If Lisa and Joey put the same amount of money every month in the savings account for David's future and the situation is plotted in a graph where time is on the x-axis, then there will be straight line with a constant slope.
As per the question statement, Lisa and Joey just became parents to their son, David and they decided to start a savings account for their newborn's future, where they agreed to put an equal amount of money every month.
We are required to determine the condition of the variables if the above-mentioned situation is plotted into graph and the account gets constantly filled with money as David grows older.
To solve this question, first let us consider the time to be plotted on the X-axis (As mentioned in question statement that "Time" is almost always on the x-axis) and the money collected to be plotted on the Y-axis.
Since, an equal amount of money is put into the account every month, therefore, taking 1 month as unit time to plot our graph, the money will grow diagonally in a straight line with a constant slope. Hence, both the variables (abscissa and ordinates) will increase on a constant ratio along the first quadrant.
Slope of a Line: In mathematics, the slope or gradient of a line is a value that describes both the direction and the steepness of the line and is calculated by the change in y coordinate with respect to the change in x coordinate.To learn more about Slope of a Line, click on the link below.
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Is the study experimental or observational?A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided.(A) ExperimentalB) Observational
Answer:
B) Observational
Explanation:
Observational studies are studies where the researchers only observe the variables and don't make changes. When the political pollster reports the percentage, it only observes the decision of the people but they can't change what makes a person select one candidate or the other.
Janelys has a points card for a movie theater. She receives 20 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs at least 165 points for a free movie ticket.
The inequality shows that the number of visits that Janelys needs at least 165 points for a free movie ticket is 12.
How to calculate the number of visits?From the information, Janelys has a points card for a movie theater and she receives 20 rewards points just for signing up and earns 12.5 points for each visit to the movie theater.
The number of visits that are needed to earn at least 165 points will be illustrated as x. This will be:
20 + 12.5x >= 165
Collect like terms
12.5x >= 165 - 20
12.5x >= 145
Divide
x >= 145 / 12.5
x >= 11.6
Therefore, she needs at least 12 visits.
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Janelys has a points card for a movie theater. She receives 20 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs at least 165 points for a free movie ticket. How may visits are needed?
Solve the equation for y. Then find the value of y for each value of x. 3x - 5y = 19; x = -1, 0, 1
please help me
Answer: y = -4.4
y = -3.8
y = -3.2
Step-by-step explanation:
What is the value of x?
(2x - 5)°
n
l
m 45°
Answer: x = 70
Step-by-step explanation: the sum of the angle 2x-5 and 45 deg should equal 180 deg, so 2x-5 should be equal to 135 because 180 - 45 = 135
So 2x -5 = 135. Add 5 to both sides to cancel it out. 2x = 140. divide both sides by 2 to cancel 2 on x. Answer is X=70
I think this is how you do it lol but I don't know for sure.
HELPPPPPPPP
What is the slope of the line?
Answer:
3
Step-by-step explanation:
The points J(-6, 0), K(3, 0), L(7, 8), and M(-2, 8) form parallelogram JKLM.
Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter
of the parallelogram. Round your answer to the nearest tenth if necessary.
Answer:
72[tex]units^{2}[/tex]
Step-by-step explanation:
See pictures
Rope A is 25 times as long as Rope B and Rope
B is 18 times as long as Rope C. If Rope A is
3,600 cm long, how long is Rope C?
Answer:
Step-by-step explanation:
A=25xB
B=18xC
A=3600cm
B=A/25
B=3600/25
B=144
C=B/18
C=144/18
C=8
Solve the following equation for x = 5.
Answer: 5= 4x + 8
-8 -8
-3= 4x
the answer is x = 0.75
i don't know if I'm right if I am not I am sorry
Compare the two groups of data. which statement is true?
The true statement is the range of Mrs Plum's class is 14 greater than the range of Mr Scarlet's class.
What is the range?A box plot is a graph that is used to describe a dataset. A box plot is made up of two lines and a box. The two lines are known as whiskers.
The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the whiskers is the range.
Range is used to measure the variation of a dataset. It is the difference between the maximum number and the minimum number.
Range = maximum number - minimum number
Range of Miss Scarlet's class = 98 - 65 = 33
Range of Miss Plum's class = 98 - 51 = 47
Difference in range = 47 - 33 = 14
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The function f(x) = |x+3| is transformed by the following transformations to a new function g(x):
A translation 2 units down.
A translation 1 unit to the right.
Reflection across the x-axis.
What is the equation of the new function g(x)?
The equation of the new function g(x) is g(x) = 2 - |x+2|
Transformation of functionTransformation is. way of changing the position of an object on an xy-plane.
Given the parent function f(x) = |x+3|.
If the function is translated 2 units down and 1 unit right, then the resulting function will be |x+3 - 1| - 2 which is equivalent to |x+2| - 2
The reflection of the resulting function across the x-axis is given as:
g(x) = -(|x+2|-2)
g(x) = 2 - |x+2|
Hence the new function g(x) if the parent function undergo the transformation is g(x) = 2 - |x+2|
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Simplify the following expression completely.
(√10 - √9)²
An operation in mathematics is a function that converts 0–n parameters or operands into a definite output value. The complexity of the operation depends on how many operands there are. The expression is equal to -5.97.
What are mathematical operations?An operation in mathematics is a function that converts 0–n parameters or operands into a definite output value. The complexity of the operation depends on how many operands there are.
The operations that are most frequently studied are binary operations (i.e., operations of arity 2), which include addition and multiplication, and unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse. A zero-arity operation, also known as the nullary operation, is a constant. An illustration of a ternary operation, also known as an operation of arity 3, is the mixed product.
Usually, it is considered that the arity is constrained. Even so, infinitary operations are occasionally considered, in which case the "normal" finite dimensionality operations are referred to as finiteary operations.
A partial operation is described as being similar to an operation but using a partial function in place of a function.
[tex](a-b)^{2} = a^{2}+b^{2}-2ab[/tex]
[tex](\sqrt{10} - \sqrt{9})^{2}[/tex])= [tex](\sqrt{10}) ^{2} + (\sqrt{9) } ^{2} - 2* \sqrt{10} * \sqrt{9}[/tex]
= 10+ 9- 18.97
=-5.97
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someone help me please
Answer:
(x + 2)² - 11, so a = 2 and b = 11
Which is NOT a solution for 5-2x ≥-3?
A 0
B 2
C 4
D 5
Answer:
D 5
Step-by-step explanation:
Solve the inequality
5-2x ≥-3
Subtract 5 from each side
5-2x-5 ≥-3-5
-2x ≥-8
Divide by -2, remembering to flip the inequality
-2x/-2 ≤-8/-2
x ≤4
The only number not less than or equal to 4 in the choices is 5.
5 is not a solution
Answer:
Answer D is correct
Step-by-step explanation:
First, let us solve for x.
[tex]5 - 2x \geqslant - 3[/tex]
First, subtract 5 by both sides.
[tex] - 2x \geqslant - 3 - 5 \\ - 2x \geqslant - 8[/tex]
Divide both sides by -2.
[tex]x \leqslant 4[/tex]
Remember that, when you divide or multiply both sides by a negative number it change the direction of the inequality sign.Now, let us identify the equality sign and write the solutions of it.
[tex] \sf \leqslant \: \: \rightarrow \: \: x \: is \: less \: than \: or \: equals \: to \: 4[/tex]
Solutions
x = { 4, 3, 2, 1, 0...}
Accordingly, as 5 is greater than 4, 5 is not a solution for this given inequality.
this question is about random samples from the \text{uniform}(0,1)uniform(0,1) distribution. recall that for a sample of size mm from a \text{uniform}(0,1)uniform(0,1) distribution, the expected value of the largest value in the sample is:
the expected value of the largest value in the sample is:
np.random.uniform(0,1,100)
this question is about random samples from the uniform(0,1) distribution.
recall that for a sample of size mm from a uniform(0,1) distribution
the expected value of the largest value in the sample is:
np.random.uniform(0,1,100)
import numpy as np
pass the random uniform generated array into x
x = np random uniform(low, high, size)
here low = 0, high = 1, size = 100
x = no. random uniform(0,1,100)
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Ali and mohammad are playing football. Ali's score is twice the difference of muhammad's score and 6. the sum of their scores is 420. write and solve to find each student's football score
Football scores of Ali and Mohammad are 213 and 207 respectively.
Given,
Sum of Ali and Mohammad's football score is 420.
Difference between Ali's football score and Mohammad's football score is 6.
Then,
A - B = 6 ⇒Equation1
Where A = Ali's football score, and B= Mohammad's football score
Let's assume,
Ali's football score =
Mohammad's football score =
Sum of Ali's football score and Mohammad's football score:
A + B = 420 ⇒Equation2
After subtracting Equation2 from Equation 1
(A+B) - (A-B) = 420 - 6
A + B - A + B = 414
Since first A is positive and second A is negative, they will cancel out each other.
2B = 414
B = 207
After putting value of B in Equation2,
A + 207 = 420
A = 420- 207
A = 213
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Trigonometry, help!!
As per the tangent angle, the value of x in the given diagram is 7cm.
Tangent angle
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
Given:
Here we have the two right angled triangle, through this we have to identify the value of x.
According to the given question, we have a diagram with two right angled triangles.
Now, in the upper right angled triangle
tan 50° = opposite side / 5
⇒ 1.19 = 0pposite side/ 5
⇒ opposite side = 1.19 × 5
⇒ opposite side = 1.2 × 5
⇒ opposite side = 6cm
Now, the opposite side with respect to the angle 50 degrees in the upper right angle triangle is a adjacent side according to angle 38 degrees in the lower right angle triangle.
So, in the lower right angle triangle.
tan 38° = x / adjacent side
⇒ 0.78 = x/6
⇒ x = 0.78 × 6
⇒ x = 4.68
⇒ x = 7cm
Hence, the value of x in the given diagram is 7cm.
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PLEASE HELP!! It's easy i'm just Dum. Solve for x, look down below for more info.
By using the fact that the two angles are vertical angles, we will write and solve a linear equation to fine that the value of x is 20.
How to find the value of x?Here we assume that both of the horizontal lines are parallel. Then the two marked angles (the ones that depend of x) are vertical angles.
This means that the measure of these angles is the same one, then we can write:
(5x - 8)° = (3x + 32)°
So we can solve that linear equation to find the value of x, we will get:
5x - 8 = 3x + 32
Grouping like terms we get:
5x - 3x = 32+ 8
2x = 40
x = 40/2
x = 20
The value of x is 20.
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The weight of a shipment, y, is directly proportional to x, the reams of paper included. If a shipment of 3 reams of paper weighs 12 lbs, find the reams of paper in a shipment that weighs 96 lbs.
Step-by-step explanation:
y = kx
3 = k × 12
.: k = 12/3 = 4
Inputting that to when y = 96 Ibs.
We have:
96 = 4 × x
96 = 4x
.: x = 96/4
x = 24 realms.
Find the equation of a line that passes through the point (2,3) and has a gradient of 3.
Leave your answer in the form
ax+by=c
Where
a and b
and c are integers.
Answer:
-3x+y = -3
Step-by-step explanation:
First, I would write this in the point slop form of a line and the translate it into the standard form of a line.
[tex]y_{1}[/tex] - y = m([tex]x_{1}[/tex] -x) If the slope from of a line. Put in the x, y and the slope. You call the gradient, what I would call the slope.
y - 3 = 3(x -2) Distribute the 3
y - 3 = 3x -6 Subtract 3 from both sides
-3x + y - 3 = -6 Add 3 to both sides
-3x + y = -6
calculate a 95% confidence interval for a sample mean of 20 with a sample standard deviation of 10 and a sample size of 9. the answer should be accurate to the nearest decimal. given t
With a 95% confidence interval, the average is between 13.4667 and 26.5333.
Confidence interval is the measure of the degree of uncertainty or certainty in a sampling method. It is equal to the sample mean, plus or minus the margin of error (z value multiplied by standard deviation divide by the square root of the sample size).
CI = x ± z(σ/√n)
where CI = confidence interval
x = mean
σ = standard deviation
n = sample mean
z = z value at the confidence interval
The corresponding z value at 95% confidence interval is 1.96.
Substitute the given into the formula and solve for CI.
CI = x ± z(σ/√n)
CI = 20 ± (1.96)(10/√9)
CI = 20 ± (1.96)(10/3)
CI = 20 ± 6.5333
CI = (13.4667, 26.5333)
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84. the centers for disease control and prevention reported in 2012 that 1 in 88 american children had been diagnosed with an autism spectrum disorder (asd). a. if a random sample of 200 american children is selected, what are the expected value and standard deviation of the number who have been diagnosed with asd?
a) The expected value is calculated to be 2.273 and b) the standard deviation is 1.499 if a random sample of 200 children is selected.
According to the report 1 in 88 American children has been diagnosed with ASD, therefore the probability can be given as;
p = 1 / 88
a) the expected value can be calculated as follows;
E (X) = n × p
here n = sample size = 200
p = probability = 1 / 88
E (X) = 200 × 1 / 88
E (X) = 2.273
b) To find the standard deviation, first, we have to determine the variance of the random variable;
V (X) = n × q × p
V (X) = 200 × 87/88 × 1/88
V (X) = 2.2468 = 2.247
Now we can calculate the standard deviation as follows;
standard deviation = √V(X)
standard deviation = √2.247
standard deviation = 1.499
Therefore, the expected value and standard deviation are calculated to be 2.273 and 1.499 respectively.
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How do division properties help you evaluate expressions?
Drag a word or number to the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When the area of a fraction is equal to −1 and the numerator is nonzero, the value of the fraction is equal to the .
Options: numerator, opposite of the numerator, denominator, opposite of the denominator, 0
The complete statement is: 'When the denominator of a fraction is equal to -1, and the numerator is nonzero, the value of the fraction is equal to the opposite of the numerator of the fraction.'
In this question, we need to fill in the blanks for the statement 'When the _______ of a fraction is equal to -1, and the numerator is nonzero, the value of the fraction is equal to ______'
We know that, a fraction is represented as:
x/y
Where, x represents the numerator,
y represents the denominator
Assume that y = -1
Then the fraction becomes x/(-1) = -x
This means, if the numerator is nonzero, and the denominator is -1, then the fraction has a value opposite of the numerator
Therefore, the complete statement is: 'When the denominator of a fraction is equal to -1, and the numerator is nonzero, the value of the fraction is equal to the opposite of the numerator of the fraction.'
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josh wrote 483 out of an expected 500 words for his essay. How would this ratio be expressed in decimal form?
there are 12 zodiac signs. assume that each of the zodiac signs is equally likely. randomly pick 4 people from our class. what is the chance that none of the 4 people share your zodiac sign?
There is a 70.6% chance that none of the 4 randomly picked people share your zodiac sign.
Probability is a branch of mathematics in which we determine how likely an event is to happen. It is used when we are not sure about the result or outcome of an event so we consider the probabilities of certain outcomes.
In this case, there are 12 zodiac signs, out of which one is yours. So the probability or chance that the 4 randomly picked people do not share your zodiac sign can be determined as follows;
Probability of one person not having your zodiac sign: 11/12
Probability of 4 people not having your zodiac sign;
11/12 × 11/12 × 11/12 × 11/12 = 0.706
Converting it into percentage:
0.706 × 100 = 70.6%
Hence, the probability that none of the 4 people share your zodiac sign is calculated to be 70.6%.
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SOMEONE HELP PLEASE
a clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 6000 shirts can be sold at a price of $81, while 10,000 shirts can be sold at a price of $45. Give a linear equation in the form p = mn + b that gives the price p they can change charge for n shirts.
Answer: p = ____
The linear equation in the form p = mn + b that gives the price p they can change charge for n- shirts is; p = (9/1000)n - 9.
What is defined as the linear equation?A linear equation is really an algebraic equation with only a constant and the first-order (linear) term of the form y=mx+b, in which m is the slope and b is indeed the y-intercept.The above is sometimes regarded to as a "linear equation of two variables," in which y and x are the variables.As per the given question;
number of shirts = n
The charge per shirt = p.
The equation describing the relation is;
p = mn + b
The price of 6000 shirts = $81.
Put the value is equation;
81 = 6,000m + b .....eq 1
The price of 10,000 shirts = $45.
45 = 10,000m + b .....eq 2
Solving eq 1 and eq 2 by elimination method.
m = 9/1000
Put the value of m in eq 2 and find b.
b = -9
Now, put the value of b and m in the equation.
p = (9/1000)n - 9
Thus, the equation in the form p = mn + b that gives the price p they can change charge for n shirts is; p = (9/1000)n - 9.
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? Work out the surface area of the
cuboid.
10m
5m
2m
The surface area of the cuboid with the, height of the cuboid being 5m, the width being 2m, and the length being 10m is 160[tex]m^{2}[/tex]
What is the surface area of the Cuboid ?Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.
As we know:
Height =5m
Width= 2m
Length= 10m
T.S.A=2(LXW) + 2(LXH) + 2(WXH)
=2(10mx2m) + 2(10mx5m) + 2(2mx5m)
=(2x20m²) + (2x50m²) + (2x10m²)
=40m² + 100m² + 20m²
=160m²
Cuboid's surface area, which was determined using the formula 2lw+2lh+2hw, is 160 square meters.
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In the number 2,222.222, what is the difference between the 2 in the tens place and the 2 in the column to its left? a. the 2 in the tens place represents of what the 2 to its left represents. b. the 2 in the tens place represents of what the 2 to its left represents. c. the 2 in the tens place represents 100 times what the 2 to its left represents. d. the 2 in the tens place represents 10 times what the 2 to its left represents.
This questions is testing the knowledge on place value and total value.
The two to the left of the 2 in the tens place is 100 times larger than the 2 in the 100ths place in the value.
The total value of the 2 in the tens position is 20.
The total value of the 2 in the tenth position is 0.2.
To obtain the difference, divide the 20 in the tens position to the 2 in the tenths position.
20/0.2 = 100
the 2 in the tens place represents 100 times what the 2 to its left represents.
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O
Lines a and b are parallel Line c is perpendicular to both line a and line b. Which
statement about lines a, b, and c is NOT always true?
☐
The sum of the slopes of line b and line c is 0.
The product of the slopes of line a and line c is -1.
Ja
9
E
G
Line a and line b have the same slope.
The product of the slopes of line c and line b is -1.
The statement "The sum of the slopes of line b and c is 0" is not always true.
Given:
Lines a and b are parallel.
Line c is perpendicular to both line a and line b.
The statements "The product of the slopes of line a and line c is -1" and "The product of the slopes of line c and line b is -1" are both True.The reason is that a perpendicular line has a slope of -1 /m when one line has a slope of m. Alternatively put, the slopes are negative reciprocals of one another.
The statement "Line a and line b have the same slope" is true.This is because two lines that are parallel have the same slope.
The statement "The sum of the slopes of line b and c is 0" is false.This is because even if the two lines are perpendicular on adding their slopes together the outcome would not be 0. For instance, if b has a slope of 2, then c will have a slope of -1/2, and their sum will be 3/2.
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Musa is on the top of cliff which is 300m. looking down at the table which is 600m from the cliff. If the angle of depression is 30 degree, construct the diagram to represent the information.
The diagram for the angle of depression is constructed.
What is described as the angle of depression?The angle of depression is defined as "an angle made between the horizontal line as well as the line of sight whenever a watcher looks directly down at an object." The term "angle of depression" refers to the following:
Observer (the individual who observes) Object (the object that is observed by the observer) Line horizontal (a horizontal line which starts from observer)Visible line of sight (the line which connects observer and object)For the given question;
The height of the cliff is 300 m.
The distance of the table from the cliff is 600 m.
The angle of depression is 30 degrees.
Thus, the diagram for the angle of depression is made.
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A computer base unit of mass 4.5 kg is dragged along a smooth desk. If the tension in each
arm of the person dragging it is 16 N and acts at 22° above the horizontal, then what is the
normal reaction force?
A computer base unit of mass 4.5 kg is dragged along smooth desk, if tension in each arm of the person dragging it is 16 N and acts at 22° above the horizontal, then what is the normal reaction force is 32.12N.
What is a force?A force is effect that can alter an object's motion according to physics. A force can cause an object with mass to accelerate when it changes its velocity, for as when it moves away from the rest. An obvious way to describe force is as push or a pull. A force is vector quantity since it has both magnitude and direction. It is calculated by using newton SI unit (N). Force is denoted by letter F. (formerly P).
The net force acting on object is equal to the rate at which its momentum varies over time, according to Newton's second law in its original formulation. This law suggests that object's acceleration is directly proportional to the net force acting on it, is in the direction of the net force, and is inversely proportional to mass of the object if the object's mass is constant.
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