactly 20% of the students wear glasses.
A binomial probability would not be used because the events are not independent of each other.
Answer:
A binomial probability density function should be used because the question asks for determining the probability that exactly 10 students wear glasses.
Step-by-step explanation:
A binomial probability density function is used when we want to know the probability of an exact value.
A cumulative distribution function is used when we want to know the probability of less than or equal to a value.
additiLet a, b, and c be real numbers with a ¤ 0. The solutions of the quadratic equation ax2 C bx C c D 0 are given by the quadratic formula, which states that the solutions are x1 and x2, where x1 D b C b 2 4ac 2a and x2 D b p b 2 4ac 2a : (a) Prove that the sum of the two solutions of the quadratic equation ax2 C bx C c D 0 is equal to b a . (b) Prove that the product of the two solutions of the quadratic equation ax2 C bx C c D 0 is equal to c
Answer:
Here is a more clearer version of the same question ;
29 1.2. Constructing Direct Proofs 1. Let a, b, and c be real numbers with a 0. The solutions of the quadratic equation ax 2 + bx + c = 0 are given by the quadratic formula, which states that the solutions are xi and x2. where and x2 2a 2a (a) Prove that the sum of the two solutions of the quadratic equation ax2 + bx + c = 0 is equal to -b/a . (b) Prove that the product of the two solutions of the quadratic equation ax2 + bx + c = 0 is equal to c/a.
The proving of both a) and b) has been done
Step-by-step explanation:
The step by step explanation has been given in the attachment below.
Answer:
ff
Step-by-step explanation:
How many 10-digit telephone numbers (area code + number) are possible if the first digit cannot be zero, the first three digits cannot be 800 or 900, and the number must end in 0000? A) 900,000 B) 898,000 C) 654.842D) 899,000
Answer: The answer is D
Step-by-step explanation:
Since the first digit must not be zero, and the first three digits must not be 900 or 800, the highest ten digits telephone number we can get is 899, since it is the highest number that is next in line to the forbidden numbers
The number of possible 10-digit telephone numbers, considering the given restrictions, is 638,000.
Explanation:To find the number of possible 10-digit telephone numbers, we need to consider the restrictions given. The first digit cannot be zero, so there are 9 options for the first digit. The next 2 digits cannot be 800 or 900, so there are 8 options for each of these digits. The remaining 6 digits can be any number from 0 to 9, so there are 10 options for each of these digits.
Therefore, the total number of possible telephone numbers is 9 x 8 x 8 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 648,000. However, the number must end in 0000, so we subtract the cases where the last 4 digits are not all zeros. There are 10 options for each of these 4 digits, so there are 10 x 10 x 10 x 10 = 10,000 cases where the number does not end in 0000.
Therefore, the final number of possible telephone numbers is 648,000 - 10,000 = 638,000. The correct answer is B) 638,000.
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Find the exact value of cot theta if csc theta = -4/3 and the terminal side of theta lies in Quadrant III.
Answer:
The exact value of cotФ is [tex]\frac{\sqrt{7}}{3}[/tex]
Step-by-step explanation:
Given as:
The value of cosec Ф = [tex]\frac{-4}{3}[/tex]
Let the value of cotФ = x
Now, According to question
∵ sinФ = [tex]\frac{1}{cosec\Theta }[/tex] .....1
Put the value of cosec Ф = [tex]\frac{-4}{3}[/tex] in eq 1
i.e sinФ = [tex]\frac{1}{\frac{-4}{3} }[/tex]
Or, sinФ = [tex]\frac{-3}{4}[/tex]
Again
∵ cosФ = [tex]\sqrt{1-sin^{2}\Theta }[/tex]
So, cosФ = [tex]\sqrt{1-(\frac{-3}{4})^{2}}[/tex]
Or, cosФ = [tex]\sqrt{1-(\frac{9}{16})}[/tex]
Or, cosФ = [tex]\sqrt{\frac{16 - 9}{16})}[/tex]
∴ cosФ = [tex]\frac{\sqrt{7}}{4}[/tex]
Again
we know that cotФ = [tex]\frac{cos\Theta }{sin\Theta }[/tex]
So, cotФ = [tex]\frac{\frac{\sqrt{7}}{4}}{\frac{-3}{4}}[/tex]
Or, cotФ = [tex]\frac{-\sqrt{7}}{3}[/tex]
As according to question sinФ lies in third quadrant
So, cotФ = [tex]\frac{\sqrt{7}}{3}[/tex]
Hence, The exact value of cotФ is [tex]\frac{\sqrt{7}}{3}[/tex] . Answer
Two spheres, one of radius 15 and the other of radius 33, have the same center. Find the side length of the largest cube that fits between them.
Final answer:
The side length of the largest cube that fits between two concentric spheres with radii of 15 and 33 is approximately 17.32.
Explanation:
To find the side length of the largest cube that fits between two concentric spheres (with the same center), we need to understand that the cube will fit within the smaller sphere and will be inscribed within it such that the diagonals of the cube's faces will be equal to the diameter of the smaller sphere.
The radius of the smaller sphere is given as 15.
Therefore, the diameter of this sphere, which is twice the radius, is 30.
Using the diagonal of a cube, which can be calculated with the formula √3 times the side length (s), it is found that
√3 × s = 30.
Solving for s gives us the maximum side length of the cube that would fit:
s = 30 / √3
s ≈ 17.32
Therefore, the side length of the largest cube is approximately 17.32.
Ivan has 15 yards of green felt and 12 yards of blue felt to make 3 quilts if Ivan uses the same total number of yards for each quilt how many yards did he use for each quilt
Answer:
9 yards
Step-by-step explanation:
Let the length of each quilt be 'l'.
Given:
Length of green felt (g) = 15 yards
Length of blue felt (b) = 12 yards
Total number of quilts = 3
Now, the length of 3 quilts is given as:
[tex]Total\ length=l+l+l=3l[/tex] ----- (1)
As per question:
Total length = Length of green felt + Length of blue felt
Total length = [tex]g+b[/tex]
[tex]Total\ length=15+12=27[/tex]--------- (2)
Now, comparing equations (1) and (2), we get:
[tex]3l=27\\\\l=\frac{27}{3}\\\\l=9\ yards[/tex]
Hence, each quilt measures 9 yards in length.
There are 18 questions on the test. Each question is worth either four or five points. The total is 80 points. How many questions of each type are on the test?
Answer: the number of four point questions in the test is 10.
the number of five point questions in the test 8
Step-by-step explanation:
Let x represent the number of four point questions in the test.
Let y represent the number of five point questions in the test.
There are 18 questions on the test. It means that
x + y = 18
Each question is worth either four or five points. The total is 80 points. This means that
4x + 5y = 80 - - - - - - - - - - - - - -1
Substituting x = 18 - y into equation 1, it becomes
4(18 - y) + 5y = 80
72 - 4y + 5y = 80
- 4y + 5y = 80 - 72
y = 8
x = 18 - y = 18 - 8
x = 10
what’s the value for X?
Answer: x = 5
Step-by-step explanation: This is an isosceles triangle, which means two sides are equal in length and two angles are equal in measurement.
Line BA = Line BC
Similarly, Angle A = Angle C
Angle A plus Angle C equals 146°
Also the sum of the interior angles of a triangle is 180°
Therefore, 146 + (6x + 4) = 180
Subtract 146 from both sides of the equation
6x + 4 = 34
Subtract 4 from both sides of the equation
6x = 30
Divide both sides of the equation by 6
x = 5
The first aircraft has 89 more seats than the second aircraft. The third aircraft has 17 fewer seats than the second aircraft. If their total number of seats is 372, find the number of seats for each aircraft.
Answer:
100
189
83
Step-by-step explanation:
Firstly, we can see that there are three aircrafts. Let the number of aircrafts in the second aircraft be x.
Then the first has 89 more seats meaning it has a total seats of x + 89
The third has 17 fewer seats meaning x - 17
Now we are expected to find the number of seats on each of the aircraft officials.
We add all and then sum to the total 372.
This means
x + x + 89 + x - 17 = 372
3x + 72 = 372
3x = 300
x = 300/3 = 100
The aircrafts thus have 100 seats, 189 and 83 seats in no particular order
Multiply. Give your answer in standard form. (3n2 + 2n + 4)(2n – 1) A. 6n3 + n2 + 6n – 4 B. 6n3 + 7n2 + 6n – 4 C. 6n3 – n2 + 10n – 4 D. 6n3 + n2 + 10n – 4
Answer:
A
Step-by-step explanation:
(3n²+2n+4)(2n-1)
to solve this multiply through by using each term in one bracket to multiply all terms in the second bracket to open the bracket.
3n²(2n-1) + 2n(2n-1) +4(2n-1)
6n³-3n² +4n²-2n+8n-4
6n³+n²+6n-4
Hence the correct option is A
Answer:
a
Step-by-step explanation:
There are 8 fish tanks in the pet shop. They just received an order of 216 goldfish. The owner of the pet shop wants each tank to have the same number of fish. How many goldfish will each rank have in it?
Answer:
Each tank would have 27 gold fish in it.
Step-by-step explanation:
Given:
Number of fish tanks = 8
Number of gold fish = 216
We need to find the number of goldfish in each tank.
Solution:
Now we know that;
Number of gold fish must be equal in each tank.
To find the number of gold fish in each tank we will divide Number of gold fish by Number of fish tanks.
framing in equation form we get;
number of gold fish in each fish tank = [tex]\frac{216}{8} = 27 \ fish[/tex]
Hence Each tank would have 27 gold fish in it.
What is the value of \dfrac{x^2}{y^4} y 4 x 2 start fraction, x, squared, divided by, y, start superscript, 4, end superscript, end fraction when x=8x=8x, equals, 8 and y=2y=2y, equals, 2?
Answer:
4
Step-by-step explanation:
Put the numbers in the expression in place of the corresponding variables and do the arithmetic.
[tex]\dfrac{8^2}{2^4}=\dfrac{64}{16}=4[/tex]
Answer:
4
Step-by-step explanation:
HELP NOW!!!
One day in the fall, Mark raked the leaves on 5 neighbors’ lawns in 2.5 hr. One day in the summer, he mowed 6 neighbors’ lawns in 1.2 hr.
The daily rate Mark rakes lawns in the fall is what percent of the daily rate he mows lawns in the summer, assuming he works at a constant rate.
Answer:
Assuming he works at a constant rate, the daily rate Mark rakes lawns in the fall is 40% of the daily rate he mows lawns in the summer.
Step-by-step explanation:
Fall:
5 neighbours' lawns / 2.5 hours = 2 lawns per hour
Summer:
6 neighbours' lawns / 1.2 hours = 5 lawns per hour
2 x 100% / 5 = 40%
2 is 40% of 5
The percent of the daily rate should be 40%.
Given information:One day in the fall, Mark raked the leaves on 5 neighbors’ lawns in 2.5 hr. One day in the summer, he mowed 6 neighbors’ lawns in 1.2 hr.
Calculation of the percent:For fall
= 5 neighbours' lawns ÷ 2.5 hours = 2 lawns per hour
For Summer:
= 6 neighbours' lawns ÷ 1.2 hours = 5 lawns per hour
Now
[tex]= 2 \times 100\% \div 5[/tex]= 40%
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Simplify and show work
Answer:
Step-by-step explanation:
11)
√(343 x^4)=√(7×7×7×x^4)=7√7 x^2
Answer: 7√ 7x^2
7 √ 7= 18.52x^2
Step-by-step explanation:
√ 343x^4 = √ 7×49x^4
=7 √ 7x^4×1/2
=7 √ 7x^2
what is the scale factor, k
Answer:
The scale factor is 2
Step-by-step explanation:
Scale factor [tex]k=\frac{Image\: length}{Corresponding\:Object\:Length}[/tex]
[tex]k=\frac{|A'B'|}{|AB|}[/tex]
We can use the Pythagoras Theorem to get:
[tex]k=\frac{\sqrt{4^2+4^2} }{\sqrt{2^2+2^2}}[/tex]
[tex]k=\frac{\sqrt{2*4^2} }{\sqrt{2*2^2}}=\frac{4\sqrt{2} }{2\sqrt{2} } =2[/tex]
The scale factor is 2
IM NOT SURE IF THE ANSWER IS ACTUALLY C
Answer:
D. 21
Step-by-step explanation:
Given:
m arc AC = 69
Segment AB is tangent to circle O at point A.
We need to find the ∠ ABC
Solution:
Now we can say that;
By inscribed angle theorem which states that;
"Central angle is equal to arc subtended by it."
m∠O = 69 (Central angle)
Also Given:
Segment AB is tangent to circle O at point A.
Now by radius tangent property which states that;
"Radius which touches to closet point on the tangent is always perpendicular."
so we can say that;
m∠OAB = 90
Now in Δ OAB.
m∠O = 69
m∠OAB = 90
Now we know that;
"Sum of all angles of triangle is 180."
m∠O + m∠OAB + m∠ABO = 180
Substituting the values we get;
[tex]69+90+m\angle ABO=180\\\\159+m\angle ABO=180[/tex]
Subtracting both side by 159 we get;
[tex]159+m\angle ABO-159=180-159\\\\m\angle ABO=21[/tex]
Now we can say that;
m∠ABO = m∠ ABC = 21 (same angles)
Hence m∠ ABC is 21.
7 people are coming over karla's House to watch a football game. She wants to make sure each person,including herself,will get 1/2 of a subway sandwich. How many sandwiches will she need to buy?
Answer:
Karla needs to bur 4 sandwiches.
Step-by-step explanation:
Given:
Amount of subway sandwich each person would get = [tex]\frac{1}{2}[/tex]
Number of people coming to watch football game = 7
Now given:
She wants to make sure each person,including herself,will get 1/2 of a subway sandwich.
Total number of people would watch the match = 8 persons
We need to find the number of sandwiches she need to buy.
Solution:
Now we know that;
to find the number of sandwiches she need to buy can be calculated by multiplying Amount of subway sandwich each person would get with Total number of people would watch the match.
framing in equation form we get;
the number of sandwiches she need to buy = [tex]\frac{1}{2}\times8 = 4[/tex]
Hence Karla needs to bur 4 sandwiches.
Solve for 1/3h+5 is greater then or equal to 1/6h+1
solving 1/3h+5 is greater then or equal to 1/6h+1 ([tex]\frac{1}{3}h+5\geq \frac{1}{6}h+1[/tex]) we get [tex]h\geq -24[/tex]
Step-by-step explanation:
We need to solve 1/3h+5 is greater then or equal to 1/6h+1
Writing in mathematical form:
[tex]\frac{1}{3}h+5\geq \frac{1}{6}h+1[/tex]
Solving and finding value of h
Adding -5 on both sides
[tex]\frac{1}{3}h+5-5\geq \frac{1}{6}h+1-5\\\frac{1}{3}h\geq \frac{1}{6}h-4[/tex]
Adding -1/6h on both sides
[tex]\frac{1}{3}h-\frac{1}{6}h\geq \frac{1}{6}h-4-\frac{1}{6}h\\\frac{1*2h-1*1h}{6}\geq -4\\\frac{2h-1h}{6}\geq -4\\\frac{1h}{6}\geq -4\\h\geq -4*6\\h\geq -24[/tex]
So, solving 1/3h+5 is greater then or equal to 1/6h+1 ([tex]\frac{1}{3}h+5\geq \frac{1}{6}h+1[/tex]) we get [tex]h\geq -24[/tex]
Keywords: Solving inequalities
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