The length And width of a rectangle each less than 1 unit long. Which statement is true about the area of the rectangle?
Answers
Area is calculated by multiplication of dimensions:
length×width= Area
both are lesser than 1, let's say 0.5 and 0.9 as examples.
0.5×0.5=0.25
0.9×0.9=0.81
you see the area is less than one and area can never be negative so first answer is the right answer.
The correct statement is option a. The area is between 0 square units and 1 square units
What is a rectangle?Any 2-diamensional figure bounded by 4 sides in which opposite sides are equal and parallel and all the 4 angles are right angled.
How to find which statement is true about the area of the rectangle?The area of rectangle can be calculated by the formula = Length x breadth( or width)Here the length and width of a rectangle each less than 1 unit long.Now, 0 unit<length<1 unit
0 unit<width<1 unit
∴ Area of the rectangle = (length x width)
We know that if any quantity whose value lies between 0 and 1 is multiplied to another quantity whose value also lies between 0 and 1 ,then the answer will also lie between 0 and 1.If the values of both the quantities are 1, then the product will be 1⇒ 0 square units <Area of the rectangle <1 square units
∴ The area of the rectangle is between 0 square units and 1 square units
The first option matches with the answer.
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Related Questions
Marita is cutting rolls of ribbon that are 3 feet long into 1/2- foot pieces. She needs fifteen 1/2- foot pieces for a project. She has 3 rolls of ribbon. Does she have enough to cut 15 pieces? Explain.
Answers
Answer: Yes
Step-by-step explanation:
3 * 2 = 6. So you can get 6 1/2 foot pieces out of 1 roll. She has 3 rolls. 6 * 3 = 18. 18 is more than 15.
Yes, She have enough ribbon to cut 15 pieces.
What is fraction?The fraction is numerical representation of the numbers in the form of numerator and denominator.
We have,
Total rolls of ribbon = 3
Length of one roll of ribbon = 3 feet,
So,
Total Length of 3 roll of ribbon = 3 * 3 = 9 feet
And,
Marita cutting rolls into [tex]\frac{1}{2}[/tex] foot pieces.
So,
1 roll cut into pieces [tex]= \frac{3}{\frac{1}{2} } = \frac{3*2}{1}[/tex] = 6 pieces,
So,
3 roll cut into pieces = 6 * 3 = 18 pieces,
i.e.
18 pieces of [tex]\frac{1}{2}[/tex] foot ,
And she needs [tex]15\frac{1}{2}[/tex] pieces of ribbon,
And total pieces of ribbon are 18.
Hence, we can say that Yes, She have enough ribbon to cut 15 pieces.
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Write an inequality to describe the relationship between -1 1/2 and -1/4
Answers
Answer: -1 1/2 < -1/4
Explanation: Since the number is negative, -1 1/2 is further to the left on the number line, meaning it has less value.
The relationship between -1 1/2 and -1/4 can be expressed as an inequality. In this case, -1 1/2 is less than -1/4, so the inequality is -1 1/2 < -1/4.
Explanation:The relationship between -1 1/2 and -1/4 may be written as an inequality. Remember, an inequality indicates that one number is larger or smaller than another. In this case, it shows which negative number, either -1 1/2 or -1/4, is larger. On the number line, a negative number situated to the right is larger than a number situated to the left. So, in terms of value, -1/4 is larger than -1 1/2 as it's less negative. This can be written as:
-1 1/2 < -1/4
.
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I have a box of 3 cupcakes. Each one is either chocolate or vanilla. What could o have in the box? What are all the ways to answer the question?
Answers
Answer:
one chocolate and two vanillatwo vanilla and one chocolatethree chocolatesthree vanillasIf it is 250 miles from New York to Boston and 120 miles from New York to Hartford, what percentage of the distance from New York to Boston is the distance from New York to Hartford?
Answers
The distance from New York to Hartford represents 48% of the distance from New York to Boston.
Explanation:To find the percentage of the distance from New York to Boston that is the distance from New York to Hartford, we need to calculate the ratio of the two distances. First, divide the distance from New York to Hartford (120 miles) by the distance from New York to Boston (250 miles):
120 / 250 = 0.48
Convert the ratio to a percentage by multiplying by 100:
0.48 * 100 = 48%
Therefore, the distance from New York to Hartford represents 48% of the distance from New York to Boston.
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What is the definition of present value?A. the current value of a future sum of moneyB. the interest paid on a current sum of moneyC. the future value of a current sum of moneyD. the interest paid on a future sum of money
Answers
Answer:
The definition of present value is the current value of a future sum of money.
Choice A
Step-by-step explanation:
Present value (PV) is the current value of a future streams of cash flows or sum of money at a given expected rate of return by the investor. Future payment streams are discounted at the rate of return. The present value increases with the decrease in the rate of return or the discount rate and vice versa.
Option A is correct, the definition of present value is the current value of a future sum of money.
Present value refers to the concept of determining the value of a future sum of money in terms of its current worth.
It takes into account factors such as the time value of money and discounting to calculate the value of future cash flows in today's terms.
By discounting future cash flows, the present value represents the amount of money that would need to be invested or received today to achieve the same value as the future sum of money.
Hence, the definition of present value of the current value of a future sum of money.
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Ashton surveyed some of the employees at his company about their cell phone habits. From the data, he concluded that most employees at his company use cell phones primarily for business. For which sample could this generalization be valid?
Answers
Answer:
It can't be A. since if you only look at managers, you are missing all the sales executives.
It may be C. this option is more random but doesn't guarantee that you will represent both groups of employee's. Also, each time you would conduct the survey, you will receive the exact same results since it is the same people.
It isn't D. for the exact same reason as A. but you're missing managers now.
Therefore the answer is B. Some managers and some sales executives selected at random. This way you get a sample from both categories, and within those groups, it is randomly selected.
I hope this helps!
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Step-by-step explanation:
The generalization could be valid for a sample that accurately represents the entire employee population of Ashton's company.
This sample should be large enough to be statistically significant and should be selected randomly to avoid bias.
To calculate the sample size needed for a valid generalization, Ashton could use a confidence level and margin of error. Let's say he wants a 95% confidence level with a margin of error of 5%.
First, he needs to find the population size (total number of employees at the company). Let's assume there are 500 employees.
Next, he can use the formula for sample size calculation:
[tex]\[n = \frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}}\][/tex]
Where:
- (n) = sample size
-(Z) = Z-score corresponding to the desired confidence level (for 95% confidence level, Z = 1.96)
- (p) = estimated proportion of employees using cell phones primarily for business (from the survey data)
- (E) = margin of error (0.05 for 5%)
Let's say from the survey, Ashton found that 70% of employees use cell phones primarily for business.
Plugging in the values:
[tex]\[n = \frac{{1.96^2 \cdot 0.70 \cdot (1-0.70)}}{{0.05^2}}\][/tex]
[tex]\[n = \frac{{3.8416 \cdot 0.70 \cdot 0.30}}{{0.0025}}\][/tex]
[tex]\[n = \frac{{0.719856}}{{0.0025}}\][/tex]
[tex]\[n ≈ 287.94\][/tex]
So, Ashton would need a sample size of approximately 288 employees to make a valid generalization about the entire company.
To ensure the generalization is valid, Ashton needs to collect data from a sample that accurately represents the entire employee population. This sample should be large enough to be statistically significant and should be selected randomly to avoid bias.
Using statistical methods, Ashton can calculate the minimum sample size needed for a valid generalization. By setting a confidence level and margin of error, he can determine the sample size required to achieve a certain level of accuracy.
In this case, Ashton chose a 95% confidence level with a margin of error of 5%. He used a formula that takes into account the population size, estimated proportion of employees using cell phones primarily for business, and the margin of error.
After plugging in the values, he calculated that he would need a sample size of approximately 288 employees to make a valid generalization about the entire company.
So, for the conclusion that most employees at his company use cell phones primarily for business to be valid, Ashton should survey at least 288 randomly selected employees.
Complete question:
Ashton surveyed some of the employees at his company about their cell phone habits. From the data, he concluded that most employees at his company use cell phones primarily for business. For which sample could this generalization be valid?
What is the surface area of the regular pyramid below?
Answers
Answer:
648 sq units
Step-by-step explanation:
Area of the base= 12×12= 144 sq. units
Perimeter of the base=4×12= 48
Total surface area= 1/2×48×21 + 144
=648 sq units
ANSWER
648 square units.
EXPLANATION
The surface area of the regular pyramid is the area of the base plus the area of the 4 triangular faces.
We use the formula;
[tex]S.A = {l}^{2} + 4 \times \frac{1}{2} bh[/tex]
where l=12 units is the length of the square base and h=21 units is the vertical height of the triangular faces.
We substitute the values to get;
[tex]S.A = 12^{2} + 4 \times \frac{1}{2} \times 12 \times 21[/tex]
[tex]S.A = 144+ 504[/tex]
[tex]S.A =648 {units}^{2} [/tex]
Simplify the expression given below 1/2x^2-4x-2/x
Answers
Answer:
We need to simplify the following expressio:
[tex]\frac{1}{2} x^{2}- 4x-\frac{2}{x}[/tex]
Multiply the whole expression by '2x':
[tex]x^{3}-8x^{2}-4[/tex]
The expression can't be more simplified.
This table shows a proportional relationship between the number of cups of sugar and flour used for a recipe.
Enter the number of cups of sugar used for 1 cup of flour. Give your answer as a fraction.
PLEASE HELP
Answers
To find the answer for one cup of flour, divide the cups of sugar by the cups of flour. Here’s how it works.
Since we want the proportion for 1 cup of flour, we divide it by itself to get 1.
Thus, we need to have equal sides, so we divide the number of cups of sugar by the amount the cups of flour divided by.
So: 2.5/7.5=1/3
1 cup of flour is proportional to 1/3 cups of sugar.
Hope this helps!
The amount of sugar for 1 cup of flour can be determined through setting up and solving a proportion based on the given proportional relationship, though specific values are required. For example, if 3 cups of sugar are needed for 2 cups of flour, then 1.5 cups of sugar would be needed for 1 cup of flour.
Explanation:Unfortunately, the specific values are not given in the question, but we can still explain how you would find the answer. In a proportional relationship, the ratios between the two quantities (in this case, sugar and flour) is constant. This means that if we know the amount of sugar used for a certain amount of flour, we can determine the amount of sugar used for 1 cup of flour by setting up an equation and solving for the unknown variable, provided we have the necessary data.
For example, if the relationship was such that for every 2 cups of flour, you used 3 cups of sugar, then the ratio of sugar to flour would be 3/2. To find out how much sugar you need for 1 cup of flour, you can create a proportion that reads 3/2 = x/1 and solve for x. In this case, x is the equivalent amount of sugar needed for 1 cup of flour.
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Which angle in the translated trapezoid is congruent to angle S?
A.
angle Q apostrophe
B.
angle T apostrophe
C.
angle R apostrophe
D.
angle S apostrophe
Answers
Answer:
Option D. angle S apostrophe
Step-by-step explanation:
we know that
The transformation of the figure is a translation
The rule of the translation is
(x,y)-----> (x-3,y-7)
That means ----> left 3 units and down 7 units
Remember that a translation does not modify the internal angles of the figure as neither the length of their sides
so
∠S=∠S'
The center of a sphere is
a line segment from the center point to the surface of the sphere.
a fixed point equidistant from all points on the surface of the sphere.
a three-dimensional circle in which all points are equidistant from a fixed point.
the same as the base of the sphere.
Answers
Answer:
A fixed point equidistant from all points on the surface of the sphere
Step-by-step explanation:
we know that
The sphere is the set of all points in the space equidistant from a fixed point called the center of the sphere
therefore
The center of a sphere is a fixed point equidistant from all points on the surface of the sphere
In Geometry, the center of a sphere is: B. a fixed point equidistant from all points on the surface of the sphere.
What is a sphere?
A sphere can be defined as a round, three-dimensional solid geometric figure that has all its surface points (every point on its surface) at equal distances (equidistant) from the center.
In this context, we can infer and logically conclude that the center of a sphere simply refers to a fixed point that is equidistant or at equal distances from all points on the surface of the sphere.
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Find the value of x.
Answers
Answer: [tex]x=76\°[/tex]
Step-by-step explanation:
By definition the angle formed by the intersection of two chords inside a circle is:
[tex]Angle\ formed\ by\ two\ Chords=\frac{sum\ of\ intercepted\ Arcs}{2}[/tex]
You can observe in the figure that the angle formed by the intersection of the two chords measures 94°, and the intercepteed arcs are: x° and 112°.
Therefore, you need to substitute these values into the formula and solve for "x to find its value. Then:
[tex]94\°=\frac{x+112\°}{2}\\\\(94\°)(2)=x+112\°\\\\188\°-112\°=x\\\\x=76\°[/tex]
Factor the expression
81-36xy
Answers
Answer: 9(9-4xy)
Step-by-step explanation:
You can factor out the 9, as 9*9 = 81 and 9*4 = 36.
So dividing both terms, you get 9(9-4xy)
ABC is reflected across the x-axis and then translated 4 units up to create A’B’C’. What are the coordinates of the vertices of A’B’C’?
Worth 25 points
Answers
The first option is the correct choice
For which k are the roots of k(x2+1)=x2+3x–3 real and distinct?
Answers
Answer:
The solution for k is the interval (-3.5,1.5)
Step-by-step explanation:
we have
[tex]k(x^{2}+1)=x^{2}+3x-3[/tex]
[tex]kx^{2}+k=x^{2}+3x-3[/tex]
[tex]x^{2}-kx^{2}+3x-3-k=0[/tex]
[tex]}[1-k]x^{2}+3x-(3+k)=0[/tex]
we know that
If the discriminant is greater than zero . then the quadratic equation has two real and distinct solutions
The discriminant is equal to
[tex]D=b^{2}-4ac[/tex]
In this problem we have
a=(1-k)
b=3
c=-(3+k)
substitute
[tex]D=3^{2}-4(1-k)(-3-k)\\ \\D=9-4(-3-k+3k+k^{2})\\ \\D=9+12+4k-12k-4k^{2}\\ \\D=21-8k-4k^{2}[/tex]
so
[tex]21-8k-4k^{2} > 0[/tex]
solve the quadratic equation by graphing
The solution for k is the interval (-3.5,1.5)
see the attached figure
Which of the following give the correct graph and phase shift for y = 3 cos ( θ +20) – 4?
Answers
Answer:
See picture attached below
Step-by-step explanation:
We can easily find the answer to your question, if we plot the equation with a graphing calculator or any plotting tool.
The equation is
y = 3 cos (θ + 20) - 4
See attached picture below
phase_shift = 20
max_amplitude = -1
min_amplitude = -7
Period = 2π
What value is equivalent to 8 · 9 − 2 · 5?
Answers
Answer:
6.4
Step-by-step explanation:
8.9 - 2.5 = 6.4
8 - 2 = 6
9 - 5 = 4
there you have it your answer 6.4
Write the equation of a line perpendicular to the given line and passing through the given point. y=3x+3(-1,-1) step by step
Answers
ANSWER
[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]
EXPLANATION
The given line is
[tex]y = 3x + 3[/tex]
The given point is
[tex](-1,-1)[/tex]
The slope of the given line is
[tex]m = 3[/tex]
We found this by comparing
[tex]y = 3x + 3[/tex]
to
[tex]y = mx + b[/tex]
If two lines are perpendicular, then one is the negative reciprocal of the other.
Hence the slope of the required line is
[tex] - \frac{1}{3} [/tex]
Using the point-slope formula or otherwise, we can find the required equation.
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the slope and point to get:
[tex]y + 1 = - \frac{1}{3} (x + 1)[/tex]
[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]
there are some roses,lilies, and orchids in the vase. The number of roses is twice the number of lilies and the number of orchids is 5 more than the number of roses. if the total is 45, find the number of each type of flower
Answers
Answer:
The number of roses is 16
The number of lilies is 8
The number of orchids is 21
Step-by-step explanation:
Let
x-----> the number of roses
y-----> the number of lilies
z-----> the number of orchids
we know that
x=2y ----> y=x/2 ----> equation A
z=x+5 ---> equation B
x+y+z=45 ----> equation C
substitute equation A and equation B in equation C and solve for x
x+(x/2)+(x+5)=45
(5/2)x=45-5
(5/2)x=40
x=40*2/5
x=16 roses
Find the value of y
y=x/2 ----> y=16/2=8 lilies
Find the value of z
z=x+5 -----> z=16+5=21 orchids
therefore
The number of roses is 16
The number of lilies is 8
The number of orchids is 21
7. If SK = 13x - 5, KY= 2x + 9, and SY = 36-x, find each value.
Answers
Answer:
SY=34, SK=21 and KY=13
Step-by-step explanation:
we have that
SY=SK+KY
substitute the given values
(36-x)=(13x-5)+(2x+9)
solve for x
36-x=15x+4
15x+x=36-4
16x=32
x=2
Find the value of SY
SY=(36-x)=36-2=34
Find the value of SK
SK=(13x-5)=13(2)-5=21
Find the value of KY
KY=(2x+9)=2(2)+9=13
To find the values of SK, KY, and SY, substitute the given expressions for x into the equations.
Explanation:To find the values of SK, KY, and SY, we need to substitute the given expressions for x into the equations.
SK = 13x - 5SK = 13(7) - 5
SK = 91 - 5
SK = 86KY = 2x + 9
KY = 2(7) + 9
KY = 14 + 9
KY = 23SY = 36 - x
SY = 36 - 7
SY = 29
Therefore, SK = 86, KY = 23, and SY = 29.
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The ratio of counselors to campers at a camp is 1 : 9. The ratio of campers who can swim to campers who cannot swim is 7 : 2. There are 13 counselors. How many campers can swim?
Answers
Answer:
91 campers can swim
Step-by-step explanation:
step 1
Find the number of campers
we know that
The ratio of counselors to campers at a camp is 1 : 9
so
by proportion
Find the number of campers if there are 13 counselors
Let
x-----> the number of campers
1/9=13/x
x=9*13=117 campers
step 2
How many campers can swim?
we know that
The ratio of campers who can swim to campers who cannot swim is 7 : 2
so
The ratio of total campers to campers who can swim is 9 : 7
by proportion
Find how many campers can swim for a total of 117 campers
Let
x----> the number of campers that can swim
9/7=117/x
x=117*7/9
x=91 campers can swim
caculaye the average rate of change of f(x)=x^2-1/x-4 for 2<=x<=6
Answers
Answer:
4.75
Step-by-step explanation:
Given
f(x)= (x^2-1)/(x-4)
The average rate of change for the interval a≤x≤b is given by:
Rate of change= (f(b)-f(a))/(b-a)
In our question,
a=2
and
b=6
So,
f(2)= ((2)^2-1)/(2-4)
=(4-1)/(-2)
= -3/2
And
f(6)= ((6)^2-1)/(6-4)
=(36-1)/2
= 35/2
Rate of change= ( 35/2-(-3/2))/(6-2)
=(35/2+3/2)/(6-2)
= ((35+3)/2)/4
=(38/2)/4
=19/4
=4.75
The average rate of change is 4.75 ..
Answer:
Average rate of change =4.75.
Step-by-step explanation:
Given function is [tex]f\left(x\right)=\frac{x^2-1}{x-4}[/tex].
Now we need to find the average rate of change of f(x) for [tex]2\le x\le6[/tex].
So plug these values into average rate of change (ARC) formula.
[tex]ARC=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]
[tex]ARC=\frac{f\left(6\right)-f\left(2\right)}{6-2}[/tex]
[tex]ARC=\frac{\frac{6^2-1}{6-4}-\frac{2^2-1}{2-4}}{4}[/tex]
[tex]ARC=\frac{\frac{36-1}{6-4}-\frac{4-1}{2-4}}{4}[/tex]
[tex]ARC=\frac{17.5-\left(-1.5\right)}{4}[/tex]
[tex]ARC=\frac{19}{4}[/tex]
[tex]ARC=4.75[/tex]
So the final answer is average rate of change =4.75.
Which of the following equations is an example of inverse variation between the variables x and y
A. Y=6/x
B. Y=x/6
C. Y=x+6
D. Y=6x
Answers
Answer:
The answer is y = 6/x ⇒ answer A
Step-by-step explanation:
* Lets revise what is the meaning of the inverse variation
- It is a mathematical relationship between two variables
- It can be expressed by an equation in which the product of two
variables is equal to a constant
- If y is in inverse variation with x
∴ y ∝ 1/x
- Change this relation to equation
∴ y = k/x, where k is the constant of the variation
- We can write it by another way
∵ y ∝ 1/x
∴ y = k/x ⇒ by using cross multiplication
∴ yx = k
* Now lets solve the problem
∵ There is an inverse variation between the two variables x and y
∴ y ∝ 1/x
∴ y = k/x
- Look to the answer
# We will chose A because
∵ y = 6/x ⇒ use the cross multiplication
∴ yx = 6 ⇒ and 6 is a constant
∴ k = 6
* The answer is y = 6/x
determine the next term in the geometric sequence 1024,512,256,128,
Answers
Answer:
64
Step-by-step explanation:
We are dividing by 2 each time
1024 /2 = 512
512/2 = 256
256/2 =128
128/2 = 64
Which of the following expressions is equivalent to 5?
7 + (-2)
2 + (-7)
7 + 2
-7 + 2
Answers
Answer:
7 + (-2) is equivalent to 5
Step-by-step explanation:
2 plus -7 would equal -5, and so would -7 plus 2. Also, 7 plus 2 is nine; leaving us with the only possible choice... 7 + (-2).
Options:
x = 2
y = 3
y = 2x
x = 4
Answers
Answer:
x = 2
Step-by-step explanation:
A vertical line has the equation x = a. This line passes through points with x-coordinate of 2, so the equation is x = 2.
Write a variable expression for a number t times 4
Answers
T*4 just go step by step
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Identify the roots of the quadratic function.
A) x = 0 and x = 4
B) y = 0 and y = 4
C) x = 0 and x = -4
D) y = 0 and y = -4
Answers
Answer:
Step-by-step explanation:
The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.
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Solve.
5(b + 6) = 18
Answers
Answer:
b = -12/5
Step-by-step explanation:
5(b+6) = 18
5b + 30 = 18
5b = -12
b = -12/5
Answer:
b = -2.4
Step-by-step explanation:
5 ( b + 6 ) = 18
→ Expand brackets
5 b + 30 = 18
→ - 30 from both sides to isolate 5 b
5 b = - 12
→ ÷ Divide both sides 5 to isolate b
b = -2.4
If p(x) = x2 – 1 and q(x) = 5(x-1), which expression is equivalent to (p – q)(x)?
A. 5(x – 1) – x2 – 1
B. (5x – 1) – (x2 – 1)
C. (x2 – 1) – 5(x – 1)
D. (x2 – 1) – 5x – 1
please help!!!
Answers
Answer:
[tex]\large\boxed{C.\ (x^2-1)-5(x-1)}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\p(x)=x^2-1,\ q(x)=5(x-1)\\\\(p-q)(x)=(x^2-1)-5(x-1)[/tex]