The amount of money with the simple interest is A = $ 1,780
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Now , the amount with simple interest A = P + I
Now , the principal P = $ 1,000
The interest rate R = 13 %
The number of years T = 6 years
And , Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
Simple Interest I = ( 1000 x 13 x 6 ) / 100
On simplifying the equation , we get
Simple Interest I = $ 780
Now , the amount after 6 years = $ 1,000 + $ 780
The amount after 6 years = $ 1,780
Hence , the simple interest is $ 780
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the property manager at a large apartment complex wants to collect a simple random sample of its tenants and use a 90% confidence interval to estimate the proportion of its tenants who have pets. of the following, which is the smallest sample size that will result in a margin of error of no more than 4 percentage points?
The minimum sample size required to ensure a margin of error of no more than 4 percentage points is 294.
A simple random sample of tenants can be used to estimate the proportion of tenants who have pets in the complex. To ensure that the margin of error is no more than 4 percentage points, the sample size needs to be calculated. The formula to calculate the sample size given a margin of error of 4 percentage points and a confidence level of 90% is:
Sample Size = (1.645/0.04)2
Plugging in the values, the sample size comes out to be 294.
Therefore, the minimum sample size required to ensure a margin of error of no more than 4 percentage points is 294.
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A 4 year-old patient, who accidentally ingests valium found in his mother's purse, is found unconscious and rushed to the ED. The child is treated by the ED physician, who inserted a tube orally into the stomach and performed a gastric lavage, removing the stomach contents. What CPT® and ICD-10-CM codes are reported?
The reported 43753, T42.4X1A, and R40.20 CPT® and ICD-10-CM codes
What is CPT® code?In order to simplify reporting, improve accuracy, and boost efficiency, doctors and other healthcare workers have access to the Current Procedural Terminology (CPT®) codes.Rationale: Gastric lavage used to treat poison ingestion is properly coded as CPT® code 43753. Gastric Lavage, Therapeutic/Intubation can be found in the CPT® Index. You can get the ICD-10-CM code for the poisoning by looking for the Valium/Poisoning, Accidental (unintentional) column in the Table of Drugs and Chemicals, which directs you to code T42.4X1-. To finish the code in the Tabular List, a seventh character is required. In light of the fact that this was the patient's first meeting, A is listed as the seventh character. The following code represents unconsciousness, which is a side effect of taking Valium. You should consult Coma R40.20 if you're looking for unconsciousness in the ICD-10-CM Alphabetic Index. The Tabular List attests to the stated unconsciousness using this code.To learn more about CPT® code, refer to:
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
10.58
Step-by-step explanation:
here we need to find out the value of x by Pythagoras theorem. By Pythagoras theorem in q right angled triangle the sum of squares of base and perpendicular is equal to the square of hypotenuse. so ,
h² = p² + b²
Now here ,
p = 12h = 16 b = x = ?on using Pythagoras theorem,
h² = p² + b²
16² = 12² + x²
256 = 144 + x²
x² = 256 -144
x² = 112
x = √112
x ≈ 10.58 [ required answer]
and we are done!
-Rishabh
Solve the equation 0 = 22² - 8x + 10.
Select all the correct answers.
= 2
= 2-i
x = 1
== -2
Ox=2+i
Oz=1-i
x = -1
Oz = 1+i
The roots of the given quadratic polynomial are-
x = 2 - ix = 2 + iWhat is meant by the term roots of polynomial?The values of such a variable where the provided polynomial equals zero are referred to as a polynomial's roots. P(a) = 0 if an is the polynomial's root for x. A polynomial's root or zero is the value(s) for X that make the polynomial equal zero (or make Y equal zero).The given quadratic polynomial is:
0 = 2x² - 8x + 10
Comparing with the general equation: ax² + bx + c = 0
a = 2, b = -8, c = 10
Using quadratic formula.
x = -b ± √(b² - 4ac) / 2a
x = 8 ± √(8² - 4*2*10) / 2*2
On solving.
x = 2 - i
x = 2 + i
Both roots are imaginary numbers.
Thus, the roots of the given quadratic polynomial are-
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what is the recursive formula for -1, -6, -36, -216
The recursive formula for the sequence is -1, -6, -36, -216
is -1[tex](-6)^{n-1}[/tex].
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16 is a geometric sequence.
We have,
-1, -6, -36, -216 is a geometric sequence.
The first term is -1,
The common ratio.
= -6/-1
= 6
Now,
The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].
So,
= -1[tex](-6)^{n-1}[/tex]
Thus,
The recursive formula is -1[tex](-6)^{n-1}[/tex].
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When given a set of cards laying face down that spell F, R, A, C, T, I, O, N, determine the probability of randomly drawing a vowel.
A. three sevenths
B. five sevenths
C. three eighths
D. five eighths
Answer:
C
Step-by-step explanation:
A,I and O are 3 vowels out of the total 8 letters in
Answer:C
Step-by-step explanation:
Please help me with this question
Answer:
19
Step-by-step explanation:
TU is 2 inches and UV is 17 so adding them together would equal TV which is 19.
Answer: 19
Step-by-step explanation:
Because point U is found on both TU and UV, we can assume that this point is a bisector, dividing line TV into two separate lines. This essentially tells us that when we add lines TU and UV together, they will equal the length of line TV. With that being said, 2 + 17 = 19, so that is the length of TV. Hope this helps!
Match the differential equations with the solution graphs labeled I-IV. Give reasons for your choices.
I 9-1-013a.gif II 9-1-013b.gif
III 9-1-013c.gif IV 9-1-013d.gif
(a)
y' = 1 + x2 + y2
y' = 1 + x2 + y2 ? (? < ? > = )1 and y' ? ? (1 ? 0 -1 -? )as x ? ?.
The only curve satisfying these conditions is labeled ? (I II III IV) .
(b)
y' = xe?x2 ? y2
y' = xe?x2 ? y2 ?( > ? ? = <) 0 if x > 0 and y' ? (? = > < ?) 0 if x < 0.
The only curve with ---Select---( negative positive horizontal vertical) tangent slopes with
x < 0
and ---Select--- positive negative horizontal vertical tangent slopes when
x > 0
is labeled ? (I II III IV) .
(c) y' =
1
1 + ex2 + y2
y' =
1
1 + ex2 + y2
? ? = ? > < 0 and y' ? ? (-? ? 1 0 -1 )as x ? ?. The only curve satisfying these conditions is labeled ?( I II III IV) .
(d)
y' = sin(xy) cos(xy)
y' = sin(xy) cos(xy) ? (> ? < ? )= 0 if y = 0,
which is the solution graph labeled ?( I II III IV) .
The solution graphs for the differential equations y' = 1 + x2 + y2, y' = xe?x2 ? y2, y' = 1/(1 + ex2 + y2), and y' = sin(xy) cos(xy) are labeled I, II, III, and IV respectively. The slope of the graphs when x is less than 0 and greater than 0, as well as the horizontal tangent line when y is equal to 0, are used to determine the correct graph for each equation.
Match the differential equations with the solution graphs labeled I-IV. Give reasons for your choices.
I 9-1-013a.gif II 9-1-013b.gif
III 9-1-013c.gif IV 9-1-013d.gif
(a)
y' = 1 + x2 + y2
y' = 1 + x2 + y2 ? (? < ? > = )1 and y' ? ? (1 ? 0 -1 -? )as x ? ?.
The only curve satisfying these conditions is labeled ? (I II III IV) .
(b)
y' = xe?x2 ? y2
y' = xe?x2 ? y2 ?( > ? ? = <) 0 if x > 0 and y' ? (? = > < ?) 0 if x < 0.
The only curve with ---Select---( negative positive horizontal vertical) tangent slopes with
x < 0
and ---Select--- positive negative horizontal vertical tangent slopes when
x > 0
is labeled ? (I II III IV) .
(c) y' =
1
1 + ex2 + y2
y' =
1
1 + ex2 + y2
? ? = ? > < 0 and y' ? ? (-? ? 1 0 -1 )as x ? ?. The only curve satisfying these conditions is labeled ?( I II III IV) .
(d)
y' = sin(xy) cos(xy)
y' = sin(xy) cos(xy) ? (> ? < ? )= 0 if y = 0,
which is the solution graph labeled ?( I II III IV) .
a) I
b) IV
c) II
d) III
a) The differential equation is y' = 1 + x2 + y2, which has a positive slope when x is less than 0 and a negative slope when x is greater than 0. The only graph with these conditions is labeled I.
b) The differential equation is y' = xe?x2 ? y2, which has negative tangent slopes when x is less than 0 and positive tangent slopes when x is greater than 0. The only graph with these conditions is labeled IV.
c) The differential equation is y' = 1/(1 + ex2 + y2), which has a negative slope when x is less than 0 and a positive slope when x is greater than 0. The only graph with these conditions is labeled II.
d) The differential equation is y' = sin(xy) cos(xy), which has a horizontal tangent line when y is equal to 0. The only graph with this condition is labeled III.
The solution graphs for the differential equations y' = 1 + x2 + y2, y' = xe?x2 ? y2, y' = 1/(1 + ex2 + y2), and y' = sin(xy) cos(xy) are labeled I, II, III, and IV respectively. The slope of the graphs when x is less than 0 and greater than 0, as well as the horizontal tangent line when y is equal to 0, are used to determine the correct graph for each equation.
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The tables show the monthly costs for two different Internet service providers.
What will be the difference in the cost of the two plans after 18 months?
The difference in the cost of the two plans after 18 months will be 240. The solution has been obtained using linear equations.
What is a linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.
According to the table, the companies increase the cost by equal amount every month.
So, the linear equations for both the companies come out to be,
Company A: y=40+35x
Company B: y=10+50x
Therefore, after 18 months cost of both the companies will be
Company A:
y=40+35(18)
y=40+630
y=670
Company B:
y=10+50(18)
y=10+900
y=910
The difference in the cost of the two plans after 18 months will be
910-670= 240
Hence, the difference in the cost of the two plans after 18 months will be 240.
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The gestation period of horses is 336 days is blank percent longer than the gestation period of dogs 65 days
The gestation period of horses is 417% longer than the gestation period of cats.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
We have been asked to find percentage change of the gestation period of horses and cats.
First of all we will find difference between our two numbers.
Difference= 336-65
=271
Now we will find percentage of our difference with respect to gestation period of cats.
Percentage change = 271/65*100
=416.92
Therefore, gestation period of horses is 417% longer than the gestation period of cats.
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Vickie sells cupcakes for $4.00 each at her bakery. Supplies to make one cupcake cost $0.20. She spent $256 on new equipment to make the cupcakes.
Complete the inequality to represent the least number of cupcakes, xx, Vickie must sell in order to make a profit. Then, complete the sentence to make a true statement.
Vickie must sell at least 64 cupcakes in order to make a profit.
The break-even point theoryThe inequality to represent the least number of cupcakes Vickie must sell in order to make a profit is 4x > 256 + 20, where x is the number of cupcakes she must sell.To make this a true statement, Vickie must sell at least 65 cupcakes to make a profit since 4x > 256 + 20 is equivalent to x > 65.In order to make a profit, Vickie must sell at least 65 cupcakes.The equation 4x > 256 + 20 can be used to represent this, where x is the number of cupcakes she must sell.Each cupcake costs $4.00 to make and sell, and supplies to make one cost $0.20. She spent $256 on new equipment to make the cupcakes.For Vickie to make a profit, she must sell at least 65 cupcakes in order to cover the cost of supplies, equipment, and make a profit.The inequality to represent the least number of cupcakes Vickie must sell in order to make a profit is: 4x - 0.2x ≥ 256.To learn more about the break-even point theory refer to:
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At a grocery store, a bag of string cheese containing 24 pieces of cheese sells for $6.96. What is the price for a box containing 36 pieces of cheese using the same unit rate?
The price for a box containing 36 pieces of cheese will be sold for $10.44
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, a bag of string cheese containing 24 pieces of cheese sells for $6.96, we need to find the price for a box containing 36 pieces of cheese using the same unit rate,
Since, 24 pieces are sold for = $6.96
Therefore,
1 piece will be sold for = 6.96 / 24 = $0.29
Therefore,
36 pieces of cheese will be sold = 0.29 x 36 = $10.44
Hence, the price for a box containing 36 pieces of cheese will be sold for $10.44
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(08.03|08.04 HC)
For the regions A and B shown in the graph:
Part A: Discuss the limits of integration. (3 points)
Part B: Set up an integral expression that represents the total area. (4 points)
Part C: Calculate the total area. (3 points)
The total area from the graph is 2.737.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
First of all, lets calculate the points of intersection (P, Q, R)
x²+3=(x+2) +5
x²-2=√(x+2)
x⁴+4-4x²=x+2
x⁴-4x²-x+2=0
(x-2)(x³+2x²-1)=0
(x-2)(x+1)(x²+x-1)=0
x=2, -1, -1±√(1+4)/2
Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2
So the limit of integration will be
P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))
Q(-1, (-1)²+3)=Q(-1, 4)
Area A:
[tex]\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx[/tex]
= [tex][\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4[/tex]
= 2.07
Area B:
[tex]\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx[/tex]
= [tex][\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}[/tex]
= 0.667
Total area = 2.07+0.667
= 2.737
Therefore, the total area from the graph is 2.737.
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which set of ordered pairs does not represent a function?
A {(6,−1),(1,−9),(6,−3),(−6,−5)}
B {(5,5),(−5,2),(4,5),(1,1)}
C {(−5,4),(3,−9),(5,−7),(4,4)}
D {(4,1),(8,6),(−5,−1),(−3,−6)}
The set that does not represent a function is the one in option A.
{(6,−1),(1,−9),(6,−3),(−6,−5)}
Which set of ordered pairs does not represent a function?A function is a relation that maps inputs into outputs, such that each input is mapped into only one output.
So, if we have a relation where an input has more than one output, then it is not a function.
And remember that the notation for the ordered pairs is (input, output)
Looking at the options, we can see the set:
{(6,−1),(1,−9),(6,−3),(−6,−5)}
Where the input x = 6 is mapped into two different outputs, -1 and -3
So this does not represent a function.
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Find the value of x in the diagram. (x - 20)° (x - 10)⁰ X = 21° 42° tº 29° (x + 14)°
Answer: x = 68.5°
Step-by-step explanation:
x - 20 + 21 + 42 + 29 + x + 14 + x + x - 10 = 360°
4x = 360 + 20 - 21 - 42 - 29 -14
4x = 380 - 106
4x = 274
x = 68.5°
(the exterior angles of a polygon adds up to 360 degrees)
Answer:71
Step-by-step explanation:
Which of the following statements is not true concerning angle measure?O The square of any side of a triangle is equal to the sum of the squares of the remaining 2 sides, minus twice the produce of the 2 remaining sides and the cos of angle between them
O Two angles in standard position are coterminal if they have the same terminal side
O The length of the leg opposite either of the pi/4 angles of a special pi/4, pi/4, pi/2 right triangle with a hypotenuse of square root of 2 is equal to 1.O The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of pi radians
The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of pi radians
What is concerning angle measure?Using a protractor, angles are measured in degrees (°). A measuring tool called a protractor is used to compute or draw angles in terms of degrees. As seen in the illustration below, for instance, the black arrow, when measured with a protractor, points to 100°, crossing 90°. As a result, the angle has a 100° measurement. A protractor is the most practical tool for measuring angles. The vertex of the angle you are measuring should be the protractor's midway. Align the protractor's zero line with one side of the angle (line with the number 0). The angle is the number of degrees at which the other side of the scale crosses.The angle created by rotating the terminal side of angle one completely counterclockwise has a radian measure of pi radians when it is in standard position.
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determine whether an observational study or an experimental study is used. a study was done on two groups of algebra students. group was given tutoring and study skills advice. group was not given any additional help. after weeks, the students took a test. the results of the two groups were compared.
This is an experimental study.
This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.
An experimental study is used to examine the effects of an intervention or treatment on a group of participants. In this case, the study involved two groups of algebra students, one of which was given additional help in the form of tutoring and study skills advice while the other was not. After a few weeks, the students took a test and the results of the two groups were compared. This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.
This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.
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A sample of an ideal gas is compressed and cooled as it is taken from state 1 to state 2. The given properties for the gas in the two states are: p1 = 95.0 kPa, V1 = 0.0500 m3, V2 = 0.0400 m3, T1 = 300. K, T2 = 260. K. Calculate the pressure of the gas in state 2.
The pressure of the gas in state 2137 kPa. The equation of state for a hypothetical perfect gas is known as the ideal gas law, sometimes known as the generic gas equation.
What is the ideal gas law state?
The Ideal Gas Law asserts that all gases contain the same number of molecules when they are at the same temperature, pressure, and volume (but not the same mass). In case you forgot, when the temperature and pressure are getting close to turning into a liquid or solid, the Ideal Gas law does not apply.The general gas equation, often known as the ideal gas law, is the equation of state for a fictitious ideal gas. It has a number of limitations, but it provides a decent approximation of the behaviour of numerous gases under various circumstances.An ideal gas is one for which both the volume of the molecules and the forces between them are so negligibly small as to not affect the behaviour of the gas. PV=nRTGiven data :
p1 = 95.0 kPa,
V1 = 0.0500 m3,
V2 = 0.0400 m3,
T1 = 300. K,
T2 = 260.
we know PV=nRT
P1 * V1 * T1 = P2 * V2 * T2
95 x 0.05 x 300 = P2 x 0.04 x 260
1425 = P2 x 10.4
P2 = 1425 / 10.4 = 137 kPa
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Find the following angle measures.
mL EAD
mL CAB
The measure of ∠EAD = 29° and ∠CAB = 119°.
How many pairs of vertically opposite pairs are formed when 2 lines intersect?When two lines intersect, 2 pairs of vertically opposite angles are formed.
Given is the figure as attached with the question.
The measure of ∠EAD = 90 - 61 = 29°
∠EAD = 29°
∠CAB = ∠EAF = 90° + 29° = 119° {vertically opposite angles are equal}
∠CAB = 119°
Therefore, the measurement of ∠EAD = 29° and ∠CAB = 119°.
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Anna is a teacher at an elementary school. She purchased 63 tickets to take the first-grade children and some parents on a field trip to the zoo. She purchased
children's tickets for $7 each and adult tickets for $20 each. She spent a total of $571. How many of each ticket did she buy?
Answer:
Anna the teacher bought 54 child tickets and 19 adult tickets
Step-by-step explanation:
NO LINKS!!!
Lin is trying to convince Andre that all circles are similar. Help her write a valid justification for why all circles are similar.
All circles are similar because their shape is same but sizes vary.
What are Similar Figures?Similar figures are those figures which have the same shape, but sizes are different.
To prove the given statement, consider two circles C and C' with radius r and r' respectively.
r can be greater than or less than r'.
Circle C can be dilated to a certain value to get the circle C'.
The shape of both the circles remain same.
But the size is different.
This is the case for any arbitrary circles.
Hence all circles are similar.
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Drag the tiles to the correct boxes to complete the pairs.
Match each data set with the value that best describes its center.
6
2
4
9
The data sets and the values that best describe the elements within the data set are as follows;
Data set A; 2, 3, 1, 4, 2, 0, 0 → 2
Data set B; 6, 4, 5, 6, 5, 7, 8, 7 → 6
Data set C: 1, 4, 0, 2, 4, 4, 6, 7 → 4
Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11 → 9
What is a descriptive statistics?Descriptive statistics is the process of providing summaries of a set of data that describes the data contained in the data set.
The descriptive statistic that can be used to find the value that best describes the data are as follows;
The mean; The average value of the data set
The mode; The most common term in the data set
The median; The data value that is at the middle of the data arranged in increasing order of magnitude
Data set A: 2, 3, 1, 4, 2, 0, 0
The mean of data set A is; (2 + 3 + 1 + 4 + 2 + 0 + 0)/7 = 12/7
12/7 = 1 5/7
The mode of the data set is; 2
The data set arranged in increasing order is; 0, 0, 1, 2, 2, 3, 4
The middle number, which is the median of the dataset is, 2
The number that best describes the data is; 2
Data set B: 6, 4, 5, 6, 5, 7, 8, 7
The mean of the data set is; (6 + 4 + 5 + 6 + 5 + 7 + 8 + 7)/8 = 48/8 = 6
The median of the numbers; 4, 5, 5, 6, 6, 7, 7, 8 is 6, therefore
The numbers with the highest frequencies in the data set includes; 5, 6, and 7
The mean and the median of the data set are both 6, therefore, the value that best describes the data set is; 6
Data set C: 1, 4, 0, 2, 4, 4, 6, 7
The mode and the median of the data set are both 4
The mean of the data is; (1 + 4 + 0 + 2 + 4 + 4 + 6 + 7)/8 = 3.5
3.5 ≈ 4
The number that best describes the data is therefore; 4
Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11
The mean of the data set is; (7 + 8 + 10 + 11 + 8 + 9 + 10 + 9 + 11)/9 = 83/9
83/9 = 9 2/9
The median is obtained as follows; 7, 8, 8, 9, 9, 10, 10, 11, 11
The middle number, therefore, the median is 9
The number that best describes the data set is; 9
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in exercises 19\[dash]22, determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system.
19.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (1 h 4) must not be equal to zero. Therefore, h cannot be equal to -4. So, the value(s) of h that make the matrix a consistent linear system is any value other than -4.
20.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (6 8 4) must not be equal to zero. Therefore, h does not affect the consistency of the system. The matrix is always consistent, regardless of the value of h.
21.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (1 -4 3) must not be equal to zero. Therefore, h does not affect the consistency of the system. The matrix is always consistent, regardless of the value of h.
22.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (2 -3 -6) must not be equal to zero. Therefore, h does not affect the consistency of the system. The matrix is always consistent, regardless of the value of h.
In summary, in all four cases, h does not affect the consistency of the system, so the matrix is always consistent regardless of the value of h.
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A ball thrown upwards hits the roof , and come back to the ground .
upward function is F(x)= t2+3t +4
downword function is given with : F(x)= - 2 t2 +t+7
find hight of the roof from the ground . s is distance in meters ,and t is time , in seconds.
The height of the roof from the ground is given as follows:
7 meters.
How to obtain the height of the roof?The quadratic functions for the motions in this problem are given as follows:
Upward: F1(t) = t² + 3t + 4.Downward F2(t) = -2t² + t + 7.The ball is in the root at time zero of the downward motion, hence the height of the roof is obtained as follows:
F2(0) = -2(0)² + 0 + 7
F2(0) = 7 meters.
Which is the y-intercept of the function for the downward motion.
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Zachary purchased a computer for $1,400 on a payment plan. Five months afyer he purchased the computer, his balance was $625. seven months after he purchased the computer, his balance was $315. what is the equationt that models the balance y after x months?
Answer:
y=-140x I think so
Step-by-step explanation:
The following sequence of steps shows why you can square binomial the short way. For each step, name the definition or property that justifies the step.
(a+b)²
a. = (a+b)(a+b)
b. = (a +b)(a) + (a+b)(b)
c. = a² + ba + ab + b²
d. = a² + 2ab + b²
Answer:
a. definition of exponent
b. distributive property
c. distributive property
d. combining like terms
Step-by-step explanation:
You want the properties that justify the steps on expanding the square of a binomial.
a. = (a+b)(a+b)The factor is repeated a number of times equal to the exponent. This is the definition of an exponent.
b. = (a +b)(a) + (a+b)(b)The first factor multiplies each term of the second factor. This is an example of the distributive property.
c. = a² + ba + ab + b²The second factor multiplies each term of the first factor. This is an example of the distributive property.
d. = a² + 2ab + b²Terms ba and ab are combined. This "collecting terms" essentially makes use of the commutative property of multiplication and the distributive property:
ba +ab = ab +ab . . . . . commutative property of multiplication
ab +ab = (1 +1)ab . . . . . distributive property
= 2ab . . . . . . . properties of integers
which of the following is the probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is: a.0.05 b.0.13. c.0.22. d.0.35. e.0.40
The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is 0.22. This means that out of 100 cars, the company will have to pay a claim of at least $4000 for 22 of them.
Step 1: Determine the probability of the insurance company having to pay a claim of at least $4000 for a randomly selected car.
Step 2: Calculate the number of cars out of 100 that will have a claim of at least $4000.
Step 3: Divide the number of cars with a claim of at least $4000 by 100 to get the probability.
The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is 0.22. This means that out of 100 cars, the company will have to pay a claim of at least $4000 for 22 of them. To calculate this probability, we first need to determine the number of cars out of 100 that will have a claim of at least $4000. Then, we divide this number by 100 to get the probability of the insurance company having to pay a claim of at least $4000 for a randomly selected car. This is a useful measure for the insurance company, as it tells them how likely it is that they will have to pay out a claim of at least $4000 for a randomly selected car.
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4. Alfonso surveyed several students in his school. He asked them to give the grade that they are in and the number of pets they have at home. The results are shown in the table below.
Survey Results
Grade
5
6
2
1
4
2
4
1
4
3
17
5
Number of
Pets
0
4
2
3
5
1
2
2
0
5
2
Find the correlation coefficient for the data. Round to the nearest hundredth
Answer:
0.35
Step-by-step explanation:
To find the correlation coefficient, we can use the formula:
r = (n * Σ(x * y) - Σx * Σy) / √((n * Σx^2 - (Σx)^2) * (n * Σy^2 - (Σy)^2))
where n is the number of data points, x is the grade, y is the number of pets, Σx is the sum of grades, and Σy is the sum of the number of pets.
To use this formula, we first need to find the sum of the grades and the sum of the number of pets from the data in the table.
Grade Number of Pets
5 0
6 4
2 2
1 3
4 5
2 1
4 2
1 2
4 0
3 5
17 2
sum of grades = 5+6+2+1+4+2+4+1+4+3+17+5 = 49
sum of number of pets = 0+4+2+3+5+1+2+2+0+5+2 = 26
Now we can substitute these values into the formula along with n = 12, the number of data points in the table:
r = (12 * (50 + 64 + 22 + 13 + 45 + 21 + 42 + 12 + 40 + 35 + 172 + 52) - (49*26)) / √((12 * (5^2 + 6^2 + 2^2 + 1^2 + 4^2 + 2^2 + 4^2 + 1^2 + 4^2 + 3^2 + 17^2 + 5^2) - 49^2) * (12 * (0^2 + 4^2 + 2^2 + 3^2 + 5^2 + 1^2 + 2^2 + 2^2 + 0^2 + 5^2 + 2^2) - 26^2))
Which after some calculation give us r=0.35,
So the correlation coefficient for the data is approximately 0.35.
1. How many feet long is the space Mr. Hamilton wants to fill with pictures?
2. Convert this length to inches.
3. How many pictures will Mr. Hamilton use? Explain how you found your answer
4. How would your answer change if the pictures were 10 inches wide? Explain
The 9.75 ft wide wall and the 5.75 feet window in the center, through the use of unit conversion
1. The space to fill 4 feet
2. 4 feet = 48 inches
3. 8 pictures
4. Tne new number of pictures with 10 inches width is 4 pictures
Whart is unit conversion?Unit conversion is the expression of the same quantity, using different a different unit of measurement
Part of the question obtained from a similar question includes;
The width of the wall Mr. Hamilton decorates with pictures = 9.75 ft
The width of the window at the center of the wall = 5 3/4 feet = 5.75 ft
Location of the window = The center of the wall
Location Mr. Hamilton will fill with the pictures = Left and right sides of the window
The width of each pictiure of a president = 6 inches
1. The length of the space Mr. Hamilton wants to fill with pictures = 9.75 ft - 5.75 ft = 4 ft.
2. The unit convertion factor from feet to cm is;1 ft = 12 inches
Therefore, 4 feet = 4 ft × 12 inches/ft = 48 inches
3. The number of pictures Mr. Hamilton will use, n, is therefore;
n = 48 inches/(6 inches/picture) = 8 pictures
The number of pictures Mr. Hamilton can use for decorating by placing pictures of presidents on the wall is 8 pictures
4. The responses to the questions if the dimensions of the picture are 10 inches are;
The space remains 4 ft4 ft = 48 inchesThe number of pictures = 40 inches ÷ 10 inches/picture = 4 picturesLearn more unit conversion here: https://brainly.ph/question/2782422
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Select the reason that justifies the step.
The correct justification to each box. The answer is 2(y − 5) + 4 = 4 given.
What is meant by box ?
A box is a type of container used to hold or convey its contents. The sides of most boxes are flat, parallel, and rectangular. Boxes come in all sizes and can be used for everything from functional to ornamental purposes.Boxes can be built from a wide range of materials, including strong ones like wood and metal and weaker ones like corrugated fiberboard and paperboard. Boxes made of corrugated metal are frequently used as shipping containers.Although rectangular prisms are the shape that boxes most frequently take, other shapes are also possible. Informally, rectangular prisms are frequently referred to as "boxes."To the complete questions is;
Drag the correct justification to each box.
2(y−5)+4=4
2y−10+4=4 []
2y−6=4 []
2y=10 []
y=5 []
2y − 10 + 4 = 4 Distributive Property
2y − 6 = 4 Addition
2y = 10 Addition Property of Equality
y = 5 Division Property of Equality
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