Answer:
The square has a greater area having an area of 9 cm more than that of the rectangle.
Step-by-step explanation:
Length of square = x
Length of rectangle = 3+x
Width of rectangle = x-3
Area of square:
=> [tex]Length*Length[/tex]
=> x × x
=> x²
Area of Rectangle:
=> [tex]Length*Width[/tex]
=> (3+x)(x-3)
Using FOIL
=> 3x-9+x²-3x
=> x²-9
From the above calculations, we come to know that the square has a greater area having an area of 9 cm more than that of the rectangle.
What is a quadrilateral and give ten examples
Answer:
A quadralateral is any shape that has 4 sides ...
Step-by-step explanation:
rectangle
square
rhombus
Answer: A quadrilateral is a two dimensional shape(closed) with four sides.
Step-by-step explanation: The sides do not have to be equal.
Square
Rectange
Trapazoid
Diamond
Any four sided shape. They will classify as a quadrilateral as long as two of the shapes are not the same.
In January of 2002(group 1),700 out of the 1700 spots were bare ground (no vegetation). Find the sample proportion of bare ground spots.
Answer:
The sample proportion of bare ground spots is 0.4118
Step-by-step explanation:
The sample proportion of bareground spots is the number of bareground sports divided by the number of spots.
In this question
700 bareground spots
1700 spots
7/17 = 0.4118
The sample proportion of bare ground spots is 0.4118
Given data:
x = 700n = 1700The formula will be:
→ [tex]Sample \ proportion = \frac{x}{n}[/tex]
By substituting the given values, we get
[tex]= \frac{700}{1700}[/tex]
[tex]= 0.4118[/tex]
Thus the response above is correct.
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People counting calories have to be careful about the estimates placed on prepackaged food. Suppose testing shows that a certain brand of doughnut has a mean calorie count of 240, so that is the amount printed on the package. However, testing shows that the calories counts vary, following a normal distribution with a standard deviation of 15 calories.
A) Find the probability that an individual doughnut for this brand contains more than 275 calories.
B) Find the probability that a random sample of 12 of these doughnuts contains a mean number of calories between 230 and 260.
Answer:
A) P(X>275) = 0.01
B) P(230<M<260) = 0.99
Step-by-step explanation:
We have a normal distribution with mean: 240 calories and standard deviation: 15 calories.
To find the probability that an individual doughnut for this brand contains more than 275 calories, we calculate the z-score for X=275 in this normal distribution, and then calculate the probability for this z-score with the standard normal distribution:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{275-240}{15}=\dfrac{35}{15}=2.33\\\\\\P(X>275)=P(z>2.33)=0.01[/tex]
In the case we are talking about a sample mean, we use the standard deviation of the sample distribution.
The standard deviation for the sample means is equal to the standard deviation of the population divided by the square root of the sample size (in this case, n=12). The mean of the sampling distirbution is expected to be equal to the population mean.
[tex]\mu_s=\mu=240\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{15}{\sqrt{12}}=\dfrac{15}{3.4641}=4.33[/tex]
We have to calculate the probability that this sample mean is within 230 and 260.
[tex]z_1=\dfrac{M_1-\mu}{\sigma}=\dfrac{230-240}{4.33}=\dfrac{-10}{4.33}=-2.309\\\\\\z_2=\dfrac{M_2-\mu}{\sigma}=\dfrac{260-240}{4.33}=\dfrac{20}{4.33}=4.619\\\\\\P(230<M<260)=P(z<4.619)-P(z<-2.309)\\\\P(230<M<260)=1-0.01=0.99[/tex]
someone pls help im so close
Answer: A) 126.6
Step-by-step explanation:
Since we know ∠B = 85° and ∠C = 53°, we can use the Triangle Sum Theorem (angles of a triangle = 180°) to calculate ∠A.
∠A + ∠B + ∠C = 180
∠A + 85 + 53 = 180
∠A + 138 = 180
∠A = 42
Now we have:
A = 42 B = 85 C = 53
a = 85 b = ??? c = ???
We have all of the information for ∠A and side a so we can use the Law of Sines to find b (AC).
[tex]\dfrac{\sin 42}{85}=\dfrac{\sin 85}{b}\\\\\\b(\sin 42)=85(\sin 85)\\\\\\b=\dfrac{85\sin 85}{\sin 42}\\\\\\b=\large\boxed{126.547}[/tex]
A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a. Write a mathematical model representing the store's constraints.
b. Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is 0.03 and that a displayed chair will be sold is 0.05. Mathematically model each of the following objectives:
1. Maximize the total pieces of furniture displayed.
2. Maximize the total expected number of daily sales.
3. Maximize the total expected daily profit.
Answer:
a) 50S + 30C ≤ 800
b) 1) MAX = S + C
2) Max = 0.03S + 0.05C
3) Max = 6S + 5C
Step-by-step explanation:
Given:
Total space = 800 square feet
Each sofa = 50 square feet
Each chair = 30 square feet
At least 5 sofas and 5 chairs are to be displayed.
a) Write a mathematical model representing the store's constraints:
Let S denote number of sofas displayed and C denote number of chairs displayed.
The mathematical model will be:
50S + 30C ≤ 800
At least 5 sofas are to be dispayed: S ≥ 5
At least 5 chairs are to be displayed: C ≥ 5
b)
1) Maximize the total pieces of furniture displayed:
S + C = MAX
2) Maximize the total expected number of daily sales:
MAX = 0.03S + 0.05C
3) Maximize the total expected daily profit:
Given:
Profit on sofas = $200
Profit on chairs = $100
Max Expected daily profit =
Max = (200S * 0.03) + (100C * 0.05)
Max = 6S + 5C
Suppose E(X) = 5 and E[X(X-1)] = 27.5. What is E(X2)? V(X)? The general relationship among the quantities E(X), E[X(X-1)], and V(X)?
Answer:
[tex]E(X^2)=32.5\\V(X)=7.5\\E[X(X-1)]=E(X^2)-E(X)\\V(X)=E(X^2)-[E(X)]^2[/tex]
Step-by-step explanation:
We have the following properties:
[tex]E( X + Y ) = E(X) + E(Y)\\V(X) = E(X^2)-[E(X)]^2[/tex]
So, if we have that E[X(X-1)] = 27.5, we can write them using the first property as:
[tex]E(X(X-1))=27.5\\E(X^2-X)=27.5\\E(X^2)-E(X)=27.5[/tex]
Then, replacing E(X) by 5 and solving for [tex]E(X^2)[/tex], we get:
[tex]E(X^2)-5=27.5\\E(X^2)=27.5+5\\E(X^2)=32.5[/tex]
Finally, using the second property and replacing [tex]E(X)[/tex] by 5 and [tex]E(X^2)[/tex] by 32.5, we get that V(X) is equal to:
[tex]V(X) = 32.5 - 5^2\\V(X) =32.5 - 25\\V(X) = 7.5[/tex]
PLS I NEED HELP SIRR
Answer: you got this!
Step-by-step explanation:
yall know the drill . whats the answer
Answer:
C. 57 degrees.
Step-by-step explanation:
It's a line, so it adds to 180 degrees. The interior angle is 180 - 114 = 66 degrees.
A triangle adds up to 180 degrees. Subtract 66 to get 114 degrees. This means the two remaining angles in the triangle add up to 114 degrees. Since they are identical (both are the same because they use the same variable), you can divide 114 by two.
The final answer is 57 degrees.
Let me know if you have any questions.
Determine if the given function can be extended to a continuous function at xequals0. If so, approximate the extended function's value at xequals0. If not, determine whether the function can be continuously extended from the left or from the right and provide the values of the extended functions at xequals0.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is A
Step-by-step explanation:
Now from the question we are given the function
[tex]f(x) = \frac{10^{2 x} -4}{x}[/tex]
Now as [tex]\lim_{x \to 0} [f(x) ] = \frac{10^{2*0} -4 }{0}[/tex]
=> [tex]\lim_{x \to 0} [f(x) ] = - \infty[/tex]
This implies that as [tex]x\to 0[/tex] the function [tex]f(x) \to -\infty[/tex] which means that at x = 0 the function is not continuous
An adult has a total of about 22.5 square feet (ft2) of skin. Use the fact that 1 m is approximately equal to 3.281 feet to convert this measurement to square meters (m2). Round your answer to the nearest hundredth. Do not type the units in the space below.
Answer:
There are about 3.281 * 3.281 = 10.764 square feet in one square meter. Therefore, 22.5 square feet is 22.5 / 10.764 = 2.09 square meters.
y=x2+3x+1 has how many real roots?
Answer:
2
Step-by-step explanation:
we will find the discriminant of the equation
d = b^2 - 4ac (here, a = 1 , b = 3 , c = 1. from the general formula: ax^2 + bx + c)
d = 9 - 4
d = 5
since d > 0, the roots are real and different
hence, the both the roots of this equation are equal
distribution of grades over the past two years is as follows: GRADE NUMBER OF STUDENTS A 80 B 75 C 90 D 30 F 25 Total 300 If this past distribution is a good indicator of future grades, what is the probability of a student receiving a C in the course
Answer:
The probability of a student receiving a C in the course is p=0.3.
Step-by-step explanation:
We have a absolute frequency for each of the grades (A to F), of a total of 300 course tests.
It is assumed that this sample gives a dood estimation of the distribution of the grades. Then, we can estimate the probability of obtaining a C in the course usign the relative frequency for C.
The relative frequency is calculated as the division between the absolute frequency (in this case, 90 for a C grade) and the size of the sample (in this example, 300).
[tex]p_C=\dfrac{X_C}{N}=\dfrac{90}{300}=0.3[/tex]
3
Select the correct answer.
What are the solutions to this equation?
16x² + 9 = 25
Answer:
Step-by-step explanation:
16x^2 + 9 = 25
16x^2 = 16
x^2 = 1
x = 1, -1
Which of the following fractions will convert to terminating decimals?
A.5/6
B. 5/2
C. 5/6
D. 5/3
E. 3/8
Answer:
B and E
Step-by-step explanation:
A terminating decimal is a decimal with a finite number of digits after the decimal point. If we input all of these fractions into a calculator, or solve them by hand, we find that B is equal to 2.5, and E is equal to 0.375, and all the others are repeating decimals.
Use the formula A=P(1+r)" to solve the following problem.
Find the rate r at which $500,000 grows to $708,050 in 2 years.
Answer:
r= 0.19
Step-by-step explanation:
A= $708,050
P=$500,000
'' = 2
$708,050= $500,000(1+r)^2
-Divide $500,000 by both sides
1.4161= (1+r)^2
-Square Root on both sides
1.19= 1+r
-Subtract 1 on both sides
r= 0.19
Which inequality is represented by the graph?
Answer:
y ≤ 2/5x - .5
Step-by-step explanation:
Well it is a solid line with it shaded down meaning the inequality starts with
y ≤,
And by look at the y axis we can tell that the line crosses the y axis at -.5 which is the y intercept.
And by looking at the line we can tell the slope is 2/5.
Hence, the inequality is y ≤ 2/5x - .5
Which scenario can be modeled using the graph below? A temperature range is within 5 degrees of 60 degrees Fahrenheit. A scientist uses more than 55 and less than 65 mL of water in an experiment. A commuter train takes less than 55 minutes or more than 65 minutes to complete one route. A worker makes greater than $55 per day but less than $65 per day.
Answer:
A temperature range is within 5 degrees of 60 degrees Fahrenheit
Step-by-step explanation:
As per the number line which has been given, the circular marks at the ends of the shaded area are also seen to be shaded, not blank. This means that the values on which these marks fall, 55 and 65, have to go along with the list. A, a temperature range within 5 degrees of 60 degrees
Fahrenheit is the only choice that suits this as 5 degrees below 60 degrees is 55 while 5 degrees higher than the degrees of 60 is 65
Answer:
the answer is A
Step-by-step explanation:
i did the test
Find the vector x determined by the given coordinate vector [x]B and the given basis B.
B = {[1 -3 1], [-3 8 3],[8 -2 3]}, [x]_B = [-3 -2 3]
a. [9 -13 0]
b. [0 -6 21]
c. [13 -24 -2]
d. [3 -13 16]
4. After paying 9 dollars for the pie, Alyssa has 50 dollars left. How much money did she have before buying the pie?
Answer:
Step-by-step explanation:
59 dollars
Answer:
59 dollarshere,
Left dollars+ paid dollars
= 50 dollars +9 dollars
=59 dollars
Hope this helps...
Good luck on your assignment..
help help help help pls
Hi !!
For f(x) = 3/x + 4 , B is correct.
• f(-3) = 3/(-3) + 4
f(-3) = - 1 + 4
f(-3) = 3
• f(-2) = 3/(-2) + 4
f(-2) = -1,5 + 4
f(-2) = 2,5
• f(1) = 3/(1) + 4
f(1) = 3 + 4
f(1) = 7
• f(2) = 3/(2) + 4
f(2) = 1,5 + 4
f(2) = 5,5
• f(3) = 3/(3) + 4
f(3) = 1 + 4
f(3) = 5
A piece of paper graph y=-3x-2
Answer:
Use an xy chart and graph the equation.
Step-by-step explanation:
A line passes through the point (4, -4) and has a slope of -5/4
Write an equation in slope intercept form for this line.
Answer:
y= -5/4x + 1
Step-by-step explanation:
Slope-intercept form: y=mx+b
M is the slope
B is the y-intercept.
The slope is -5/4.
M = -5/4
y = -5/4 + b
We're looking for the y-intercept. Substitute point in.
(4,-4) x= 4 y= -4
-4 = -5/4(4) + b
-4 = -5+b
b= 1
y= -5/4x + 1
HELP PLEASE!!!! I NEED HELP ASAP Which statement best describes the expression 3 + y ÷ 2? The quotient of 2 and the sum of 3 and y The quotient of the sum of 3 and y, and 2 The sum of 3 and the quotient of 2 and y The sum of 3 and the quotient of y and 2
Answer:
I believe it is D
Answer:
The sum of 3 and the quotient of y and 2.
Step-by-step explanation:
The order of operations requires that you evaluate the expression ...
3 + y ÷ 2
by first performing the division, then the addition. So, the addition gives you the sum of 3 and a quotient, because the quotient must be evaluated first.
The quotient is of y and 2 (not 2 and y), because the wording "the quotient of a and b" is always interpreted to mean a÷b.
So, the expression can be described as ...
the sum of 3 and the quotient of y and 2.
What is the volume of a cone with radius 7 cm and height 11 cm? Round your answer to two decimal places.
Answer:
D. 564.44 cm^3
Step-by-step explanation:
V = (1/3)(pi)r^2h
V = (1/3)(3.14159)(7 cm)^2(11 cm)
V = 564.44 cm^3
calculate find the area f a rectangle measuring 25 feet long by 8 feet wide
Answer: 200 ft²
Step-by-step explanation:
The area of a rectangle is length times width
So, simply do 25 * 8 = 200
Hey there! :)
Answer:
A = 200 ft².
Step-by-step explanation:
Use the formula A = l × w to determine the area of a rectangle:
A = 25 × 8
Multiply:
A = 200 ft².
1. The graph shows the number of miles Peter's car traveled and the gallons of gas used.
MILEAGE OF PETER'S CAR
160
140
120
100
Milco Traveled
BO
(5, 1201
60
40
20
1 2 3 4 5 6 7 8 9 10
Gallons of Gas
slope =¥
Which equation can be used to find the distance in miles, d, that the car can travel on g
gallons of gas?
A. d = 169
B. d=209
cd=249
D. d = 309
Slzo
28
10
Answer:
C. d = 24g
Step-by-step explanation:
The problem boils down to determining the ratio between d and g. That is, for some equation ...
d = k·g
we want to determine the value of k. Solving the equation for that value, we find ...
k = d/g
So, we need only to read a point from the graph with sufficient accuracy to determine a good estimate for k.
(gallons, miles) = (g, d) = (5, 120) is a suitable point
Then ...
k = d/g = 120/5 = 24
The equation is d = 24g.
Thirteen cards numbered 1,...,13 are shuffled and dealt one at a time. Say a match occurs on deal k if the kth card revealed is card number k. Let N be the total number of matches that occur in the thirteen cards. Determine E[N].
Answer:
E[N] = 1
Step-by-step explanation:
Here is the hint we are given on this problem - " Write N = [tex]1_{A_1}[/tex] + [tex]1_{A_2}[/tex] + · · · + [tex]1_{A_{ 13}[/tex]where [tex]A_k[/tex] is the event that a match occurs on deal k. "
_____
Now the standard thing is to do is let [tex]X_i[/tex] = 1, if there is a match on the [tex]i[/tex]-th pick and 0 otherwise. The number of matches is given to be [tex]X_1[/tex] + [tex]X_2[/tex] . . . + [tex]X_{13}[/tex]. Knowing that, we can use the linearity of expectation -
There are 13 cards and for [tex]i[/tex]-th pick, the probability of having a card with [tex]i[/tex] number is 1 / 13. Therefore, E[N] = E[[tex]X_1[/tex] + [tex]X_2[/tex] . . . + [tex]X_{13}[/tex]] = 1
_____
Solution: E[N] = 1
Find the critical value z Subscript alpha divided by 2 that corresponds to the confidence level 90%.
Answer:
,.........................................................
The freezing point of methanol is -97.6. What is the freezing point of methanol in Fahrenheit
Answer:
-143.68°F
Step-by-step explanation:
Celsius to Fahrenheit Conversion Formula: F = 1.8C + 32
Simply plug in c as -97.6:
F = 1.8(-97.6) + 32
F = -175.68 + 32
F = -143.68
Answer:
Fahrenheit= Celsius x 1.8 + 32
Step-by-step explanation:
-97.6 x 1.8 = -175.68
-175.68 + 32 = -143.68 / -143.7
A Semi-circle sits on top of a rectangle to form the figure below. Find it’s area and perimeter. Use 3.14 for Pie.
Answer:
B
Step-by-step explanation:
Area of semicircle=(r^2×3.14)/2
=(4×3.14)÷2
=6.28
area of rectangle=3×4
12+6.28=18.28
perimeter of semicircle is =(d×3.14)/2
=4×3.14/2
6.28+3+3+4
6+10
perimeter=16.28
The area & perimeter of the figure are,
B.) A≈18.28sq.inch & P≈16.28inch.
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
Here,
Area of semicircle=(r^2×3.14)/2
=(4×3.14)÷2
=6.28
area of rectangle=3×4=12
So, total area of the figure =12+6.28=18.28 sq. inch
Again, perimeter of semicircle is =(d×3.14)/2
=4×3.14/2
=6.28
Total perimeter of the figure =6.28+3+3+4
=6.28+10
perimeter=16.28 inch
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