Answer:
8
Step-by-step explanation:
2 rows with 4 oranges each -> 2*4 = 8
3/8 to the 2nd power
Answer:
9/64
Step-by-step explanation:
it is just 3/8 x 3/8
Which one of the following is discreate data
Number of people in a room is the discreate data .
What is meant by discrete data ?Data that only accepts specific values is referred to as discrete data or discrete values. This type of data, which can be counted and has a finite number of values, is frequently expressed as whole numbers or integers.
Information that only has a limited range of values is said to be discrete. These values don't have to be whole numbers (a child's shoe size might be 3.5 or a company's profit might be £3456.25), but they must be fixed values; a child's shoe size cannot be 3.72!
Discrete means "made up of individual, separate units" (not to be confused with "discreet," a completely different word that just so happens to sound similar). Discrete entities, such as logical statements and (obviously) integers, are the focus of discrete mathematics.
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Part A: What is the equation of the least-squares regression line? (4 points)
Part B: If a basketball player wears a size 11.5 and is 73 inches tall, what their residual? Show all mathematical work. (3 points)
Part C: Interpret the meaning of the residual from part B. (3 points)
Shoe Size (U.S.) Height (inches)
7 64.5
10 70
12.5 72
8.5 71
9 69
10 70
11 75
12.5 69
13 71
10.5 68
Answer:
12.5 72
Step-by-step explanation:
Because shows that the basketball player wear size 11.5 73 inches tall so basically the answer would be 12.5 72
The equation of the regression line is y = 0.77x + 61.95. The residual is 2.2 inches. The residual means that the gap between the estimated and anticipated values is 2.2 inches.
What is the regression line?A regression line shows a linear connection between the y-dependent axis's variables and the x-independent axis's variables. The connection is determined by examining the data pattern created by the variables.
From the table, the points are given as follows:
(7, 64.5), (10, 70), (12.5, 72), (8.5, 71), (9, 69), (10, 70), (11, 75), (12.5, 69), (13, 71), (10.5, 68).
Inserting these points into the linear regression calculator, the equation is given as follows:
y = 0.77x + 61.95 ...(i)
For a shoe size of 11.5 inches, the predicted height is given as below:
y = 0.77(11.5) + 61.95 = 70.8 inches.
The residual is the gap between the estimated and anticipated values, hence:
Residual = 73 inches - 70.8 inches = 2.2 inches.
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The diameter of the steering wheel of the actual car is 15 inches. What is the diameter of a toy car's steering wheel if the toy is a 1:40 scale model of the real car?
Answer:
Step-by-step explanation 43 453 645
7×3,012=7×(3,000+12)? Step by step
Answer:
Yes they are equal
Step-by-step explanation:
First we simplify the left side of the equation
7 x 3,012 = 21084
Next we simplify the right side of the equation. Using PEMDAS we know that we must add whatever is inside the parentheses first.
7 x (3,012)
We then multiply 7 x (3,012) = 21084
21084 = 21084
They are equal.
The tech group built a go cart with 10in diameter
wheels. This cart must travel 20 FEET to complete the
race. How many rotations will be required to travel this
distance?
The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation.
Distance traveled in one rotation = Perimeter of the wheel.
⇒ 2π(5) = 31.42 inches
The number of rotations = (20×12)/31.42 = 7.63
Hence "The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64".
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What is Consumidores secundarios?
Consumidores secundarios are organisms in an ecosystem that feed on primary consumers, which in turn feed on producers.
They occupy the second trophic level in a food chain or food web.
Nathan has a $75 budget to rent a car for a day. The daily rental charge is $29.50 and then he will also have to pay 0.55 per mile. How many miles can he drive the car without exceeding his budget? (All partial miles are counted as full miles.)
Answer:
82 miles
Step-by-step explanation:
75-29.50 = 45.50
45.50/0.55 = 82.7272727273
82 x 0.55 = 45.10
45.10+29.50 = 74.60
Data is collected about the number of wins and losses by a random sample of teams
with an animal mascot and those with another kind of mascot. The column relative
frequencies are shown in the table. Based on the information in the table, is there an
association between the variables? Explain your reasoning.
wins
losses
animal mascot
74%
26%
other type of mascot
49%
51%
The relative percentages of the column-wise frequencies are different, indicating that there is indeed an association between the variables.
What does association mean in data?A user-defined collection of related groups and items is referred to as a data association. It may include one or more groupings, as well as some, all, or neither of the items found inside those groups. It is helpful to initially identify various groups and components that you believe to be connected in some way before establishing Rules of Visibility.
Because of the differences in the relative percentages of the column-wise frequencies, there is a link between the variables. The animal mascot in the first column has 74% victories and 26% defeats. These percentages fluctuate greatly from one another. The other type of mascot, which similarly has a significant disparity between them, has 49% victories and 51% losses. The association between the variables is stronger the larger the difference.
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here is a bag with only milk and dark chocolates. The probability of randomly choosing a dark chocolate is 7/12 . There are 56 dark chocolates in the bag and each is equally likely to be chosen. Work out how many milk chocolates there must be.
Answer:
Step-by-step explanation:
We are told that P(dark) = 5/12 and Nd = 25. Plugging these numbers in we get:
5/12 = 25 / (25 + Nw)
Solving this equation for Nw yields Nw = 35.
Therefore, there must be 35 milk chocolates in the bag.
What is the opposite of l3l
The opposite of |3| = - |3|
What is Modulus Function?
Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x If x = 0, then f(x) = 0 If x < 0, then f(x) = -xGiven data ,
Let the number be x
x = |3|
Now , the opposite of the number x = -x
So ,
The opposite of |x| = -|x|
And ,
The opposite of |3| = - |3|
Hence , The opposite of |3| = - |3|
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You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 20 inches long. The first bend is made 6 inches from one end. Describe two ways you could complete the triangle.
The two ways of forming isosceles triangle by bending the metal strip using length by length by base are
6 by 6 by 87 by 7 by 6What is an isosceles triangle?A triangle that have the two sides equal is referred to as an isosceles triangle.
Using a strip of 20 inches long to construct an isosceles triangle means that the perimeter of the triangle is 20 inches
the perimeter is equal to base + length + length
bending 6 inches already means one of the dimensions is gotten then fo the other is based on if
the 6 is base the 6 is lengthif the 6 is base then minus the 6 from 20 and divide the rest for the length
20 - 6 = 14
the two lengths is 14 one length is 7. so we have 6 + 7 + 7 = 20
If the 6 is length then get another 6 and the rest is base
20 - 6 = 14
14 - 6 = 8
therefore we have 6 + 6 +8 = 20 inches
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HELP ME IT SAyS RECTANGLE AT THE CUT OFF BIT
The area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].
What is the area of the rectangle?
If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be computed as
Area = l * b
Given data:
The width of the rectangle is 3x/5 cm.
And its length is four times its width so length = 4 * 3x/5
= 12x/5 cm.
Then the area will be
Area = length * breadth
= 12x/5 * 3x/5
= 36x²/25
[tex]=(\frac{6x}{5})^2[/tex]
Hence, the area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].
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how do i solve for this
Answer:
x = -4
Step-by-step explanation:
[tex] \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } = 2[/tex]
[tex] {( \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } )}^{3} = {2}^{3} [/tex]
[tex] \frac{6x}{2x + 5} = 8[/tex]
[tex]6x = 8(2x + 5)[/tex]
[tex]6x = 16x + 40[/tex]
[tex] - 10x = 40[/tex]
[tex]x = - 4[/tex]
[tex] \frac{ \sqrt[3]{6( - 4)} }{ \sqrt[3]{2( - 4) + 5} } = 2[/tex]
[tex] \frac{ \sqrt[3]{ - 24} }{ \sqrt[3]{ - 3} } = 2[/tex]
[tex] \sqrt[3]{ \frac{ - 24}{ - 3} } = 2[/tex]
[tex] \sqrt[3]{8} = 2[/tex]
Question 8 of 8
Which of the following is equal to the expression?
45 x 12+ 45 x 32
45 × 12 + 32
45+ (12 + 32)
45 x (12 x 32)
45 x (12 + 32)
Step-by-step explanation:
the expression is
45 × 12 + 45 × 32
this is the same as
45 × (12 + 32)
you can extract a common factor from a sum and make it the central factor for the sum.
it is the opposite operation of simplifying this central multiplication, where you have to multiply every part of the left factor with every part of the right factor and sin things up according to the resulting signs.
so, the 4th answer is correct.
In a class of 29 students 9 play an instrument and 23 play a sport there are 5 students who play an instrument and also play a sport. What is the probability that a student plays an instrument given that they play a sport?
The probability for the given case is 5/23.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
Total number of students is 29.
The students who play instrument are 23.
Those who play a sport are 9.
And, those who play both are 5.
Given problem is the case of conditional probability which can be solved by Bayes's theorem as,
P(A|B) = P(A ∩ B) / P(B)
Suppose, A be the event the students play instrument.
B be the event the students play a sport.
And, A ∩ B is the event they play th both.
Then A|B implies the event when a student play instrument given he plays sport.
Apply the rule of probability in the equation for Bayes's theorem to get,
P(A|B) = (5/29) / (23/29)
= 5/23
Hence, the probability that a student plays an instrument given that they play a sport is 5/23.
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Write an inequality that compares the given numbers -4;-1
The inequality that compares the given numbers -4;-1 is -4 < -1.
What is an inequality?Inequalities are created through the connection of two expressions.
It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, it should be noted -4 is less than -1. Therefore, the inequality will be -4 < -1.
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Find the limit, if it exists, analytically using special trig limits
[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos^2(7x)}{8x^2(~~1-sin^2(7x)~~)}~\hfill \boxed{u=7x\implies \cfrac{u}{7}=x\implies \cfrac{u^2}{49}=x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1-cos^2(u)}{8\left(\frac{u^2}{49} \right)(~~1-sin^2(u)~~)}\implies \cfrac{1-cos^2(u)}{ ~~ \frac{8u^2(~~1-sin^2(u)~~)}{49} ~~ }\implies \cfrac{[1-cos^2(u)]49}{8u^2(~~1-sin^2(u)~~)} \\\\\\ \cfrac{[1-cos(u)][1-cos(u)]49}{8u^2(~~1-sin^2(u)~~)}\implies \cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]}\implies \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\\\ \displaystyle \lim_{x\to 0}~\cfrac{1-cos(7x)}{7x}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]} \\\\\\ \displaystyle \text{\LARGE 0}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]}\implies \text{\LARGE 0}[/tex]
There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula T=34+0.3c
where T represents the temperature in degrees Fahrenheit and
c represents the number of times the cricket chirps in one minute. What is the meaning of the c-value when T=65?
A) The change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
B) The expected temperature in degrees Fahrenheit if the cricket has chirped 0 times per minute.
C)The expected temperature in degrees Fahrenheit if the cricket has chirped 65 times per minute.
D) The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
The meaning of the c-value when T=65 is: The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
The correct answer is an option (D)
In this question, we have been given a linear relationship.
For a certain type of cricket, this relationship can be expressed using the formula T=34+0.3c,
where T represents the temperature in degrees Fahrenheit and
c represents the number of times the cricket chirps in one minute.
We need to interpret the value of c when T = 65.
T = 34 + 0.3c
65 = 34 + 0.3c
c = 103.33
c = 103.33 represents the number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
Therefore, the meaning of the c-value when T=65 is: The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
The correct answer is an option (D)
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ABCD is a rhombus. Solve y.
12yº.
A
y=
B
4x + 15
F
D
C
(4y − 1)º
7x+2
Here in the rhombus ABCD the value of y is 7.5.
What is rhombus?A rhombus is a unique kind of quadrilateral with four equal sides and perpendicular diagonals that cut the angles and one another in half.
So here 4x+15 = 7x+2 and
12y = 90.
To find the remaining values by first solving for each variable, then substituting as necessary.
4x+15=7x+2
15=3x+2
13=3x
13/3 = x
BC is 4x+15
= 4(13/3)+15
= 52/3 + 45/3
= 97/3
CD is 7x+2
= 7(13/3)+2
= 91/3 + 6/3 = 97/3
Then, find 12y=90 and y=7.5.
AFB is a 90° angle (12(7.5)).
BCF is a 4y-1 = 4(7.5)-1 = 29 angle.
Because the diagonal cuts the angle in half, angle BCD is equal to 58. Angle ABC thus becomes 180-58 = 122.
Therefore the value of y is 7.5 .
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Given the point (-4, 2) and the y intercept (0, -5) write the equation of the line in slope-
intercept form.
The equation of the line in slope - intercept form is [tex]y=\frac{-7}{4}x-5[/tex]
Explain what the slope-intercept form is?
Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This expression is sometimes referred to as y = mx + b form
Given: x = -4 , y = 2 and b = -5
y = mx + b
2 = m (-4) + (-5)
m = [tex]\frac{-7}{4}[/tex]
By putting the value of m we get equation of line
[tex]y=\frac{-7}{4}x-5[/tex]
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Rewrite 6/11 each as a multiplecation equation
Answer:
11 x 6
Step-by-step explanation:
Calculate and give the result as an irreducible fraction
please ;)
=9/7+7/3×-9/4
=[4/5-2]×[3/4-2/3]
In the fractions given 2/3 + 7/3 * -9/4 and (4/5 - 2) * (3/4 - 2/3) the results of the expressions are -55/12 and -1/10 respectively
FractionsA fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
In the first expression;
2/3 + 7/3 * -9/4
Applying PEDMAS
2/3 + 7/3 * -9/4 = -55/12
In the second expression;
(4/5 - 2) * (3/4 - 2/3) = - 1/10
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SOLVE AND GRAPH THE INEQUALITY X + 8 > 0
x>-8
look at the image below for the graph answer.
Identify each of the following as rational or
irrational.
√23
104.42
√64
49.396
10.97846727460
Complete the table of values for the equation 9x+2y=18
Answer:
[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]
Step-by-step explanation:
Given equation:
[tex]9x+2y=18[/tex]
Substitute x = 0 into the given equation and solve for y:
[tex]\begin{aligned}x=0 \implies 9(0)+2y&=18\\2y&=18\\\dfrac{2y}{2}&=\dfrac{18}{2}\\y&=9\end{aligned}[/tex]
Substitute y = 0 into the given equation and solve for x:
[tex]\begin{aligned}y=0 \implies 9x+2(0)&=18\\9x&=18\\\dfrac{9x}{9}&=\dfrac{18}{9}\\x&=2\end{aligned}[/tex]
Substitute x = 4 into the given equation and solve for y:
[tex]\begin{aligned}x=4 \implies 9(4)+2y&=18\\36+2y&=18\\36+2y-36&=18-36\\2y&=-18\\\dfrac{2y}{2}&=\dfrac{-18}{2}\\y&=-9\end{aligned}[/tex]
Therefore:
[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]
A square on a coordinate plane has one vertex at (0.5,1) and a perimeter of 6 units. If all of the vertices are located in Quadrant I, what are the coordinates of the other 3 vertice s?
The coordinates of the other 3 vertice s are; Vertex 2 = (0.5, 2.5)
Vertex 3 = (2, 1), Vertex 4 =(2, 2.5 )
What is perimeter?Its the sum of length of the sides used to made the given figure.
Given that the Perimeter, P = 6 units
The Perimeter of a square = 4s ; s = side length
6 = 4s
s = 6/4
s = 1.5 units
If Vertex 1 =(0.5,1) and all vertexes are located in Quadrant I
Vertex 2 = (0.5,1 + 1.5) =(0.5, 2.5)
Vertex 3 = (0.5 + 1.5 ,1) = (2, 1)
Vertex 4 = (2, 1 + 1.5) = (2, 2.5 )
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10 points!
Write a compound inequality to
represent a budget to spend
between $5 and $25 at
Starbucks in a month.
The required compound inequality is given as 5 < x < 25.
Given that,
To determine a compound inequality to represent a budget to spend between $5 and $25 at Starbucks in a month.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let x be the amount to be spend at Starbucks in a month,
According to the question,
X should not be less than 5 and should not be greater than 25,
So X > 5 and x < 25
Compounding the above inequalities,
5 < x < 25
Thus, the required compound inequality is given as 5 < x < 25.
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I-ready 3/8+n=7/8 n=
The required value of n is [tex]\frac{1}{2}[/tex] .
What is an algebraic equation?
The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
Given, [tex]\frac{3}{8} +n=\frac{7}{8}[/tex]
or, [tex]n=\frac{7}{8}- \frac{3}{8}[/tex]
or, [tex]n=\frac{7-3}{8}[/tex]
or, [tex]n=\frac{4}{8} = \frac{1}{2}[/tex]
Hence, the value of n is [tex]\frac{1}{2}[/tex] .
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Line h passes through (2,6) and is parallel to a line that passes through (−3,4) and (1,1).
The equation of line h that passes through (2,6) and is parallel to a line passing through (-3, 4) and (1, 1) is 4y + 3x = 30
What is slope?Slope is the ratio of the change in the y-coordinates to the change in the x-coordintes of any two given points.
It is a measure of the steepness of a line.
Slope may be positive or negative
slope of the line joining the the points (-3,4) and (1,1)
slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
[tex]x_{1}[/tex] = -3, [tex]x_{2}[/tex] = 1, [tex]y_{1}[/tex] = 4, [tex]y_{2}[/tex] = 1
slope = 1-4 / 1 - -3
slope = -3/4
since the two lines are parallel their slopes are equal.
equation of first line
y = mx + c
where y = 6, x = 2, m = -3/4
6 = -3/4(2) + c
6 = -3/2 + c
c = 6 + 3/2
c = 15/2
Equation, y = -3/4x + 15/2
multiply through by 4
2y = -3x +30
2y + 3x = 30
In conclusion the equation of the line passing through the given point is 2y + 3x = 30
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