Final Answer:
Rectangular Prism: A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent. Like all three-dimensional shapes, a rectangular prism also has volume and surface area.
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solve for y
-4=-2+y/2
Answer:
y = -4
Step-by-step explanation:
-4 = -2 + y/2
-2 = y/2
2(-2) = y
y = -4
The area of the square is 1 square unit. Two small triangles can be put
together to make a square or to make a medium triangle.
Answer:
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11. Intervals. Given the intervals I₁ = (2.5, 5.5], 1₂ =[3, 6], 1,=[5.5, 7] and I₁ = (5.5, 10]. Find
(a) I, or 1₂ or 1₂ =
(c) I, and I, =
(b)
(d)
I, and I₂ =
I, and I₁ =
12. Intervals.
1) Given the interval (1.5, 3.5). Find (a) the middle point:
13. Equations. Solve the following equations:
(b) the width (length):
2) Find the interval for which the middle and the width are equal to 2 and 6, respectively:
The interval of I₁ or I₂ or I₄ is (2.5 ,10].
The interval of I₁ and I₂ is [3 , 5.5] .
The interval of I₁ and I₃ is [5.5]
The interval of I₁ and I₄ is (5.6 , 7]
In arithmetic, a (real) interval could be a set of real numbers that contains all real numbers lying between any 2 numbers of the set.For instance, the set of numbers x satisfying zero zero x ≤ one is associate degree interval that contains zero, 1, and every one numbers in between.(a) because the all 3 intervals square measure connected by or which suggests they're going to all embrace the quantity lying from interval one to three and is given by (2.5 ,10].
(b) because the interval square measure connected by and which suggests the common numbers lying in interval one and a couple of and is given by [3 , 5.5] .
(c) because the interval square measure connected by and which suggests the common numbers lying in interval one and three and is given by [5.5]
(d)As the interval square measure connected by and which suggests the common numbers lying in interval one and four and is given by (5.6 , 7] .
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The complete question is given below :
Given the intervals I₁ = (2.5, 5.5], I₂ =[3, 6], I₃=[5.5, 7] and I₄ = (5.5, 10]. Find
(a) I₁ or I₂ or I₄
(b) I₁ and I₂
(c) I₁ and I₃
(d) I₁ and I₄
Write each equation in logarithmic form. 2⁻³=0.125
[tex]log_{2} ( 0.125) = -3[/tex] is exponential equation in logarithmic form.
How can you tell whether an exponential function is growing or deteriorating?
As the exponential's base is greater than 1, which occurs when those numbers increase, we are seeing exponential growth. When the exponential's base is between 1 and 0, and those numbers decrease, we have exponential decay.Convert the exponential equation to a logarithmic equation using the logarithm base (2) of the right side ( 0.125) equals the exponent
( -3 )
[tex]log_{2} ( 0.125) = -3[/tex]
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Simplify each expression.
log (a²-10a+25) + 1/2 log 1/(a-5)³ - log (√a-5)
After simplifying logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]log_{10}(a^2-10a+25) + \frac{1}{2} log_{10}\frac{1}{(a-5)^3} - log_{10}(\sqrt{a} -5)\\\\[/tex]
apply formulas for log a + log b and log a - log b
[tex]log_{10}(a^2-10a+25) + log_{10}(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}(a^2-10a+25).(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}\frac{(a^2-10a+25). (\frac{1}{(a-5)^3})}{(\sqrt{a} -5) } \\\\= > log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
Thus, after solving the logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
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Use synthetic division to find the quotient. 2x⁴ - 4 - 7x - 38x²/x - 4
Answer: A binomial (of the form ax+b).
Step-by-step explanation:
2x⁴ - 4 - 7x - 38x²/x-4=ax+b , hope this is correct
d)
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e)
What is the value of X in the equation3/2{4x-1}-3x=5/4-{x+2}?
Answer:
x = 3/16
Step-by-step explanation:
Answer: x = 3/4 or X = - 1/8
Step-by-step explanation:
Joseph buys a subway pass for $55. Every time he rides the subway, money is deducted from the value of the pass. He rode the subway 5 times and $40 was deducted from the value of the pass. How much was deducted from Joseph's account for each ticket? Write a mathematical expression to represent this situation; then find the answer.
The amount deducted from Joseph's account for each ticket is $8
The mathematical expression representing the situation is:15=55-5x
What is the total amount deducted from the subway pass?
On the premise that Joseph's subway pass was deducted each time he passes through the subway and that $40 was deducted in all for his number of passes, the total cost of $40 can be modeled into an equation as shown below:
amount left after the deductions=55-40
amount left after the deductions=15
15=total amount paid-(number of passes*cost per subway pass)
total amount paid=55
number of passes=5
cost per subway=x
15=55-5x
5x=55-15
5x=40
x=40/5
x=$8
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A certain population grows exponentially. The population grows from 3500 people to 6425 people in 8 years. What is the growth rate of the population?
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6425\\ P=\textit{initial amount}\dotfill &3500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &8\\ \end{cases}[/tex]
[tex]6425=3500(1 + \frac{r}{100})^{8} \implies \cfrac{6425}{3500}=\left( \cfrac{100+r}{100} \right)^8\implies \cfrac{257}{140}=\left( \cfrac{100+r}{100} \right)^8 \\\\\\ \sqrt[8]{\cfrac{257}{140}}=\cfrac{100+r}{100}\implies 100\sqrt[8]{\cfrac{257}{140}}=100+r \\\\\\ 100\sqrt[8]{\cfrac{257}{140}}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{7.89}\approx r \end{array}}[/tex]
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The expression 9x²y⁻³, for x = 5 and y = 3 simplifies to 25/3.
What is an improper fraction?A fraction in which the numerator is greater than the denominator is called an improper fraction.A fraction is called a proper fraction when the denominator is greater than the numerator.
Given an expression with exponents 9x²y⁻³, for x = 5 and y = 3.
In this, we have to replace the variables x and y with their numerical value in the given expression.
So, 9x²y⁻³, for x = 5 and y = 3 is,
= 9(5)²(3)⁻³
= 9(5)²/(3)³.
= 9.(25)/27.
= 1.(25)/3.
= 25/3.
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if 251x=100 two, find x
Answer:
X = 102/251
Step-by-step explanation:
251x = 102
/ /
251 251
X= 102/251
luis is making a wooden model of a flag for his school project. He found a bargain on square pieces of plywood. If his flag is to be 18 inches by 12 inches,what is a reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood?
NEED SOON
The reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood would be 216 sq inches.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We have been given that the flag is to be 18 inches by 12 inches, then;
The area of the rectangle = length × Width
The area of the rectangle = 18 x 12
= 216
Since the area of flag will be equal to area for the square piece of plywood.
The area of a square of side length l is given by l squared;
A(l) = l²
216 = 14.6²
Hence, the reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood would be 216 sq inches.
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A manufacturer of candies has daily costs of T(x)=2x2−3200x+6800. T is the total cost in dollars and x is the number of units produced. How many units need to be produced to have minimum cost?
The units that need to be produced to have minimum cost is 800 units.
How to calculate the units?From the information, the manufacturer of candies has daily costs of T(x)=2x² - 3200x+6800.
Therefore, we will differentiate with respect to x. This will be:
T(x)=2x² - 3200x+6800.
4x - 3200
4x - 3200 = 0
4x = 3200
Divide
x = 3200/4
x = 800
Therefore, the units that need to be produced to have minimum cost is 800 units.
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Evaluate each expression for the given value of x
2x for x=3
Value of the expression 2x at x=3 is 6.
By considering the given expression
2x=2(3)=6
A mathematical expression is created when we successfully combine numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
Expression. Equation. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
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A typical paper bag at a grocery store cannot hold more than 49 pounds. Let p represent the number of pounds a typical paper bag can hold.
Create an inequality to represent the situation. Move a symbol to the lines to create the inequality.
P___49
Answer: = is it maybe
if not sry
p≤49 is the inequality to represent the situation.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that a typical paper bag at a grocery store cannot hold more than 49 pounds.
Let p represent the number of pounds a typical paper bag can hold.
We have to find the inequality to represent the situation
As grocery store cannot hold more than 49 pounds which means it holds less than or equal to 49.
p≤49
Hence, p≤49 is the inequality to represent the situation.
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Lourdes can buy 3-packs of paper for $10.50, or she can buy 4-packs of paper for $13.50. She wants to buy 12 packs of paper. How much more will she spend if she buys only 3-packs of paper? Explain why.
If Lourdes buys 12 packs of paper in terms of 3 packs each she has to pay 0.5 dollars more.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given Lourdes can buy 3-packs of paper for $10.50.
∴ The cost of per pack of paper is = (10.50/3) = $3.5.
In this case, if she can buy 4-packs of paper for $13.50,
The cost per paper pack is = (13.50/4) = $3.375.
To buy 12 packs in terms of 3 packs each Lourdes has to pay,
(3.5×12) dollars.
= 42 dollars.
To buy 12 packs of paper in terms of 4 packs each she has to pay,
(3.375×12) dollars.
= 40.5 dollars.
∴ She has to pay (40.5 - 40) = 0.5 dollars more.
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If 0²/₃=0 , why is 0⁻²/₃ undefined?
0²/₃ = 0 but 0⁻²/₃ is undefined because 1/0 is undefined.
Consider 0²/₃. So here, 0 has a positive power though a rational at that.
Any positive powers of 0 is considered as 0 itself. This expression also means that the square of the cubic root of zero. We know that cubic root of 0 is 0 and 0² = 0 itself. So we can conclude that 0²/₃ = 0.
Now consider 0⁻²/₃ .
We have [tex]a^{-b}=\frac{1}{a^b}[/tex].
So here, 0⁻²/₃ = [tex]\frac{1}{0^{\frac{2}{3}} }[/tex]
From the previous case, 0²/₃ = 0
So we get 0⁻²/₃ = 1/0, which is undefined.
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A random sample of 49 people are selected from a population and it is found that 12 people in the sample are over six feet tall. what is the best point estimate of the proportion of people in the population who are over 6 feet tall? write your answer as a decimal using the appropriate rounding rule.
If a random sample of 49 people is selected from a population and it is found that 12 people in the sample are over six feet tall, then the best point estimate of the proportion of people in the population who are over six feet tall is 0.24
The point estimate is a term used in mathematics to calculate a single value as an approximate of a parameter of a population.
Point estimate can be given the formula:
point estimate = Number of successes / Total number of samples
In this case, the total number of samples = 49
number of people over six feet tall (successes) = 12
Therefore,
proportion of people over six feet tall = 12 / 49
proportion of people over six feet tall = 0.2448
Decimal can be rounded to two decimal places, if the third digit is less than 5, round the second digit down. On the other hand, if the third digit is more than 5, round the second digit up.
Therefore,
proportion of people over six feet tall = 0.2448 = 0.24
Thus the point estimate of the proportion of people in the population who are over 6 feet tall is calculated to be 0.24
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A Gallup poll asked americans how many hours of sleep they usually get. The difference between the percent of adults who slept s’more than the recommended amount of time and the percent who slept less than the recommended amount of time is 3%. In total, these groups make up 25% of the population. What percent of the population sleeps more than the recommended number of hours, and what percent sleeps less?
The percent of the population sleeps more than the recommended number of hours will be 30%.
How to illustrate the information?From the information, it should be noted that the difference between the percent of adults who slept more than the recommended amount of time and the percent who slept less than the recommended amount of time is 3%.
It should be noted that this was 25% of the population.
Therefore, the percent of the population sleeps more than the recommended number of hours will be:
= 27% + 3%
= 30%
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ASAPPP!!!
PLSSS RQQ ANSWER JUST FOR THE LAST QUESTION AT THE VERY BOTTOM!!!
Based on the probability of getting a yellow on one spin, the number of yellows expected from 420 spins is 210 yellows
How many yellows are expected?The number of yellows you can expect are:
= Number of spins x Probability of getting yellow
Solving gives:
= 420 x 1/2
= 420 / 2
= 210 yellows
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6c4 what is the combination
Answer: 6 CHOOSE 4 can also be denoted as 6C4.
Draw 4 out of 6 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
In 15 possible combinations, AB and BA are not considered as different events.
AB and BA considered as a single combination in 15 events.
Step-by-step explanation:
Angles of Triangles #3: Find the angles below
All the angles in the given diagram are;
∠5 = 81°
∠1 = 128°
∠2 = 52°
∠3 = 47°
∠4 = 133°
How to find Congruent Angles?
We are given different angles. Thus;
52 + ∠5 + 47 = 180
This is because sum of angles on a straight line is 180°. Thus;
99 + ∠5 = 180
∠5 = 180 - 99
∠5 = 81°
∠1 = ∠5 + 47° because of the definition of corresponding angles. Thus;
∠1 = 81° + 47°
∠1 = 128°
∠2 = 52° because they are corresponding angles.
∠3 = 47° because they are corresponding angles.
∠4 = 180 - 47° because sum of angles on a straight line is 180°.
∠4 = 133°
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5/12 simplified as a fraction
Answer:
Step-by-step explanation:
You can't simplify 5/12 any more. That is the simplest form
Answer:
5/12 is the simplest form already
Suppose a line perpendicular to a pair of parallel lines intersects the lines at the points (a, 4) and (0,6). If the distance between the parallel lines is √5 , find the value of a and the equations of the parallel lines.
There are two possibilities: (i) Perpendicular line: y = 2 · x + 6, Parallel lines: y = - (1 / 2) · x + 7 / 2, y = - (1 / 2) · x + 6, (ii) Perpendicular line: y = - 2 · x + 6, Parallel lines: y = (1 / 2) · x + 7 / 2, y = (1 / 2) · x + 6.
How to determine the equations of a line and the two lines perpendicular to the former
The missing coordinate of one of the points of intersection can be found by using the least distance between the two parallel lines and the Pythagorean theorem:
(a - 0)² + (4 - 6)² = 5
a² + (- 2)² = 5
a² + 4 = 5
a² = 1
a = ± 1
There are two possibilities: (x₁, y₁) = (- 1, 4), (x₂, y₂) = (1, 4). Now we proceed to find the equations associated to each case:
(x₁, y₁) = (- 1, 4), (x₃, y₃) = (0, 6)
The equation of the perpendicular line is:
Slope
m = (6 - 4) / [0 - (- 1)]
m = 2
Equation of the line
y - 4 = 2 · (x + 1)
y - 4 = 2 · x + 2
y = 2 · x + 6
The slope of the two parallel lines is:
m' = - 1 / m
m' = - 1 / 2
First parallel line
y - 4 = (- 1 / 2) · (x + 1)
y - 4 = - (1 / 2) · x - 1 / 2
y = - (1 / 2) · x + 7 / 2
Second parallel line
y - 6 = - (1 / 2) · x
y = - (1 / 2) · x + 6
(x₂, y₂) = (1, 4), (x₃, y₃) = (0, 6)
The equation of the perpendicular line is:
Slope
m = (6 - 4) / (0 - 1)
m = - 2
Equation of the line
y - 4 = - 2 · (x - 1)
y - 4 = - 2 · x + 2
y = - 2 · x + 6
The slope of the two parallel lines:
m' = - 1 / m
m' = 1 / 2
First parallel line
y - 4 = (1 / 2) · (x - 1)
y - 4 = (1 / 2) · x - 1 / 2
y = (1 / 2) · x + 7 / 2
Second parallel line
y - 6 = (1 / 2) · x
y = (1 / 2) · x + 6
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The distance between two numbers on the number line is 8. If one of the numbers is 5, what are the two
possibilities for the other number?
smaller possible number =
larger possible number =
Answer:
(adding/subtracting 8 from 5)
smaller number is -3
larger number is 13
or it could be -4 and 14
since the question says the distance is 8
Es urgente por favooor
Tres compañeros se reparten un premio que han ganado en un
concurso. Carlos se lleva 1/3 del premio, Luisa los 2/5 del premio y
Carmen, el resto, que son 62’40 €.
a) ¿A cuánto ascendía el premio?
b) ¿Cuánto corresponde a Carlos y a Luisa?
Which of these describes the location of the ordered pair (0.8, −1.2)?
A: Quadrant I
B: X-axis
C: y-axis
D: Quadrant IV
A glider begins its flight 3/4
mile above the ground. After 45 minutes, it is 3/10
mile above the ground. Find the change in height of the glider. If it continues to descend at this rate, how long does the entire descent last?
The change in height is
mile(s).
The entire descent lasts
hour(s).
Skip to navigation
Answer:Answer One: 3 miles. Answer Two: 105.
Step-by-step explanation:
i need help pls i give brainist
Answer:
0.000027 ÷ 0.000009
= 2.7 x 10^-5 ÷ 9.0 x 10^-6
= (2.7/9) x 10^(-5 - (-6))
= .3 x 10^1
= 3
Step-by-step explanation: