Answer:
Step-by-step explanation: 23.4
a rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. the photograph measures $8$ inches high and $10$ inches wide. what is the area of the border, in square inches?
The area of the border is 72 square inches - 80 square inches = -8 square inches.
What is rectangle ?
A rectangle is a four-sided geometric shape with four right angles. The opposite sides of a rectangle are of equal length and parallel to each other, and the opposite angles are equal. The length and width of a rectangle are its two dimensions, with the length being the longer side and the width being the shorter side.
To find the area of the border, subtract the area of the photograph from the total area of the photograph and the frame. The total area of the photograph and the frame is the area of the frame (which is just the border) plus the area of the photograph.
The area of the photograph is 8 inches * 10 inches = 80 square inches
The area of the frame is the perimeter of the photograph (28 + 210) multiplied by the width of the border, which is 2 inches. So the area of the frame is 2*(28 + 210) = 2*36 = 72 square inches.
Therefore, the area of the border is 72 square inches - 80 square inches = -8 square inches.
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work out 16^3/2 ??????????????????????
Answer:
2048
Step-by-step explanation:
Find out what [tex]16^{3}[/tex] is:
16x16x16 =
4096.
Now lets divide it by 2:
4096/2 =
2048.
2048 would be your answer to your problem.
The graph represents the function f(x). Which set of points lie on its inverse f^-1(x)?
Answer:
Third choice: (1, -3); (2, 2); (3, 7)
Step-by-step explanation:
There are two ways to solve this
The easiest way to solve this is to understand that the inverse of a function f(x), denoted by f⁻¹(x) is nothing but a reflection of the function about the line y = x
What that means is that if (x, y) is a specific point on the line, then the inverse point will be (y, x). Basically we are swapping the x, y values
The 3 points on f(x) and the corresponding points on f⁻¹(x) are given below:
f(x) f⁻¹(x)
------ --------
(-3, 1) (1, -3)
(2, 2) (2, 2)
(7, 3) (3, 7)
From the options given we see that the 3rd choice gives the correct values
So answer:
Third choice: (1, -3); (2, 2); (3, 7)
I have not taken the trouble of finding the equation for the line and finding the inverse of that equation since it is not needed in this question
solve these proportion for the variable x. Use the reasoning of scalling to solve
The value of x from the given proportion is given as x = 10 after scalling both side of the equation.
What is Ratio and Proportion ?A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is often read as "x is to y" but may also be written as "x: y" or "x/y." The proportion equation, on the other hand, states that two ratios are equal.
The equality of two ratios is referred to as proportion. There is never a difference between two comparable ratios. The ratio sign (::) is used to express proportions, which aid in solving problems with ambiguous amounts. To put it another way, a percentage is an equation or a claim that shows the equality of two ratios or fractions. If a: b = c: d, then four non-zero values, a, b, c, are said to be in proportion. Let's now compare the two ratios, 3:5 and 15:25. In this case, 3:5 and 15:25 may both be written as 3:5 = 3/5 and 0.6, respectively. We may argue that these two ratios are proportionate because they are both equal.
There are two types of proportions :
Direct ProportionInverse ProportionThe proportion is given by ,
x/12 = 15/18
⇒ multipling both side with 12 we get ,
x = (12*15)/18
⇒ x = 5 * 2 = 10
The value of x from the given proportion is given as x = 10.
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The value of x from the given proportion is given as x = 10 after scalling both side of the equation.
What is meant by equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.An equation that expresses a significant relationship between two or more variables is called a formula.There are two types of proportions :
==>Direct Proportion
==>Inverse Proportion
The proportion is given by ,
x/12 = 15/18
⇒ multipling both side with 12 we get ,
x = (12*15)/18
⇒ x = 5 * 2 = 10
The value of x from the given proportion is given as x = 10.
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In which situation is the distance traveled proportional to time?
Answer:
Step-by-step explanation:
honolululuulu
4hk/20h^2k in simplest form
The simplified form of the expression 4hk/20h²k is 1/5h.
What is the simplified form of the expression?Given the expression in the question;
4hk / 20h²k
To simplify, first cancel out the common factor of 4 and 20.
4hk / 20h²k
4(hk) / 4(5h²k)
hk / 5h²k
Next, cancel out the common factor of h and h²
h(k) / h(5hk)
k / 5hk
Now, cancel out the common factor of k
k(1) / k(5h)
1/5h
Therefore, the simplified form is 1/5h.
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in a scientific research, a statistical test resulted in a -value of 0.026. match each value with the correct decision. (a) do not reject h0 (b) reject h0
Any p-value less than 0.05 is a cause to reject the null hypothesis.
What is Null Hypothesis?
The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.
In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).
Any p-value less than 0.05 is a cause to reject the null hypothesis.
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The ratio of the measures of the angles of a triangle is 5:7:9. How many degrees is the largest angle? Round answer to the nearest whole number.
please help giving 20 points
Answer:
well the best I can say is maybe multiply all of the numbers
Step-by-step explanation: The first stepunderstanding[tex]5 \times 7 \times 9 = x \div 3[/tex]
second stepproving35*9=x÷3
315÷3
just do the 315÷3 and you should get an answer
Jerry baked 5 apple pies to share equally among 3 of his friends. Jerry thinks each friend will get 3/5 of an apple pie. Do you agree? Support your answer
Yes, 3 apple pies divided among 5 people
Now, According to the question:
"Information available from the question"
Apple shared equally
Portion of each person = 3/5
A possible way that shows how the pies were shared.
7/5 is the ration of the pie to each individual (Jerry and his friends).
Provided that each individual got equal ration....
The ration can be divided into two
The numerator = 3
The denominator = 5.
The numerator shows the number of things that were shared.
Hence, 3 apples were shared.
The denominator shows the number of people involved.
Hence, 5 people were involved.
So, we can conclude that 3 apples were divided among 5 people.
Hence, 3 apple pies divided among 5 people.
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in any 15-minute interval, there is a 20% probability that you will see at least one shooting star. what is the probability that you see at least one shooting star in the period of an hour
So, the probability that you see at least one shooting star in the period of an hour is 59.04%.
The probability of seeing at least one shooting star in a 15-minute interval is 20%, so the probability of not seeing a shooting star in that interval is 80%. The probability of not seeing a shooting star in an hour-long period is the product of the probability of not seeing a shooting star in each of the four 15-minute intervals, which is 0.8 * 0.8 * 0.8 * 0.8 = 0.4096 or 40.96%. Therefore, the probability of seeing at least one shooting star in an hour-long period is 1 - 0.4096 = 59.04%.
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Dan is a software salesman. His monthly salary is $1800 plus an additional $60 for every copy of English is Fun he sells.
Let S represent his total salary this month (in dollars), and let N represent the number of copies of English is Fun he sells. Write an equation relating S to N, and then graph your equation using the axes below.
The linear function relating S to N is given as follows:
S(n) = 1800 + 60n.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the amount earned for each extra copy.b is the intercept, representing the base monthly salary.The parameter values for this problem are given as follows:
m = 60, b = 1800.
Hence the function is defined as follows:
S(n) = 1800 + 60n.
The function is graphed on the image given at the end of the answer.
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What is 3.5 as a fraction in simplest form
Answer:
Mixed Number: [tex]\frac{7}{2}[/tex]
Regular [tex]3\frac{1}{2}[/tex]
Explantion \/ \/
Term to term rule is subtract 2 and multiply 4 the third term is 248 what is the two previous term
The two previous terms of 248 are 64 and 18.
A term-to-term rule is a rule that will describe calculating the following terms of a sequence given by the previous term.
In the given problem, the rule is to subtract 2 and multiply by 4.
Considering that the third term is 248. we can utilize the rule to figure out the subsequent term.
248 = (4 * (x - 2))
248 = 4x - 8
256 = 4x
x = 64
So the subsequent term is 64.
To find the initial term, we can utilize a similar rule once more
64 = (4 * (x - 2))
64 = 4x - 8
72 = 4x
x = 18
So the initial term is 18.
Therefore, the two previous terms of 248 are 64 and 18.
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In an isosceles triangle, the length of sides b and c are 8. The length of median B is 7. Find the length of the base of the triangle
The length of the base is 2√15 units. The median of an isosceles triangle divides the triangle into two equal parts.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
A median in a triangle is a line that runs from one corner (or vertice) to the centre of the other side. Triangle congruence makes it easy to demonstrate an isosceles triangle's property that the median to the base is perpendicular to the base.
According to the Pythagorean theorem,
AD² + BD² = AB²
7² + BD² = 8²
BD² = 64 - 49
BD² = 15
BD = √15
The median divides the base into two equal parts.
The length of the base is 2√15.
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Photo attached. Please help.
Answer:
There is no real solution set for this equation
Step-by-step explanation:
We have
[tex]\sqrt{2x-1}+7=4[/tex]
Move 7 to the right side:
[tex]\sqrt{2x-1}+7-7=4-7\\\\\sqrt{2x-1}=-3\\\\[/tex]
If we treat 2x - 1 as a function f(x) then we are getting
[tex]\sqrt{f(x)} = -3\\\\[/tex]
But the square root of a function cannot be negative for real values of x
Hence there is no real solution set
PLEASE HELP FINAL QUESTION TO UNIT TEST
A company makes cars at two factories. Some of the cars need repairs in the first year and some do not. This two-way frequency table shows the proportion of cars at each factory that need repairs or do not need repairs in the first year.
Which conclusions can be made from this table?
Select each correct answer.
Responses
Compared to Factory A, Factory B has a larger percentage of cars that do not need repairs.
Compared to Factory A, Factory B has a larger percentage of cars that do not need repairs.
More cars from Factory B need repairs than do not need repairs in the first year.
More cars from Factory B need repairs than do not need repairs in the first year.
For both factories, more cars need repairs than do not need repairs in the first year.
For both factories, more cars need repairs than do not need repairs in the first year.
Among cars from Factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
Among cars from Factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
Need repairs in first year Do not need repairs in first year
Factory A 0.05 0.95
Factory B 0.02 0.98
The conclusions that can be made from this table include:
Compared to Factory A, B has a larger percentage of cars that do not need repairs.Among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first yearHow to explain the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
From the information, factory A for those who need repairs is 0.05 in the first year. In this case, among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
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jacy arrnanged cans on a store shelf. there are 126 cans in all. jacy makes rows of 6 cans how many rows will she make?
Answer:
126 cans in total / 6 cans per row
126/6 = 21 rows of cans
A circular plot of land has a diameter of 6ft. if the walkway around this piece of land has a width of 2x, what is the total area of the land and walkway combined?
The area of the circle, as a function of x, will be:
A(x) = 3.14*(3ft + 2x)²
What is the total area of the land and walkway combined?We know that for a circle of radius R, the area is:
A = pi*R²
Where pi = 3.14
In this case we have a circular plot of land with a diameter of 6ft, then the radius (half of that) is:
R = 6ft/2 = 3ft
And then we have a walkway with a width of 2x, then the radius of the circle that includes the walkway is:
R' = 3ft + 2x
Replacing that in the area equation we will get:
A(x) = 3.14*(3ft + 2x)²
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A) BCD is a straight line.
Triangle ABC is equilateral.
CE = DE
E
Not drawn
accurately
32
A
X
B
C
D
Work out the size of angle x.
(4)
+
PLEASE HELP ME I AM REALLY STUCK!!!
The size of angle x = 46 degree.
Now, According to the question:
A triangle in which at least two sides are equal is called an isosceles triangle. Following this fact, if two sides of a triangle are equal, then the angles opposite to those sides are also equal.
"Information available from the question"
Since Δ ABC is equilateral then interior angles = 60°
Since CE = DE then Δ CDE is isosceles and the base angles are congruent,
So,
∠ ECD = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74 degree
BCD is a straight line, then the 3 angles on it sum to 180°, that is
60° + 74° + x = 180°
134° + x = 180° ( subtract 134° from both sides )
Hence, The size of angle x = 46°
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Mr.Honkenberg I planning for hi Superbowl party.If he he buy 18 chicken wing for $15 what i the cot of the wing in wing per dollar?
The cost of the wings per dollar is 1.2 wings per dollar ($15 / 18 wings = $0.83 per wing). The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18).
1. Divide the total cost of the wings ($15) by the number of wings (18).
2. The result of this calculation is the cost of each wing ($15 / 18 = $0.83).
3. Divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar).
The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18). This calculation will give the cost of each wing ($15 / 18 = $0.83). To find the number of wings per dollar, divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar). This means that for every dollar spent, 1.2 wings can be purchased.
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Part 3: Put It All Together- The table below lists the costs and prices for four businesses involved in
making, distributing, and selling bread. Use the information to answer the questions below.
Cost of Inputs
$0
$0.50
$1.50
$2.25
Price of Output
$0.50
$1.50
Farmer Fred
Baker Bob
Trucker Tom
$2.25
Retail Rob
$3.50
16. Calculate the GDP using value-added approach. Explain how you got your answer.
The GDP using value added approach is $3.50
How to calculate the GDP?GDP using value added approach is calculated by obtaining the sum total of value added by each production unit.
Value added by Farmer Fred = Price of output - Cost of inputs = $0.50 - $0 = $0.50
Value added by Baker Bob = Price of output - Cost of inputs = $1.50 - $0.50 = $1.00
Value added by Trucker Tom = Price of output - Cost of inputs = $2.25 - $1.50 = $0.75
Value added by Retail Rob = Price of output - Cost of inputs = $3.50 - $2.25 = $1.25
GDP = Value added by Farmer Fred + Value added by Baker Bob + Value added by Trucker Tom + Value Added by Retail Rob
GDP = $0.50 + $1.00 + $0.75 + $1.25
GDP = $3.50
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A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale
What is the volume of the file cabinet?
The volume of file cabinet is equal to 26 / 3 cubic feet.
How to determine the volume of the file cabinet
The statement let us infer that file cabinet has the form of right prism with rectangular base, whose formula is shown below:
V = b · h · l
Where:
V - Volume, in cubic feet.b - Base width, in feet.h - Height, in feet.l - Base length, in feet.If we know that b = 2 1 / 6 ft (13 / 6 ft), h = 1 1 / 2 ft (3 / 2 ft) and l = 2 2 / 3 ft (8 / 3 ft), then the volume of the file cabinet is:
V = (13 / 6 ft) · (3 / 2 ft) · (8 / 3 ft)
V = 26 / 3 ft³
RemarkStatement present an anomalous character "2", correct statement is introduced below:
A locker measurement at the bottom as 2 1 / 6 ft wide, 1 1 / 2 ft high and 2 2 / 3 ft long.
Picture is missing but question can be solved by inferential approach.
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Part A
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000. Was the change in price a positive or negative change?
Answer:
Positive
V
Part B
What was the percentage of change in the price of the house?
Answer:
%
There was a 125% change in the price of the house.
The answer can be deduced to be above 100% because the revised price represented an increase from the initial 100,000.
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000.
Whatever the case, in order to solve this problem,
you must divide 100,000 by 125,000 to discover the answer. 125,000/100,000=1.25.
Then 1.25 can be converted to 125%.
So, There was a 125% change in the price of the house.
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Solve the system of linear equations by substitution. 4x−2y=14 y=1/2x−1
4x−2y=14
Step-by-step explanation:
Answer:
The solution to the system of linear equations is x = 4, y = 1.
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}4x-2y=14\\y=\dfrac{1}{2}x-1\end{cases}[/tex]
To solve the system of linear equations by the method of substitution, substitute the second equation into the first equation:
[tex]\implies 4x-2\left(\dfrac{1}{2}x-1\right)=14[/tex]
Solve the equation for x:
[tex]\implies 4x-x+2=14[/tex]
[tex]\implies 3x+2=14[/tex]
[tex]\implies 3x=12[/tex]
[tex]\implies x=4[/tex]
Substitute the found value of x into the second equation and solve for y:
[tex]\implies y=\dfrac{1}{2}(4)-1[/tex]
[tex]\implies y=2-1[/tex]
[tex]\implies y=1[/tex]
Therefore, the solution to the system of linear equations is:
x = 4, y = 1Tenisha Gist has a sheet of brass that is 36 inches wide and cuts two pieces that are each 8 3/4 inches wide. What is the width of the leftover brass?
The width of the leftover brass is 18 1/2 inches.
How to determine the width of the leftover brass?From the question, we have the following parameters that can be used in our computation:
Initial length = 36 inches
Length of each piece = 8 3/4 inches
The width of the leftover brass is then calculated as
Width = Initial length - 2 * Length of each piece
substitute the known values in the above equation, so, we have the following representation
Width = 36 - 2 * (8 3/4)
Evaluate
Width = 18 1/2
hence, the width is 18 1/2 inches
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On a team, 3 girls and 2 boys scored a total of 27 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 15. Each girl scored the same number of points, and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answer: Let x be the number of points scored by each girl and y be the number of points scored by each boy.
We know that:
3x + 2y = 27 (the total number of points scored by the 3 girls and 2 boys)
3x - 2y = 15 (the difference between the number of points scored by the girls and the number of points scored by the boys)
We can use the second equation to find the value of one of the variables and substitute it into the first equation.
3x - 2y = 15
3x = 15 + 2y
Substitute this into the first equation:
(15 + 2y) + 2y = 27
2y = 12
y = 6
Now that we know that each boy scored 6 points, we can substitute that back into the second equation to find the number of points each girl scored:
3x - 2y = 15
3x - 2(6) = 15
3x = 27
x = 9
So each girl scored 9 points and each boy scored 6 points.
Step-by-step explanation:
On a team have 3 girls and 2 boys
Let say each girl points scored=x
Let say each boy points scored=y
Total scored by 3 girls and 2 boys =27
3x +2y=27----------1
The difference between points of 3 girls and 2 boys =15
3x-2y=15---------2
Solve equation 1 and 2
From 2nd equation
we can rewrite as :
3x=15+2y---------3
Submit 3rd equation in 1st equation.
15+2y+2y=27
4y=27-15
4y=12
y=3
Therfore, each boy points scored=3
For find each girl scored points
Submit y=3 in 1st equation.
3x+2(3)=27
3x=27-6
3x=21
x=7
Therfore, each girl points scored=7
Therfore,number of points each boy scored by =3points
Therfore,number of points each girl scored by =7points
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use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class.
(a)The class width = 3
(b) The class midpoint of the first class = 51
(c) The class boundaries of the first class = (49.5, 52.5)
Consider the frequency distribution in the following image.
We know that in frequency distribution the class width is nothing but the distance between the lower limits of consecutive classes.
Whereas the range is the difference between the maximum and minimum data entries.
The smallest number is 50, and the largest is 62.
So the range is 62 - 50 = 12
We know that the formula for the class width:
Class width= upper limit – lower limit +1
So, the class width = 52 - 50 + 1
= 3
The formula for the midpoint of each class:
midpoint = (lower limit of class + upper limit of class)/2
Let us assume that m be the midpoint of the first class.
Using above formula of midpoint:
m = (50 + 52)/2
m = 51
We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.
So, the class boundaries of the first class = (49.5, 52.5)
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If I take a loan of 4500€ at 6.5% and pay it back in 4 years, how much interest will i pay?
The required simple interest would be the amount of 1,170€ on a 4500€ principal deposited for four years at a rate of 6.5%
We have been given data as:
Principal (P) = 4500€
Rate of Interest (R) = 6.5% = 6.5/100 = 0.065
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 4500 × 6.5% × 4
⇒ Simple interest = 4500 × 6.5/100 × 4
⇒ Simple interest = 4500 × 0.065 × 4
Apply the multiplication operation, and we get
⇒ Simple interest = 1,170€
Therefore, the required simple interest would be the amount of 1,170€.
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Find y and x in the following figure
The measure of x is 105° and the measure of y is 45°.
What is a square?A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
The given quadrilateral is square.
The diagonals of a square are angle bisectors. Therefore, the diagonals split the right angles of the square into two 45° angles.
Here, y°=45°
Here, a+60° =180°
a=120°
In quadrilateral y°+x°+a°+90°=360°
45°+x°+120°+90°=360°
x°+255°=360°
x°=105°
Therefore, the measure of x is 105° and the measure of y is 45°.
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Angle
x
= 076° and angle
y
= 111°.
Find the bearing of point A from point O.
The bearing of point A from point O is 256°.
What are bearings?In mathematics, a bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.
Given that, angle x= 076° and angle y = 111°.
Now, the bearing of point A from point O is
180°+ 076°
= 256°
Therefore, the bearing of point A from point O is 256°.
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