In the town of Centralburg (Figure 1), which is laid out in a uniform block grid, the grocery store is three blocks East and four blocks North of the post office. Which of the following is a correct equation for the quantities represented in this scenario?
Answers
Answer:
tan(θ)= dn/de
θ=arctan(dn/de)
Step-by-step explanation:
Related Questions
Given f(x)=|x| , after performing the following transformations: shift to the left 40 units, compress vertically by a factor of 1/49 and shift downward 45 units, the new function g(x)=
Answers
The new function after the transformation will be g(x) = (1/49) |x + 40| - 45.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = a|x - h| + k
The parent function is given below.
f(x) = |x|
Shift to the left 40 units, compress vertically by a factor of 1/49 and shift downward 45 units. Then the vertex is given as,
(h, k) = (-40, -45)
And the leading coefficient is given as,
a = 1/49
Then the new function after the transformation will be given as,
g(x) = (1/49) |x + 40| - 45
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Which parallelogram (if any) is a rectangle? By what property?
B
90°
A
1
C B
DA
88°
||
OD. Neither I nor II
88
D
OA. Both I and II; congruent diagonals property
B. I only; one pair of opposite sides property
C. I only; one right angle property
Answers
4. Declare is to say as ask is to
A. exclaim
B. question
C. think
D. know
Answers
Answer:
B) Declare is to say, and ask is to question.
Step-by-step explanation:
Hope it helps! =D
What is the range of the given function?
h
O x 1 x=-5. 1.4.6)
4,
Oyly=-7.-1.0.9}
Ox|x=-7. -5, -1, 0, 1, 4, 6, 9}
Oyly=-7.-5. -1, 0, 1, 4, 6, 9)
Answers
The range for the given function will be B i.e. {-7, -1, 0, 9}.
what is range of a function?
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
Domain
The set of all possible values which qualify as inputs to a function is known as the domain of the function, or it can also be defined as the entire set of values possible for independent variables. The domain can be found in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive. (In the case of a function with fraction values).
We can see from the image the values given for y i.e. range={-7, -1, 0, 9}.
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consider the equation 7x + 4 = ax + b.
for each pair of values for a and b, determine the number of solutions that the equation has.
select no solution, one solution, or infinitely many solutions for each pair of values.
1. a = 7, b = -4
2. a = 4, b = 7
3. a = 7, b = 4
4. a = -7, b = 4
Answers
Answer:
a = 7, b = -4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are equal, the equation becomes 7x = ax - 4, we can see that the equation has only one solution.
a = 4, b = 7:
This equation can be rewritten as 7x = ax + b - 7.
Since the coefficients of x on both sides are different, the equation becomes 7x = 4x + 7, we can see that the equation has no solution.
a = 7, b = 4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are equal, the equation becomes 7x = 7x + 4, we can see that the equation has infinitely many solutions.
a = -7, b = 4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are different, the equation becomes 7x = -7x + 4, we can see that the equation has no solution.
Step-by-step explanation:
If angle C is a right angle and angle A equals 50º, then prove that the measure of angle B equals 40º. Which of the following would be the first step to assume in order to prove the statement above by contradiction using an indirect proof?
The measure of angle B equals 40º.
Angle C is not a right angle.
The measure of angle A equals 50º.
Angle C is a right angle.
The measure of angle B does not equal 40º.
Answers
The first step would be to assume that "the measure of angle B does not equal 40º".
Which would be the first step to prove the contradiction using an indirect proof?The first step to assume in order to prove the statement above by contradiction using an indirect proof would be to assume the opposite of what you are trying to prove.
In this case, the opposite of the statement "the measure of angle B equals 40º" is "the measure of angle B does not equal 40º".
So, the first step would be to assume that "the measure of angle B does not equal 40º".
This assumption will be used to reach a contradiction, which will ultimately prove that the original statement is true.
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Write the proportion.
5.4 hours is to 9.0 hours as
3.3 hours is to 5.5 hours.
PLEASE HELP!!!
Answers
Find the value of c ÷ 7 when c = 49
Answers
Answer: 7
Step-by-step explanation: Plug in 49 for c.
49 divided by 7 is 7.
Answer:
c ÷ 7 = 7
Step-by-step explanation:
because if c = 49 then 49 ÷ 7 = 7
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A holiday tree is formed by extending single strands of lights from the top of a 22 foot pole to an anchor point on the ground. Each strand's anchor point is on the circumference of a circle, where the bottom of the pole is the center of the circle. If the angle formed between the ground and a strand of lights is 5π/18
find the length of a light strand.
Round to the nearest hundredth of a foot, if necessary.
The length of a light strand is _______________
Answers
The length of the light strand is 28.72 feet.
What are trigonometric functions?Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given A holiday tree is formed by extending single strands of lights,
height of pole = 22 feet
angle made by strands of light = 5π/18
it forms a right angle with the ground,
with the sine function, we can calculate the length of the strand,
here height of the pole is perpendicular and strands form a hypotenuse,
sinФ = perpendicular/hypotenuse
Ф = 5π/18
sin(5π/18) = 0.766
sin(5π/18) = 22/hypotenuse
hypotenuse = 22/0.766
hypotenuse = 28.72 feet
Hence the length is 28.72 feet.
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an animal can travel 4/7 meters in 1/8 of an hour. what is the rate in meters per hour?
Answers
An animal traveling 4/7 meters in 1/8 hours has a speed rate of 32/7 meters per hour in fractional form.
What is a fraction?
In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
The distance the animal can travel is = 4/7 meters
The time in which the animal can travel the specified distance = 1/8 hours
The distance and time is given in fractional form.
To get the speed rate follow the formula for speed -
Speed = Distance / Time
Find the value in fractional form.
Substitute the values in the equation -
Speed = (4/7) / (1/8)
The fraction in the denominator will be reciprocated and then multiplied with the fraction in the numerator.
Speed = 4/7 × 8/1
Speed = 32/7
Therefore, the speed rate is 32/7 meters per hour.
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Fill in the blank if point A always begins at 45 and point B at 69.
A) Points A and B are units apart.
b) If A moves 2 units to the right, and B moves 2 units to the left, the points will be ______ units apart.
c) If A moves 2 units to the left, and B moves 2 units to the right, the points will be _____ units apart.
D) If A moves 10 units to the right, and B moves 10 units to the left, the points will be _____ units apart.
e) If A moves 12 units to the right, and B moves 12 units to the left, the points will be _____ units apart.
f) A moved units to the left, B moved the same number of units to the right, and the points became 48 units apart.
Answers
Using simple Subtraction, following is the required data.
point A always begins at 45 and point B at 69,
b) If A moves 2 units to the right, and B moves 2 units to the left, the points will be 20 units apart. (47 - 67)
c) If A moves 2 units to the left, and B moves 2 units to the right, the points will be 28 units apart. (43 - 71)
D) If A moves 10 units to the right, and B moves 10 units to the left, the points will be 4 units apart. (59 - 55)
e) If A moves 12 units to the right, and B moves 12 units to the left, the points will be 0 units apart.
f) A moved units to the left, B moved the same number of units to the right, and the points became 48 units apart.
Where Can Subtraction Be Used?We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.
Subtraction can be applied in a variety of real-world situations.
Assume you had five apples and your friend had three. The number of remaining apples may be determined by subtracting: 5 - 3 = 2. Therefore, you are left with 2 apples. Similar to the previous example, if a class has 16 students, 9 of them are girls, we can determine the number of boys in the class by deducting 9 from 16. (16 - 9 = 7). There are 7 lads in the class, as far as we know.
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What place is the underlined number the number is 506.34 and the underlined digit is four
Answers
Answer:
It is the hundredth place which is underlined.
What is the angle of elevation of the sun when a 47 ft mast casts a 26 ft shadow. Round to the nearest degree.
Answers
The angle of elevation of the sun will be 61.04°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the angle of elevation of the sun when a 47 ft mast casts a 26 ft shadow.
tanθ = 47 / 26
θ = tan⁻¹ ( 47 / 26 )
θ = 61.04°
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A rose garden is formed by joining a rectangle and a semicircle, as shown below. The retangle is 32 ft long and 24 ft wide. If the gardener wants to build a fence around how many feet of fence
Answers
The length, width, and fence of a semicircle are the parameters for the garden fence.The required fence length is 118.54 feet.
How is the fence of the semicircle calculated?As shown below, a rose garden is created by connecting a rectangle with a semicircle.The rectangle is 22 feet broad by 31 feet long.
The necessary fence is computed by multiplying the rectangle's length and width by its radius.
Radius = Diameter /2 22/2 = 11 gives the radius of the semicircle.
And the semicircle's garden fence's measurements are:
11*3.14
= 34.54
Therefore,
The length, width, and fence of a semicircle are the parameters for the garden fence.
Garden fencing is necessary and equals 22+31+31+34.54
The garden fence length is 118.54 feet.
Consequently, 118.54 feet of fence
The required fence length is 118.54 feet.
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Write down three vectors a, b, and c that make 0◦ , 90◦ , and 180◦ angles with w.
w is a vector: w = <1, 2>
Answers
The solutions to the vectors a, b, and c are infinite. Given that there is just one equation and two variables
What is vector?A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation.
Given, three vectors a, b, and c that make 0◦, 90◦, and 180◦ angles with w.
w is a vector: w = <1, 2>
Since magnitude is not given we will form the equation in the terms of x and y for all three vectors
a makes a 0-degree angle with w
So, the multiple of a and w will be 1
x + 2y = -1
b makes a 90-degree angle with w
So, the multiple of a and w will be 0
x + 2y = 0
c makes a 180-degree angle with w
So, the multiple of a and w will be -1
x + 2y = 1
Therefore, Vector a, b, and c will have infinite solutions Since there are two variables and one equation only
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Each small cube has edges that are 1/3 yard long
. Which expression can you use to find the volume
Answers
The expression is B=2×4×5×1/3×1/3×1/3.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the edge length of the each cube is 1/3 yard.
We know that volume of a rectangular prism =l×b×h
Therefore volume=4/3×2/3×5/3
=1.481
From the given expressions the expression is B=2×4×5×1/3×1/3×1/3
Hence, the expression is B=2×4×5×1/3×1/3×1/3.
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Hello I need help with my math question three please thank you
Answers
The lengths of the unknown sides and angles are: 12.3, 229.6, 24.6, 53, 139, and 28 respectively
How to find lengths of triangles?We are to use the trigonometric in finding the unknown sides
1a) From the trig ratio of cosine
Cos A = opposite/Adjacent
Cos35 = a/15
a=15*cos35
a = 15*0.8192
a=12.3
1b) Cos A = opposite/Adjacent
Cos25 = a/250
a=250*cos25
a = 250*0.9063
a = 226.6
2) Using the sine ratio
sinA = opposite/hypothenuse
sin A = 5/12
Sin A= 0.4167
Taking the sine inverse we have
A=24.6 degrees
2b) Using the ration of cosine
CosX = 12/15
Cos x = 0.8000
x= Cos⁻¹0.8000
x=53 degrees
3) Using Pythagoras theorem to find length AB = c
c²=a²+b²
c²=123²+65²
c²= 15129+4225
= 19354
c=√19354
c= 139
To find the angle,
SinA = 69/139
Sin A = 0.4676
Taking the sine inverse
A= 28⁰
The second angle B is 90-28 = 62⁰
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NO LINKS!! Use the diagram to name each of the following pairs of angles. If the name doesn't exist say "none" Part 3
k. <3 and <6
l. <2 and <12
Answers
Answer:
k) Alternate exterior angles
l) Same-side exterior angles
Step-by-step explanation:
Part k∠3 and ∠6 and alternate exterior angles.Alternate exterior angles
When two lines are intersected by a transversal, the angles that are exterior to the two lines and are on opposite sides of the transversal line are called "alternate exterior angles".
Part l∠2 and ∠12 are same-side exterior angles.Same-side exterior angles
When two lines are intersected by a transversal, the angles that are exterior to the two lines and on the same side of the transversal line are called "same-side exterior angles".
100 POINTS HELP PLEASE FAST THERE IS A PICTURE JUST CLICK ON IT PLEASE
Answers
The graph for the inequality x + 5y ≤ 10 and x - y < 3 is plotted and the correct option is option B.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given inequality equations is -
x + 5y ≤ 10
x - y < 3
In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.
So, the graph of inequality x + 5y ≤ 10 will have a straight line.
And, the graph of inequality x - y < 3 will have a dotted line.
Now, writing the inequality x + 5y ≤ 10 and x - y < 3 in slope-intercept form y = mx + b -
5y = -x + 10
-y = -x + 3
Substituting the values of x and y with origin (0,0) -
5(0) = -(0) + 10
0 = 10
-(0) = -(0) + 3
0 = 3
Putting the inequality symbol back -
0 ≤ 10
0 < 3
Since, 0 ≤ 10 and 0 < 3 is true hence the shaded region of graph will cover the origin.
Therefore, the graph for the inequality x + 5y ≤ 10 and x - y < 3 is plotted.
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Answer:
Graph B
Step-by-step explanation:
Given inequalities:
[tex]x + 5y \leq 10[/tex]
[tex]x-y < 3[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Rewrite the inequalities so that y is the subject:
[tex]\begin{aligned}\implies x + 5y &\leq 10\\5y &\leq -x+10\\y &\leq -\dfrac{1}{5}x+2\end{aligned}[/tex]
[tex]\begin{aligned}\implies x-y & < 3\\x& < y+3\\x-3& < y\\y& > x-3\end{aligned}[/tex]
[tex]\textsf{Therefore, the graph of}\;\;y \leq -\dfrac{1}{5}x+2\;\; \sf is:[/tex]
A solid line with a negative slope and shading under the line.[tex]\textsf{Therefore, the graph of}\;\;y > x-3\;\;\sf is:[/tex]
A dashed line with a positive slope and shading above the line.The only graph that displays this is graph B.
A tiling pattern is defined by the pattern rule equation n=5+3pn=5+3p, where p is the position number and n is the number of tiles. How many tiles would there be in position 26?
Answers
The number of titles would there be in the position 26 is 83 titles.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
A tiling pattern is defined by the pattern rule equation 'n = 5+ 3p.
where p denotes the position number and n denotes the no of titles.
Based on the above information, the calculation is as follows:
n = 5+ 3p
n= 5 + 3(26)
n = 5 + 78
n = 83
Hence, we can conclude that the number of titles would there be in the position 26 is 83 titles.
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1 You’re a travelling sales rep. You live in city A and need to drive to City B and then on to City C for business. You then need to drive back to city A. You will rent a new car in each city. The distance from A to B is 250 miles, from B to C is 175 miles and from A to C is 320 miles. You start at A and go the shortest route next to B then to C and then back to A. The car rented in City A gets 10 km per liter of fuel. The car rented in City B gets 18 km per liter and the car rented in city C 24 km per liter. Gas costs $4.25 US per gal. You drive From City A to City B at an average speed of 120 km per hr. You drive from City B to City C at an average speed of 100 km per hr. You drive from City C to City A at an average speed of 140 km per hr. The exchange rate is 0.85 Euro per $1. 1) How far is the total distance in Kilometers? 2) How much will you spend on gas in euros? 3) How long will it take you to make the round trip not including any rest? Driving time only in minutes. 4) Suppose that while you are in City B you find out that you do not need to go to city C and decide to keep your initial car and drive back to City A. How much will this trip cost for gas in euros?
Answers
Answer:
Total distance = 250 miles + 175 miles + 320 miles = 745 miles = 1207.2 km
Total cost = (250 miles / 10 km/L * 4.25 $/gal + 175 miles / 18 km/L * 4.25 $/gal + 320 miles / 24 km/L * 4.25 $/gal) * 0.85 Euro/$ = €113.55
Total driving time = (250 miles / 120 mph * 60 min/hr + 175 miles / 100 mph * 60 min/hr + 320 miles / 140 mph * 60 min/hr) = 5.0417 hours = 304 min
Cost of trip back to City A = 250 miles / 10 km/L * 4.25 $/gal * 0.85 Euro/$ = €52.88
Step-by-step explanation:
Find the dimensions of the cube Volume= 64 in
Answers
Answer:
96'' 2 is the answer
Step-by-step explanation:
the Formula for a cube is a x a x a x a
8 divided by 18 divided by 7 multiply by 24 divided by 16
Answers
Answer:
0.0952381
Step-by-step explanation:
I used my calculator
The table shows ordered pairs of the function y=8-2x. Whta is the value of y when x =8?
Answers
Answer:24
Step-by-step explanation:
if x = 8 that mean 2 times 8 which makes 16 and added up to another 8 would be 24 so y=24
i need help with the worksheet
Answers
The slope and intercept of the linear functions are written as follows
a. 2y + 3x = 10
slope = -3/2
intercept = 5
b. x + 2y = 6
slope = -1/2
intercept = 3
c. 3y + 12 = 5x
slope = 5/3
intercept = -4
6. The coordinates of common point in the linear function is
(-6, -14)
How to find the slope and intercept of the linear functionThe slope and intercept of linear function is gotten by rewriting the equation to be in the form
y = mx + b
m = slope
b = intercept
a. 2y + 3x = 10
rearranging the equation
2y = -3x + 10
y = -3/2 x + 5
slope = -3/2
intercept = 5
b. x + 2y = 6
rearranging the equation
2y = -x + 6
y = -1/2 x + 3
slope = -1/2
intercept = 3
c. 3y + 12 = 5x
rearranging the equation
3y = 5x - 12
y = 5/3 x - 4
slope = 5/3
intercept = -4
6. The coordinates of common point in the linear function is solved using graph. From the graph the point is (-6, -14)
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Help on bottom one please and thanks!
Answers
The total investment if £3000 is in a bank after 4 years investment of 3% is £3376.5
Explain about compound interest? Compound interest is a type of interest which is calculated based on the initial principal, as well as the accumulated interest from previous periods. It is an effective way of earning interest on the total sum of money which is invested. The total investment is calculated by using the formula A=P(1+r/n)^nt, where A is the total amount, P is the principal amount, r is the interest rate, n is the number of compounding periods, and t is the time period. The total investment will be the sum of the principal amount and the accumulated interest. For example, if an investor invests $100 at a rate of 10% for two years, the total investment will be $121 ($100 principal + $21 accumulated interest). Therefore, compound interest can be a great way to grow your savings over time.Solution:
Therefore, the total investment after 4 years at a rate of 3% is given by
Total investment = P × (1 + r/n)^nt
Total investment = £3000 × (1 + 0.03)^4
= £3000 × (1.03)^4
= £3376.52
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The graph shows the height y in feet of a balloon that is launched from a platform 13.5 feet high as a quadratic function of x the time in seconds
what is the domain of this function in this situation?
Answers
Answer:
Domain is 0 ≤ x ≤ 54
Interval notation: [0, 54]
Step-by-step explanation:
I am a little confused by the question and even more so when I look at the answer choices you provided as a comment.
The domain of any function y = f(x) is the range of values of x that result in a defined real value for y.
Your answers provide the choices as single values which is not correct
Let's find the equation of the quadratic function y = f(x)
Given a vertex (h, k) , the quadratic equation is
[tex]y = a(x - h)^2 + k\\\\[/tex]
Here we have h = 24.5 and y = 43.5
So the equation is
[tex]y = a(x - 24.5)^2 + 43.5\\\\[/tex]
To find a, plug in coordinates of a point on this quadratic function from the graph. We see the function has (0, 13,5) as a point
So:
[tex]13.5 = a(0-24.5)^2 + 43.5\\\\13.5 = a(-24.5)^2 + 43.5\\\\a = \dfrac{-30}{(-24.5)^2}\\\\\\\textrm{which results in }\\a = -0.05 (rounded)[/tex]
We can find the x-intercepts of this parabola which are the domain values by plugging in 0 for y and solving for x
[tex]0 = -0.05(x-24.5)^2 + 43.5\\\\-0.05(x - 24.5)^2 = -43.5\\\\(x - 24.5)^2 = \dfrac{-43.5}{-0.05} = 870\\\\\\x - 24.5 = \pm \sqrt{870}\\\\x - 24.5 = \pm 29.5\\x = 24.5 \pm 29.5\\\\x = (-5, 54)\\\\[/tex]
So this should be the domain of x; Note however, that we cannot have negative values for x and the parabola graph does show it starts at x = 0
Domain of this function is 0 ≤ x ≤ 54
which is written in interval notation as
[0, 54]
A small pond contains four catfish and two bluegill. If four fish are caught at random, what is the probability that all of them are catfish?
a) 1/15 ≈ 6.667%
b) 1/4080 ≈ 0.025%
c) 1/720 ≈ 0.139%
d) 1/20 ≈ 5%
Answers
the probability that all of them are catfish 1/15 ≈ 6.667%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
A small pond contains four catfish and two bluegill.
Total there are a total of 2+4=6 fish
p(1st) = 4/6
p(2nd) = 3/5
p(3rd) =2/4
p(4th)= 1/3
to calculate the probability of catching 4 catfish multiply the separate probabilities together = 4/6*3/5*2/4*1/3 = 1/15
Hence the probability that all of them are catfish 1/15 ≈ 6.667%.
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6th GRADE!! HELP ME ASAP PLEASEE DUE IN 20 MIN :((
A student's scores in a history class are listed.
60, 65, 65, 73, 74, 78, 83, 83, 85, 89, 91, 92, 100
Which of the following histograms correctly represents the data?
{Option 1} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is a shaded bar for 41 to 50 that stops at 1, for 51 to 60 that stops at 2, for 61 to 70 that stops at 2, for 71 to 80 that stops at 4, for 81 to 90 that stops at 2, and for 91 to 100 that stops at 3.
{Option 2} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is a shaded bar for 41 to 50 that stops at 1, for 51 to 60 that stops at 1, for 61 to 70 that stops at 4, for 71 to 80 that stops at 3, for 81 to 90 that stops at 2, and for 91 to 100 that stops at 2.
{Option 4} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is no shaded bar for 41 to 50. There is a shaded bar for 51 to 60 that stops at 1, 61 to 70 that stops at 2, 71 to 80 that stops at 3, 81 to 90 that stops at 4, and 91 to 100 that stops at 3.
{Option 3} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is a shaded bar for 41 to 50 that stops at 2, 51 to 60 that stops at 1, 61 to 70 that stops at 1, 71 to 80 that stops at 4, 81 to 90 that stops at 3, and 90 to 100 that stops at 2.
Answers
Answer:
{Option 4}
A histogram titled Grades in History Class.
The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100.
The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9.
There is no shaded bar for 41 to 50.
There is a shaded bar for 51 to 60 that stops at 1, 61 to 70 that stops at 2, 71 to 80 that stops at 3, 81 to 90 that stops at 4, and 91 to 100 that stops at 3.
Step-by-step explanation:
The data provided is
60, 65, 65, 73, 74, 78, 83, 83, 85, 89, 91, 92, 100
Breaking this into intervals,
we get
Interval Frequency count
51- 60 1
61-70 2
71-80 3
81-90 4
91-100 3
Out of the 4 histograms shown, 3 have a bar height of 1 for the interval 41-50
But the student has no score 50 and above
So the bar height should be zero. In other words there should be no bar corresponding to the interval 41-50 and one should start the x-axis at 51
Only one histogram corresponding to Option 4 has the interval 41-50 has no bar and that is the right answer.
There is really no need to check the other histograms. Just this fact alone can eliminate the other 3 options.
But if you look at my table above, each of the frequency counts corresponds to the height of the bar for that interval so we get the correct option as Option 4 and the correct histogram picture is as attached in my answer
Answer:
{Option 4} A histogram titled Grades in History Class.
The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100.
The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9.
There is no shaded bar for 41 to 50.
There is a shaded bar for 51 to 60 that stops at 1, 61 to 70 that stops at 2, 71 to 80 that stops at 3, 81 to 90 that stops at 4, and 91 to 100 that stops at 3.
The length of a rectangle in inches is sixteen less than seven times the width. If the perimeter of the rectangle is
48 inches, what is the length, in inches?
A. 5
B. 8
C. 19
D. 40
Answers
Step-by-step explanation:
Let's call the width of the rectangle "w".
The length of the rectangle is 7w - 16.
The perimeter of the rectangle is 48, so:
2w + 2(7w - 16) = 48
Expanding the second term:
2w + 14w - 32 = 48
Combining like terms:
16w = 80
Dividing both sides by 16:
w = 5
So the width is 5 inches.
To find the length, use the formula for the length:
7w - 16 = 7 * 5 - 16 = 24 - 16 = 8
The length is 8 inches.
Therefore, the answer is:
B. 8 inches.