The total cost of an item that sells for $12 is $12.96
How to determine the total cost of an item that sells for $12?From the question, we have the following parameters that can be used in our computation:
Selling price = $12
Sales tax = 8%
The total cost of an item that sells for $12 is then calculated as
Total cost = Selling price * (1 + Sales tax)
Substitute the known values in the above equation, so, we have the following representation
Total cost = 12 * (1 + 8%)
Evaluate
Total cost = 12.96
Hence, the total cost is $12.96
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It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle
formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.
Distance between first base to home plate and from home plate to third plate are equal.
Given : It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by the third base to home plate ,and from home plate to third base.
The given situation and distance between first base to home plate and from home plate to third plate are equal.
On Converting the given situation into a geometry problem. So we name the require points.
Let A be the home plate,
B is first base,
C is the second base,
And D is the third base.
Now, we can present a geometrical proof:
Statement and their reasons
(1) BC = CD - ( Given )
(2) AC = AC - ( Reflexive Property )
(3) Δ ACD = Δ ACB - ( SAS Congruence - side angle side)
(4) AD = AB - ( CPCTC - Congruent Parts of Congruent Triangles are Congruent )
Therefore, the gap from 1st base to home plate, and from home plate to 3rd plate are equal.
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What is the formula of perimeter Class 6?
The perimeter of a closed shape is the overall length of the boundary. As a result, the perimeter of that shape is determined by adding up all of its sides. Therefore, Perimeter(P) = Sum of All Sides is the perimeter formula.
The formula is:
Perimeter = (the distance all the way around the outside of the figure).
How to calculate the distance all the way around the outside of the figure
is different for every shape.
A few of them are:
The perimeter of a Square, (P) = 4 × Side units.
The perimeter of a Rectangle, (P) = 2(l + b) units.
The perimeter of a Triangle is = Sum of all three sides.
The perimeter of a Circle = 2 π r = π d.
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The ages of the winners of a cycling tournament are approximately? bell-shaped. The mean age is 36. The ages of the winners of a cycling tournament are approximately? bell-shaped. The mean age is 28. 2 ?years, with a standard deviation of 3. 5 years. Transform into a z score
Therefore , the solution of the given problem of median comes out to be
a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.
Specify median.
The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
Given : mean age is 36.
Standard deviation = 3.5
a) z - score = (34 - 28.3)/3.8 = 1.50
b) Interpretation:
An age of 34 is about 1.50 standard deviations above the mean.
c) Option B is correct.
Therefore , the solution of the given problem of median comes out to be
a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.
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What is the angle between the lines 2x 3y =- Z and 6x =- Y =- 4z?
90° is the angle between the lines 2x = 3y = -z and 6x = -y = -2z and explained with directions of ratios as below
Direction ratios of line 2x = 3y = -z which can be mentioned as [tex]\frac{x}{1/2} = \frac{y}{1/3} = \frac{z}{-1}[/tex] hence [tex](\frac{1}{2} , \frac{1}{3} ,-1 )[/tex]
Direction ratios of line 6x = -y = -2z which can be mentioned as
[tex]\frac{x}{1/6} = \frac{y}{-1} =\frac{z}{-1/4}[/tex] hence [tex](\frac{1}{6} , -1 , \frac{-1}{4} )[/tex]
hence the dot product of the direction ratio of two line is
[tex]\frac{1}{2} .\frac{1}{6} + \frac{1}{3} . (-1) + (-1) . \frac{-1}{4}[/tex]
= [tex]\frac{1}{12} -\frac{1}{3} + \frac{1}{4}[/tex]
= 0
hence this shows that angle between the given equations is 90°
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determine the number of 8x8x16 concrete masonry units needed to construct a foundation wall 104" high with a 120" perimeter. include 10% for waste
The number of concrete masonry units needed to construct a foundation wall is 102.
What is volume?The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given, a foundation wall 104" high with a 120" perimeter.
Since, perimeter of square = 4 * side
120 = 4 * side
side = 30"
Hence area of the foundation wall = side²
area of the foundation wall = 30² = 900
volume of the foundation wall = area * height
the volume of the foundation wall = 104 * 900 = 93,600"
The volume of the concrete masonry whose length, width, and depth are 16, 8, and 8 respectively is
Volume of masonry = 8 * 8 * 16
The volume of masonry = 1024
since 10 % of masonry goes to waste.
Thus the effective volume of the masonry = 1024*0.9 = 921.6
total masonry required = 93600/ 921.6 = 101.56
therefore, To build a foundation wall, 102 concrete masonry units are required.
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A shoe store recorded the number of customers who made a purchase out of a sample of 100 customers who entered the store each day. The boxplot shown summarizes the recorded data for one year. Based on the boxplot, which of the following statements is true?
A. The range of the number of customers making a purchase is greater than 32.
B. The interquartile range of the number of customers making a purchase is 25.
C. The number of days that had at least 26 customers making a purchase is greater than the number of days that had at most 11 customers making a purchase
D. The number of days that had from 11 to 26 customers making a purchase is equal to the number of days that had at most 14 customers making a purchase.
E.The difference between the median and the lower quartile for the customers making a purchase is less than 2.
Explain your thinking.
Less than 2 units separate the median from the lower quartile for customers making purchases.
What is meant by quartile deviation?The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q1. The median or second quartile is also referred to as Q2. Third quartile: Also referred to as the higher quartile or Q3.
Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q3) and lower quartile (Q1) can be used to depict quartile deviation as the letters QD. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.
The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.
Therefore, the correct answer is option E. The difference between the median and the lower quartile for the customers making a purchase is less than 2.
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Angle J and Angle M are base angles of isosceles trapezoid JKLM. If angle j= 23x+5, and angle m = 13x+15 , find measure k .
The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:
23x + 5 = 13x + 15
23x - 13x = 15 - 5 {collect like terms}
10x = 10 {divide through by 10}
x = 1
angle J = 23(1) + 5 = 28°
Angle K and angle J are supplementary so:
K = 180 - 28
K = 152°
Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°
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Melee has 1/8 of her candy bar left valid has 3/8 of his candy bar left if they put their candy together which fraction of candy bar do they have
Answer:
4/8
3/8 + 1/8 = 4/8
URGENT!!
Which of the following lists is in order from least to greatest?
Answer:
It's B, -2, v/5 4, and 3².
What is an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35?
Answer:
4x - 5y = 10
Step-by-step explanation:
We can use the point-slope form to find the line equation:
[tex] \displaystyle{y - y_1 = m(x - x_1)}[/tex]
Where (x1,y1) is the point that the line intersects and m is slope. We know the line passes through (-5,-6) and the slope is parallel to the line 4x - 5y = 35. Meaning the slope of that line is equal to slope of 4x - 5y = 35.
In this equation form Ax + By = C, we can find slope by m = - A/B. Therefore, m = -4/-5 which equals to 4/5. Hence, the slope is 4/5
[tex] \displaystyle{y - y_1 = \dfrac{4}{5}(x - x_1)}[/tex]
And also it intersects the point (-5,-6). Therefore:
[tex] \displaystyle{y - ( - 6) = \dfrac{4}{5}(x - ( - 5))} \\ \\ \displaystyle{y + 6 = \dfrac{4}{5}(x + 5)}[/tex]
Then convert to Ax + By = C to match with the given equation in problem:
[tex] \displaystyle{5(y + 6 )= 5 \left(\dfrac{4}{5}(x + 5) \right)} \\ \\ \displaystyle{5y + 30 = 4(x + 5)} \\ \\ \displaystyle{5y + 30 = 4x + 20} \\ \\ \displaystyle{ \therefore 4x - 5y = 10}[/tex]
Courtney is in the process of buying a minivan. The car she wants to buy is $29,999. The required down payment is 20% . How much will she need to put down in order to purchase this car
Car insurance coverage covers damages caused by or other mishaps. The following damages are covered claims except :
A. A head on collisions .
B. A tree falls in your car during a windstorm
C. The sun weathers the paint on your car and it must be repainted
D. A thief breaks your back window and steals the guitar from your back seat
On observing the provided question we can say that - the function f(x) = a^x is Range : (−∞,∞) or all real numbers
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the number and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
The answer to the question is that all real numbers or (−∞,∞)
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What is Y =- 2 on a graph?
The graph of y is a straight line parallel to the x−axis through the point (0,-2)
Now, According to the question:
What is slope and example?
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
The given equation is Y = -2
y = -2 is a line in which all points have the y-value -2. The line has a slope of 0 (horizontal line) since the y-value does not change for any value of x.
The point-intercept form for the equation of a line is:
y = mx + b
We can write y = -2
As y = 0x - 2;
slope = 0, y-intercept = -2
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Which tables of (x, y) values given below could represent functional relationships? Explain your thinking.
Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.
what is function ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
y = x+5
2.When x = 10,y = x+5 = 10+5 = 15
3.When x =15,y = x+5 = 15+5 = 20
4.When x = 20,y = x+5 = 20+5 = 25
Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.
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What kind of transformation converts the graph of f(x)= – 2x–10 into the graph of g(x)= – 2x+10?
Answer: Shift right 20 units
Fill in the blank so that products unloaded and time are in a proportional relationship.
A conveyer belt unloads 48 products in 6 minutes. The same conveyor belt unloads
⬜ products in 1 minute.
Answer: 8 products in 1 minute
Step-by-step explanation:
6 min=48 products
48/6=8
1 min= 8 products
How many five ounce glasses of wine have the same alcohol content as one 12-ounce beer? responses one one two two three three four
A total of 3 five ounces glass are needed so have the same alcohol as that of a 12 ounce glass.
In order to find the number of glass of capacity five ounces that will have the same capacity as that of the twelve ounce glass can be calculated as followed,
Let us say that n number of five ounces glasses are required to equate 12 ounce glass.
Now, we can write the relation,
using simple algebra,
n(Five ounces glasses) = 1 Ounce alcohol content
n = 12/5
n = 2.4
But, we have to answer an integral value, so, we will say that the required number of the glasses is 3.
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Every tread of a staircase is 8 in. deep, and every riser is 6 in. high. How would you find the angle the staircase makes with the floor? Explain.
Answer:
36.9°
Step-by-step explanation:
You want to know the pitch angle of a staircase with a riser height of 6 inches and a tread depth of 8 inches.
TangentThe tangent of an angle is the ratio of the side opposite to the side adjacent:
Tan = Opposite/Adjacent
ApplicationThe tangent of the staircase angle to the floor will be the ratio of the riser height to the tread depth:
tan(α) = (6 in)/(8 in) = 3/4
The angle is found using the inverse tangent function.
α = arctan(3/4) ≈ 36.9°
__
Additional comment
You need to be a little bit careful here. Different authors define "tread depth" differently. For the purpose of this question, it must be defined as the horizontal distance between corresponding points on adjacent treads, as shown in the attached illustration.
Some authors define tread depth as the distance from the nosing to the riser. If that definition is used, the "run" of the step will be the tread depth less the nosing depth. The pitch angle will be the arctangent of the ratio of riser height to "run".
The tread depth of 8 inches is a little too narrow to be in compliance with some building codes. A more usual minimum is about 10 inches with a riser height of 7 1/2 inches.
Answer:
0.75 tangent 0.75
Step-by-step explanation:
Neegan paddles a kayak 21 miles upstream in 4.2 hours. the return trip downstream takes him 3 hours. what is the rate that neegan paddles in still water? what is the rate of the current?
The speed of Neegan paddles in still water will be 6 miles/Hr, while the rate of the current will be 1 mile/Hr.
Neegan paddles a kayak 21 miles upstream in 4.2 hours.
As he is moving in Upstream, so during returning the flow will be downstream
Downstream refers to the direction of the flow's termination, which is at the other end of the canal from the source. You are travelling upstream, for instance, if you are sailing from Kingston to Toronto. You are travelling downstream if you are moving from Kingston to Cornwall.
Let the speed of Neegan paddles in still water = x miles/Hr.
Let the rate of the current be = y miles/Hr.
As Speed = Distance/Time
So, for Upstream speed, Speed will be = x-y
For downstream, the speed will be = x+y
From question,
(x-y) = 21/4.2 = 5-----(i)
(x+y)= 21/3 = 7 -----(ii)
Solving (i) and (ii)
2x = 12
=> x = 6
So, the value of y (From (i), will be = (x-5) = 6-5 = 1
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Solve each system of inequalities. SHOW WORK.
[tex]\left \{ {{0.7x-2.1\ \textless \ 0} \atop {\frac{2}{3} x\ \textgreater \ 1}} \right.[/tex]
Answer:
Solve linear or quadratic inequalities with our free step-by-step algebra calculator. ... Example 1 Solve for x and check: x + 5 = 3. Solution.
Missing: [tex 0.7x-2.1\ \textless \atop \textgreater tex]
How many people are at chrissys birthday party?
22 1\2 divide 1 1/4
Answer:
The answer is 18
Step-by-step explanation:
22½ = [(22 × 2) + 1] ÷ 2 = 45/2
1 ¼ = [(1 × 4) + 1] ÷ 4 = 5/4
Now,
45/2 ÷ 5/4
45/2 × 4/5
(45 × 4) ÷ (2 × 5)
180/10 = 18
Thus, 18 people are at Chrissy's birthday party.
In the decathlon event at large track meets, male athletes compete in a total of 10 events. Their combined performance in each of the events is used to determine the winner. Two of the events are the 200-meter dash and the javelin throw. For 12 athletes at a large international competition, performances in these two events are recorded and placed in a scatterplot. The value of r for this scatterplot is 0.369.
A graph titled decathlon Events has 200-meter dash time (seconds) on the x-axis, and Javelin throw distance (meters) on the y-axis. Points are grouped loosely together in a line with positive slope.
Which of the following best describes the relationship between the variables in the scatterplot?
Those with lower 200-meter times tend to have longer javelin distances. The relationship is strong.
Those with higher 200-meter times tend to have longer javelin distances. The relationship is strong.
Those with lower 200-meter times tend to have longer javelin distances. The relationship is moderate.
Those with higher 200-meter times tend to have longer javelin distances. The relationship is moderate.
answer is D
Based on the information provided, the best description of the relationship between the variables in the scatterplot is: option D, "Those with higher 200-meter times tend to have longer javelin distances. The relationship is moderate."
What is the relationship about?The scatterplot shows a positive relationship between the two variables, as indicated by the points being grouped loosely together in a line with a positive slope.
This means that as the 200-meter dash time increases, the javelin throw distance also tends to increase. The coefficient of correlation, r, also supports this relationship, as a value of 0.369 indicates a moderate positive correlation between the two variables. Though the correlation is moderate, it's important to note that this does not imply causality.
Therefore, note that, based on the description in the question, the relationship is moderate, not strong. The statement is accurate only when the correlation coefficient is between 0.3-0.7 which is considered as moderate correlation.
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Answer:
d
Step-by-step explanation:
Evan completed his math homework in 23 minutes. It took Troy 2 times as long
to complete his math homework. How long did it take Troy to complete his
homework?
minutes
Answer:
46
Step-by-step explanation:
You multiply 23×2 and that is how I got my answer.
HELP THIS IS MY LAST PROBLEM
The percentage markup the store made before selling those speakers
are 136.33%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A store bought a set of speakers for $82.86 and sold them for
$195.82.
So, The amount of profit is $(195.82 - 82.86).
= $112.96.
Now, The markup percentage can be obtained by the concept of the percentage change.
Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,
= (112.96/82.86)×100%.
= 136.33%.
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Solve the inequality. Graph the solution.
-1/3h > or equal to 8
(step by step equation)
We can solve the inequality to get:
h ≤ -3
And its graph can be seen below.
How to solve the inequality?Here we have the following inequality:
-(1/3)*h ≥ 8
To solve the inequality, we need to isolate h.
So we can multiply both sides by -3 (notice that this will change the sign of the inequality symbol)
So we will get:
-3*(-1/3)*h ≤ -3*h
h ≤ -3
Now to graph this, we need to draw a closed circle at -3, and draw an arrow that gose to the left.
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A line with a slope of 0 passes through the points (-2,0) and (-8,c). What is the value of c?
The value of c will be 0.
What is a slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
m = y2 - y1 / x2 - x1
where m = 0
y2 = c
y1 = 0
x1 = -2
x2 = -8
0 = c - 0 / -8 - -(2)
0 = c - 0 / -8 + 2
0 = c - 0 / -6
c - 0 = -6(0)
c - 0 = 0
c = 0
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Can u please help............
Answer:
PF = 9
Step-by-step explanation:
the incentre of a triangle is equally distant from the triangle's 3 sides, that is
PD = PE = PF
using PD = PE to solve for x
5x - 6 = 3x ( subtract 3x from both sides )
2x - 6 = 0 ( add 6 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3
then
PE = 3x = 3 × 3 = 9
PF = PE = 9
Solve: 8w + 5= 4 (2 w+1)=
Answer: No Solutions
Step-by-step explanation:
8w + 5= 4 (2 w+1)=
8w+5=(4)(2w)+(4)(1)
8w+5=8w+4
-8w -8w
5=4
-5 -5
0=-1
Which means there are No Solutions.
Answer:
8w+5=4(2w+1)
8w+5=8w+4
collect like terms
8w-8w = 4-5
0=-1
there is no solution
If p(x) = b² - 16b +32 and q(x) = -32b-32 what values of x does p(x)=q(x)?
The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.
Given that,
The functions are p(x) = b² - 16b +32 and q(x) = -32b-32
We have to find the x value when the functions are equivalent to each other.
We know that,
Take the functions
p(x) = b² - 16b +32 and q(x) = -32b-32
When the function are equivalent
p(x) = q(x)
b² - 16b +32 = -32b-32
b² - 16b +32 +32b+32=0
b² + 16b +64 = 0
Now find the factors for 64
64 = 8×8
b² + 8b + 8b +64 = 0
Taking common terms
b(b + 8) + 8(b + 8)=0
(b + 8)(b + 8)=0
b=8
Therefore, The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.
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The table shown represents a linear relationship. x 0 1 3 4 y −8 −6 −2 0 Based on the table, what is the equation of the linear relationship in slope-intercept form? y = 2x − 8 y = 2x + 8 y = −2x + 4 y = −2x − 4
Based on the table, an equation of the linear relationship in slope-intercept form include the following: A. y = 2x − 8
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept.Next, we would determine the slope of the data points in this table as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-6 - (-8))/(1 - 0)
Slope, m = 2/1
Slope, m = 2.
At point (0, -8), an equation of this line can be calculated in slope-intercept form as follows:
Note: The y-intercept is equal to -8.
y = mx + c
y = 2x + (-8)
y = 2x - 8.
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Answer:
A. y = 2x − 8
Step-by-step explanation:
Draw the image of quadrilateral ABCD under the translation (x, y) to (x-7, y+1).
help me please!