The car selling price is $34.30
From the question, we have
Selling price = 40* 95/100*95/100*95/100
=$34.30
The car selling price is $34.30
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2 x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is _______
(Type an integer or decimal rounded to the nearest tenth as needed.)
The solution to the questions are:
The width, labelled x in the figure is 87.5 metersThe length, labelled 350-2 x in the figure, is 175 metersThe largest area that can be enclosed is 15312.5 square metersHow to determine the width and the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 350 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (350 - 2x) * x
Evaluate
A = 350x - 2x²
Differentiate and set to 0
350 - 4x = 0
So, we have
4x = 350
Divide by 4
x = 87.5
Recall that
Length = 350 - 2x
So, we have
Length = 350 - 2 x 87.5
Evaluate
Length = 175
The area is then calculated as
Area = Length x Width
So, we have
Area = 175 x 87.5
Evaluate
Area = 15312.5 square meters
Hence, the area is 15312.5 square meters
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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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Solve the following quadratic by
completing the square.
y = x^2 - 6x+7
Answer:
{3 - √2; 3 + √2}Step-by-step explanation:
GivenQuadratic function y = x² - 6x + 7Solving by completing the square x² - 6x + 7 = 0 Givenx² - 2*3x + 3² - 3² + 7 = 0 Add, subtract 3²(x - 3)² - 9 + 7 = 0 Simplify(x - 3)² - 2 = 0 Difference of squares(x - 3 + √2)(x - 3 - √2) = 0 Factorizex - 3 + √2 = 0 and x - 3 - √2 = 0 Solve each rootx = 3 - √2 and x = 3 + √2 AnswerAnswer:
[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]y = x^2 - 6x+7[/tex]
To complete the square, begin by adding and subtracting the square of half the coefficient of the term in x:
[tex]\implies y = x^2 - 6x+\left(\dfrac{-6}{2}\right)^2-\left(\dfrac{-6}{2}\right)^2+7[/tex]
[tex]\implies y = x^2 - 6x+\left(-3\right)^2-\left(-3\right)^2+7[/tex]
[tex]\implies y = x^2 - 6x+9-9+7[/tex]
Factor the perfect square trinomial:
[tex]\implies y=(x-3)^2-9+7[/tex]
[tex]\implies y=(x-3)^2-2[/tex]
To solve the quadratic, set it to zero and solve for x:
[tex]\implies (x-3)^2-2=0[/tex]
[tex]\implies (x-3)^2-2+2=0+2[/tex]
[tex]\implies (x-3)^2=2[/tex]
[tex]\implies \sqrt{(x-3)^2}=\sqrt{2}[/tex]
[tex]\implies x-3= \pm\sqrt{2}[/tex]
[tex]\implies x-3+3= 3\pm\sqrt{2}[/tex]
[tex]\implies x= 3\pm\sqrt{2}[/tex]
Therefore, the solution to the given quadratic equation is:
[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]
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]
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
Wiyot is earning money for a longboard by selling lemonade at the soccer fields. Being a precocious and poorly-supervised 12 year old, Wiyot has no transportation and decides to use water from a nearby river.
Business is booming! He sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up. How many TOTAL cups of giardia-laced lemonade will Wiyot have sold by the time his parents get a call from county health officials on day 8?
________
The cups of giardia-laced lemonade that Wiyot will have sold by the time his parents get a call from county health officials on day 8 is 75 cups.
How to calculate the value?From the information, Wiyot sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up.
This is an arithmetic sequence and will be expressed as:
= a + (n - 1)d
a = first term = 33
d = common difference = 6
n = 8
This will be:
= a + (n - 1)d
= 33 + (8 - 1)6
= 33 + (7 × 6)
= 33 + 42
= 75
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Write 64 % as a decimal and as a simplified fraction.
O 6.4 and 64/100
O 0.64 and 64/100
O 6400 and 6400/1
0.64 and 16/25
Answer:
b. 0.64 and 64/100
Step-by-step explanation:
hope this helps!!
Answer: B.) 0.64 and 64/100
Step-by-step explanation:
A percentage is x/100
For example, 4% = 4/100.
So 64% = 64/100
64/100 = 0.64
The volume of a cube is 125 cubic inches.
What is the area of one face of the cube?
(Square Inches)
Answer:
The area of one face of the cube is 25 square inches.
Step-by-step explana
Della has 72 red beads and 32 blue beads. She would like to make bracelets for of beads. She does not want any beads left over. What is the maximum number her friends. She wants all the bracelets to have the same number of each colour bracelets she could make? How many beads of each colour would each bracelet have?
Answer:
8 bracelets can be made from given beads.
Step-by-step explanation:
To make similar bracelets using all the beads, we have to find the highest common factor of no of beads
Factors of 72 => 1, 2, 3, 4, 6, 8 , 9, 12, 18, 24, 36, 72
Factors of 32=> 1 , 2, 4 , 8 , 16 , 32
Observing this data, HCF of 72and 32 will be 8.
Therefore, total 8 bracelets can be made from given beads.
3/8 to the 2nd power
Answer:
9/64
Step-by-step explanation:
it is just 3/8 x 3/8
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.
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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find a number which is 12 morethan its 3/4
Answer:
46
Step-by-step explanation:
What is 12 more than 34?
We are looking for a new number which is 12 more than 34.
We will get the new number by adding 12 to 34.
We write it down as:
34+12=46
And finally the solution for: What number is 12 more than 34?
is 46
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]
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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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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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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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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Find the scale factor. tell whether the dilation is a reduction or an enlargement. Then find the values of the variables.
1.
The dilation is an enlargement.The scale factor is of 3.The values of the variables are: x = 15, y = 18.2.
The dilation is a reduction.The scale factor is of 0.4167.The values of the variable is: x = 2.5.What is a dilation?A dilation occurs when each of the side lengths of an image are multiplied by a constant, which is called scale factor.
For item a, the scale factor is of:
12/4 = 3.
The scale factor is greater than 1, hence it represents an enlargement, and the missing values are found multiplying the equivalent sides by 3, hence:
x = 5 x 3 = 15.y = 6 x 3 = 18.For item b, the scale factor is of:
5/12 = 0.4167.
The scale factor is less than 1, hence it is a reduction, and the missing value is of:
x = 6 x 0.4167 = 2.5.
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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
How many quarters and dimes do you need to make $1.45?
Answer:
.25 * 5 = 1.25
.1 * 2 = . 2
1.45
Step-by-step explanation:
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.
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.
SOLVE AND GRAPH THE INEQUALITY X + 8 > 0
x>-8
look at the image below for the graph answer.
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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Identify each of the following as rational or
irrational.
√23
104.42
√64
49.396
10.97846727460
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 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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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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A player throws a basketball toward a hoop. The basketball follows a
parabolic path that can be modeled by the equation
y=125x² +2.08x + 4. The table models the parabolic path of another
basketball thrown from somewhere else on the court. If the center of the
hoop is at (12,11), will each ball pass through the hoop?
Will the basketball that follows a parabolic path modeled by y=-.125x² +2.08x + 4 pass through the hoop?
yes
No
Will the other basketball, whose path is modeled by the table, pass through the
hoop?!
Yes
No
1. in this exercise you must substitute the value of of x = 12 in the equation of the parable given, if the result is 10 then the ball pass through the hoop
2. Y = (-.125)(12)^2+ (1.84)(12)+6 = -18+22.08+6 = 10.06≅10 , of this form it is demonstrated, that the ball pass through the hoop
