Answer:
Step-by-step explanation: make a table of values, followed be a column for the 1st and another for the 2nd difference
0 0
1 1 -- 1
2 4-- 3 -- 2
3 9 --5 -- 2
4 16 --7 -- 2
5 25 --9 --2
6 36 ------- etc
looks like the 2nd difference is 2
For the vectors u = (-4,-1) and v= (1,3), express u as the sum u=p+n, where p is parallel to v and n is orthogonal to v. + 7 21 33 11 u=p+n= 10 10 10 10 (Type integers or simplified fractions. List the terms in the same order as they appear in the original list.)
The vector u can be expressed as a sum of n and p when n= (-33/10, 11/10) and p= (-7/10, -21/10).
To find the vector p that is parallel to v, we need to project u onto v. We can use the formula for projection:
p = (u . v) / (||v||^2) * v
where . represents dot product and ||v|| represents the magnitude of v.
First, we need to find the dot product of u and v:
(-4,-1) . (1,3) = -4*1 + -1*3 = -4 + -3 = -7
Next, we need to find the magnitude of v:
||v|| = sqrt(1^2 + 3^2) = sqrt(1 + 9) = sqrt(10)
Then, we can plug these values into the projection formula:
p = (-7) / (sqrt(10))^2 * (1,3) = (-7/10) * (1,3) = (-7/10, -21/10)
So the vector p that is parallel to v is (-7/10, -21/10)
To find the vector n that is orthogonal to v, we can subtract p from u:
n = u - p = (-4,-1) - (-7/10, -21/10) = (-4 + 7/10, -1 + 21/10) = (-33/10, 11/10)
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Write each proof. Finish the table.
[tex]\overline{AB}[/tex]1) The proof for to show that ΔJKN ≅ΔMKL is given as follows:
Given:
∠N≅∠L
[tex]\overline{JK}[/tex] ≅ [tex]\overline{MK}[/tex]
Thus,
ΔJKN ≅ΔMKL:
Reason: Angle - Angle - Side Theorem
Note that Vertical ∡s are ≅ (Congruent)
2) Given:
[tex]\overline{DE}[/tex] || [tex]\overline{FG}[/tex]
∠E ≅ ∠G
Since
[tex]\overline{DE}[/tex] || [tex]\overline{FG}[/tex], it means that ∠EDF ≅ ∠GFD, is because Alternate Angles of parallel lines are ≅ (Congruent). Given that ∠E ≅ ∠G. On the basis of reflexive property, [tex]\overline{DF}[/tex] ≅ [tex]\overline{FD}[/tex].
Hence, by the rule of Angle - Angle - Side, ΔFDE ≅ΔDFG.
In geometry, the reflexive property of congruence asserts that every angle, line, and figure/shape is congruent to itself.
This characteristic is commonly utilized in proofs such as establishing two triangles are congruent and parallel lines are parallel.
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If $1,800 gains $882 in interest in seven years, what was the interest rate per year?
Answer:
rate = 7%
Step-by-step explanation:
From the question
Principal = $1,800
Time = 7 years
simple interest = $882
Rate = ?
rate = 100 × ST
P × T
rate = 100 × $882
$1,800 × 7
rate = $88200
12,600
rate = 7%
PLSSS HELP IF YOU TURLY KNOW THISSSS
Answer:
x = 16Step-by-step explanation:
x - 5 = 11x = 11 + 5x = 16-Hope this helps!
Answer: x = 16
Step-by-step explanation:
To solve for x, add 5 and 11.
5 + 11 = 16
16 - 5 = 11
x = 16
The price of the computer was $52 on the day he bought it. The next day it had been marked up by 40%. What was the new price after the sale?
Answer:
72.8
Step-by-step explanation:
52*1.4=72.8
Answer: $70.80
Step-by-step explanation:
This is a two-step equation. First, you need to find what 40% of 52 is. You do this by multiplying 52 by 0.40. Then you would get the answer 20.8, but that isn't the final answer. Next, you add 52 and 20.8 together to get the final solution.
a. Find the scale factor from triangle JKL to triangle PQR.
b. List all pairs of corresponding angles.
c. Write the ratios of the corresponding side lengths in a statement of proportionality.
a. The scale factor is: 3/2
b. The pairs of corresponding angles are, <J and <P; <K and <Q; <L and <R.
c. The ratios are: JK/PQ = KL/QR = JL/PR.
How to Find the Scale Factor?The scale factor, also known as the ratio of similitude, is used to describe the relationship between the size of two similar figures. It is the ratio of the corresponding measurement of the new figure to the original figure.
a. scale factor from triangle JKL to triangle PQR = PQ/JK
= 9/6
= 3/2
b. The pairs of corresponding angles are:
<J and <P
<K and <Q
<L and <R
c. The ratios of the corresponding side lengths in a statement of proportionality will be: JK/PQ = KL/QR = JL/PR.
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If f(x)= 3x+2 and g(x)= x2−x find the value of g(-6)
The value of g(-6) is 42
What is a linear function?A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
For example if f(x) = 3x-2, the value of f(3) is derived by substituting 3 for x In the function. Therefore f(x) = 3(3) -2 = 9-2 = 7
Similarly to solve g(-6) we substitute -6 for x in the function
g(-6) = -6² -(-6)
g(-6) = 36 + 6
g(-6) = 42
therefore the value of g(-6) = 42
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In each question, lines AI and GJ are parallel and intersected by the transversal line FE.
Angles EBI and BCJ are corresponding angles. Use a transformation that takes angle EBI to angle BCJ to prove that corresponding angles are congruent
Angle EBI and angle BCJ are congruent is proved as follow.
To prove that corresponding angles are congruent, we can use the transformation that takes angle EBI to angle BCJ.
First, we place angle EBI in the plane.Next, we use a transformation, such as a translation or rotation, to move angle EBI to the position of angle BCJ.Since the transformation preserves the angle measure and the angles have been superimposed on each other, we can see that angle EBI and angle BCJ have the same measure.Therefore, we can conclude that corresponding angles are congruent.
Alternatively, we can use the fact that if two lines are parallel, then the alternate interior angles are congruent and corresponding angles are congruent. Since AI and GJ are parallel, angle EBI and angle BCJ are congruent.
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What is an equation of the line that passes through the point
(
−
2
,
−
3
)
(−2,−3) and is parallel to the line
4
�
−
�
=
1
4x−y=1?
Answer:
To find an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1, we know that the slope of the line we are looking for must be the same as the slope of the line 4x-y = 1. We can find the slope of 4x-y = 1 by rearranging it to the slope-intercept form y = mx + b.
4x - y = 1
y = -4x + 1
The slope of this line is -4
Now that we know the slope of the line we are looking for is -4, we can use the point-slope form of a linear equation, which is:
y - y1 = m (x - x1)
where (x1, y1) is a point on the line, and m is the slope.
We know that the point (-2, -3) is on the line we are looking for, so we can substitute these values into the point-slope form:
y - (-3) = -4 (x - (-2))
y + 3 = -4x + 8
y = -4x + 5
So an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1 is y = -4x + 5.
Jack pin a fair ix-ided pinner 240 time. What i the probability that he will core more than 45 ixe?
Give your anwer to 2 d.p.
The probability of scoring more than 45 ixe is 0.91. P(X<=45) = (240C0 * (1/2)^0 * (1/2)^240) + (240C1 * (1/2)^1 * (1/2)^239) + (240C2 * (1/2)^2 * (1/2)^238) + ... + (240C45 * (1/2)^45 * (1/2)^195)
P(X<=45) = 0.0909
The probability of scoring more than 45 ixe can be calculated by using the Binomial Probability formula.
The formula is: P(X>45) = 1 - P(X<=45)
Where P(X<=45) is the probability of scoring 45 or less ixe.
P(X<=45) = (240C0 * (1/2)^0 * (1/2)^240) + (240C1 * (1/2)^1 * (1/2)^239) + (240C2 * (1/2)^2 * (1/2)^238) + ... + (240C45 * (1/2)^45 * (1/2)^195)
P(X<=45) = 0.0909
Therefore, P(X>45) = 1 - 0.0909 = 0.9091
The probability of scoring more than 45 ixe is 0.91 (to 2 d.p.).
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a person or object that is a member of the group being studied.
A population is a person or object that is a member of the sample being studied while a sample is the entire group that is being studied.
In a research study, a sample is a relatively small group of people from whom data is collected. The population is the bigger group to whom the information is then generalized.
All citizens, whether they are living there permanently or are only visiting, are referred to as the "people."
This indicator shows the average population density of a given area. The annual population fluctuations brought on by births, deaths, and net migration are known as growth rates.
A population is any large group that has at least one attribute in common. Not all populations are made up of people.
Populations can include, but are not limited to, people, animals, groups, organizations, buildings, houses, trucks, farms, and things.
Of the 7.8 billion people on the planet, 1%, or around 78 million individuals, would be there. One percent of the 7.8 billion people on the planet, or 78 million people, live there.
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Complete question -
A person or object that is a member of the group being studied is called ______.
Help!!
Find the value of x
A. X=2
B. X=3
C. X=4
D. X=6
The value of x is 3. Option B
How to determine the valueIt is important to note that the given shape is a parallelogram.
The properties of a parallelogram are;
Opposite sides of the parallelogram are parallelOpposite sides are equalOpposite angles are equalThe interior angles are supplementaryDiagonal of a parallelogram separates it into two congruent trianglesThe diagonals of a parallelogram bisect each other at right angleNow, let's equate the sides, we have;
4x - 1 = 6x - 5
collect like terms
4x - 6x = -5 -1
Subtract like terms
-2x = -6
Make 'x' the subject of formula
x = -6/-2
x = 3
Hence, the value is 3
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. Describe the association between the two sets of
data in the scatter plot.
The association between the two sets of data in the scatterplot is; Positive.
What is the association of the scatterplot?A scatter plot is a graph that shows the association that exists between two variables. A scatter plot matrix shows all the pairwise scatter plots for a lot of variables.
Now, If the variables tend to increase and decrease together, the association is said to be positive. However, If one variable tends to increase as the other decreases, then the association is said to be negative. Finally, If there is no pattern, then the association is said to be zero.
When a straight line is used to describe the relationship between the variables, then the association is said to be linear. When a constantly increasing or decreasing nonlinear function describes the relationship, the association is monotonic.
The scatterplot given shows us that the association is positive as increasing x values lead to increasing y values.
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the ratio of the length to the width to the height of a rectangular solid is 10 to 4 to 1, and the total surface area of the rectangular solid is 972. what is the volume of the rectangular solid?
Using the information in the issue and the formulas for the total surface area and volume of a rectangular solid, we can determine the volume of the rectangle solid in detail.
First, we calculate the rectangular solid's overall surface area using the following formula:
2(lw + lh + wh) = 972
Where the rectangular solid's dimensions are l for length, w for width, and h for height.
We can describe the three sides in terms of x, so that l = 10x, w = 4x, and h = x, since the ratio of the length to the breadth to the height is 10:4:1.
Now, we change the variables in the equation for the total surface area to match these values:
The formula is 2(lw + lh + wh) = 2(10x * 4x + 10x * x + 4x * x) = 972.
The equation will become more precise and give us:
80x^2 = 972
x^2 = 12.15
x = 3.5
Now that we have one side's value (height), we can use the following formula to get the solid's volume:
V = lwh
V = (10x)(4x)(x)
V = 40x^3
V = 40 * (3.5)^3
V = 40 * 42.875
V = 1715 cubic units
As a result, the rectangular solid has a volume of 1715 cubic units.
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One year Roger had the lowest ERA​ (earned-run average, mean number of runs yielded per nine innings​ pitched) of any male pitcher at his​ school, with an ERA of 3. 14. €‹Also, Amber had the lowest ERA of any female pitcher at the school with an ERA of 3. 38. For the​ males, the mean ERA was 4. 371 and the standard deviation was 0. 787. For the​ females, the mean ERA was 4. 363 and the standard deviation was 0. 869. Find their respective​ z-scores. Which player had the better year relative to their​ peers, Roger or Amber​? ​(Note: In​ general, the lower the​ ERA, the better the​ pitcher. ) Roger had an ERA with a​ z-score of nothing. Amber had an ERA with a​ z-score of nothing
The z-score is greater in the case of Amber than in Roger so Amber had a better year relative to their peers.
First for Roger:
We have
Mean, μ = 4.371
Standard deviation, s = 0.787
so z-score for X = 3.14 will be
z = (X-μ)/s = (3.14 - 4.371)/0.787
or z = -1.564
Now In the case of Amber:
We have
μ = 4.363
s = 0.869
X = 3.38
so z = (X-μ)/s = (3.38 - 4.363)/0.869
or z = -1.131
Therefore, The z-score is greater in the case of Amber than Roger so Amber had a better year relative to their peers.
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1) Mean 12, 12, 16, 11, 19, 18, 10 Median: Mode: Range:
what part of an hour is 45 minutes
1. Jake is reading a book for a class assignment. He creates a plan to read the book over an 8 day
period. Use the table below to create a graph of this accounts. Y
Day's
0
2
4
6
8
Pages
Read
0
54
108
162
216
a. What does x represent?
b. What does y represent?
c. Describe the slope of the line.
What does it represent?
d.what is the slope?
The analysis of the data in the table, which is a linear relationship between the pages Jake reads to the number of days is as follows;
1. Please find attached the graph of the data in the table created with MS Excel
a. The variable x represents the number of days Jake reads the book
b. The variable y represents the number of pages Jake reads
c. The slope is the rate of change of the pages Jake reads to the number of days he has been reading the book
d. The slope is 27 pages per day
What is a linear relationship?A linear relationship is a relationship that has a straight line graph when plotted on the coordinate plane.
1. The data in the table are presented as follows;
Days[tex]{}[/tex] Pages Read
0[tex]{}[/tex] 0
2[tex]{}[/tex] 54
4[tex]{}[/tex] 108
6[tex]{}[/tex] 162
8[tex]{}[/tex] 216
Please find attached the graph created with the above data in the table for the Days and the number of Pages Jake read, created with MS Excel.
a. The input variable is normally represented by x, while the output variable is normally represented by y.
The input variable, which is the variable that determines or indicates the number of pages Jake reads is the number of days, therefore;
The value of x represents the number of days
b. The output variable obtained from the input variable which is the number of days is the number of books Jake reads, therefore;
The output variable, y, represents the number of books Jake reads
c. The slope is the rate of change of the number of pages Jake reads per unit time. Therefore, the slope represents the number of pages Jake reads per day.
d. The graph of the data in the table indicates that the relationship is a straight line relationship,the slope can therefore be obtained using two points as follows;
Slope, m = (108 - 0)/(4 - 0) = 27
The slope of the line is 27 pages per day
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Olivia flips a coin and rolls a number cube with sides labeled 1, 2, 3, 4, 5, and 6. After 90 trials of the experiment, the relative frequency of flipping heads and rolling a number less than 3 is 2/15 . What is the difference between the number of expected outcomes and the number of actual outcomes?
Answer:
3
Step-by-step explanation:
Experimental probability is based on the actual outcomes of an experiment (gathered by experimenting repeatedly).
Theoretical probability is based on the possible outcomes (expected outcomes).
Probability formula
[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Theoretical probability of flipping a head
A coin has two sides: one side is a "head", the other side is a "tail".
The number of ways flipping a head can occur is 1.
The total number of possible outcomes is 2.
Therefore, the theoretical probability of flipping a head is 1/2.
Theoretical probability of rolling a number less than 3
The cube has six sides labelled 1, 2, 3, 4, 5 and 6.
The number of ways that rolling less than 3 can occur is 2 (rolling 1 or 2).
The total number of possible outcomes is 6.
Therefore, the theoretical probability of rolling a number less than 3 is 2/6 = 1/3.
Therefore, the theoretical probability of flipping a head and rolling a number less than 3 is:
[tex]\sf P(head)\; and\; P(X < 3)=\dfrac{1}{2} \times \dfrac{1}{3}=\dfrac{1}{6}[/tex]
To calculate the number of actual outcomes and expected outcomes after 90 trials, multiply the number of trials by the probability for each outcome:
[tex]\textsf{Number of actual outcomes}=90 \times \dfrac{2}{15}=12[/tex]
[tex]\textsf{Number of expected outcomes}=90 \times \dfrac{1}{6}=15[/tex]
Therefore, the difference between the number of expected outcomes and the number of actual outcomes is:
[tex]\implies 15-12=3[/tex]
Note: If Olivia continued to flip the coin and roll the number cube, as the number of trials increased, we would expect the experimental probability of 2/15 to get nearer to the theoretical probability of 1/6 and so the difference between the number of actual and expected outcomes would become smaller.
solve the inequality 7/2 is greater than or equal to b + 9/5
Answer: b ≤ 17/10
Step-by-step explanation:
7/2 ≥ b + 9/5
7/2 - 9/5 ≥ b
17/10 ≥ b
b ≤ 17/10
Which value is equal to 2 square root 98 times square root 2?
The value of the expression is 28
How to determine the value of the expressionFrom the question, we have the following parameters that can be used in our computation:
2 square root 98 times square root 2
Express properly
So, we have the following representation
2√98 * √2
Evaluate the products
This gives
2√196
Take the square root of 196
2 * 14
So, we have
28
hence, the solution is 28
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Evaluate 11.5x+10.9y when x=7 and y=8.
Answer: 167.7
Step-by-step explanation:
Step 1:
Substitute
11.5(7) + 10.9(8)
Step 2:
Multiply:
80.5 + 87.2
Step 3:
Add:
167.7
167.7
Step-by-step explanation:Variables are letters within math that represent numbers.
The Expression
The question above is written as an expression. An expression is a mathematical statement that does not contain an equal sign. This is an expression because it's an addition statement without an equal sign.
Within the expression, there are 2 variables. Both x and y are variables because they're letters within the expression that are intended to represent numbers.
Solving the Expression
Now, to solve the expression we can plug the numbers we were given for each variable.
11.5(7) + 10.9(8) = 167.7So, the answer to the expression 167.7.
In parallelogram lmno, what is the measure of angle m? 20° 60° 80° 100°
In parallelogram lmno measure of angle m m∠M = 80°
In a parallelogram, opposite sides and opposite angles are congruent to each other.
⇒ m∠N = m∠L and m∠M = m∠O ..........(1)
Also, the sum of any two consecutive angles of a parallelogram is supplementary that is 180°
⇒ m∠M + m∠L = 180° ...........(2)
Now, using equation (1)
m∠N = m∠L
⇒ 5x = 3x + 40
⇒ 5x - 3x = 40
⇒ 2x = 40
⇒ x = 20
⇒ m∠N = m∠L = 5x = 100°
Now, from equation (2)
m∠M + m∠L = 180°
⇒ m∠M + 100 = 180
⇒ m∠M = 80°
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7-5p+3q when
�
=
1
p=1p, equals, 1 and
�
=
7
q=7q, equals, 7
The solution to the equation is 23
How to determine the solution to the expression?From the question, we have the following parameters that can be used to solve the question
7 - 5p + 3q
Also, we have the following values
p = 1 and q = 7
Substitute the know values in the given expression, so we have the following representation
7 - 5(1) + 3(7)
Evaluate the products
This gives
7 - 5 + 21
Evaluate the like terms
23
Hence the solution is 23
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Parallel lines e and f are cut by transversal b.
Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees.
What is the value of y?
Using the congruency of the top-right angles, it is found that the value of y is of 130.
What are parallel lines ?
Parallel lines can be defined as the lines which are equi distant from each other and they never intersect.
When two parallel lines are cut by a transversal, the top-right angles are congruent, that is, they have the same measure.
In this question, their measures are of (2x + 18)º and (4x - 14)º. Thus, with this, we can find x:
4x-14 = 2x+18
4x-2x = 18+14
2x = 32
x = 32/2
x = 16
Thus, the measure of the top right angles is given by, in degrees:
4x-14 = 4*16 - 14 = 64 - 14 = 50
The top-right and the bottom-right angles are supplementary, that is, the sum of their measures is 180º.
The measure of the top-right angle is of 50º.
The measure of the bottom-right angle is of y.
Thus:
y + 50 = 180
y = 180 - 50
y = 130
Hence, The value of y is of 130.
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if one full-time student who is a freshman or sophomore is selected at random, what is the probability that the student will be a student who lives on campus?
The probability that the student will be a student who lives on campus is 0.24
In math the term probability is referred as the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
Here we have given that one full-time student who is a freshman or sophomore is selected at random.
Here we need to find the probability that the student will be a student who lives on campus.
Here we know that the probability that a student is a sophomore is calculated as,
=> P(S) = 19/42 = 0.45.
Whereas the probability that a student has a freshman is calculated as,
=>P(H)=25/42=0.6.
Then the probability that the student will be a student who lives on campus is calculated as,
=> P(H∩S)=P(S)+P(H)−P(S∪H)
Apply the values then simplify this one then we get,
=> 0.45+0.6−(42−8)/42=0.24
Complete Question:
Suppose that a certain college class contains 42 students and then if one full-time student who is a freshman or sophomore is selected at random, what is the probability that the student will be a student who lives on campus?
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Given that a = 8 cm and b = 21 cm, work out A rounded to 1 DP.
Given that a = 8 cm and b = 21 cm, the value of A is 20.9 degrees
How to work out the measure of AThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
a = 8 cm and b = 21 cm
Using the tangent function, we have
tan(A) = a/b
So, we have
tan(A) = 8/21
Evaluate
tan(A) = 0.3810
Take the arctan of both sides
A = 20.9 degrees
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What is 16.281 rounded to the nearest whole number?
Answer:
16.281 rounded to the nearest whole number is 16.
This is because since 2 in the tenths place is bellow 5, the 16 will not round up to 17, and remain the same.
Step-by-step explanation:
Hope it helps! =D
A shipping crate holds 20 shoeboxes. The dimensions of a shoebox are 6“ x 4“ x 12“. For numbers 1a-1c, write the number that makes the sentence true.
1a. Each shoebox have a volume of____ cubic inches.
1b. Each crate has a volume of about _____ cubic inches.
1c. If the crate could hold 27 shoeboxes, the volume of the crate would be about____ cubic inches.
a. Each shoebox has a volume of 288 cubic inches.
b. Each crate has a volume of about 5,760 cubic inches.
c. If the crate could hold 27 shoeboxes, the total volume would be of about 7,776 cubic inches.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism is obtained by the multiplication of the dimensions of the prism.
Hence the volume of the box in this problem is of:
6 x 4 x 12 = 288 cubic inches.
For the crates, we have that:
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Answer:
A.288
B.5,760
C.27 shoeboxes
Step-by-step explanation:
Helen has to buy all the butter she needs to make 60 biscuits.
She buys the butter in 250 g packs.
What is the exact amount of butter she needs?
For making of 60 biscuits the quantity and packs of butter required by Helen is :
a. The exact amount of butter is 480 grams to make 60 biscuits.
b. Number of packs of butter Helen needs to buy is 2 packs.
Amount of sugar need to make 15 biscuits = 60 grams
Flour is three time of sugar to make 15 biscuits = 60 × 3
= 180 grams
Amount of flour to make 60 biscuits = 180 × 4
= 720 grams
Butter is two times as sugar to make 15 biscuits= 60 × 2
= 120grams
a. Exact amount of butter to make 60 biscuits is:
Butter required to make 60 biscuits = 120 × 4
= 480 grams
b. One pack is of 250 grams
Number of packs of butter she need to buy = 480 / 250
= 1,92
≈ 2packs
Therefore, the quantity of butter and number of packs of butter is given by :
a. The exact amount of butter required to make 60 biscuits is 480 grams.
b. The number of packs she needs to purchase is 2 packs.
The above question is incomplete, the complete question is :
Helen has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250g packs.
(i) What is the exact amount of butter she needs?
(ii) How many packs of butter will she have to buy?
Figure is attached.
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