Answers
The area of the rectangle is 4 (7-2) unit².
What is rectangular shape?A rectangle is a quadrilateral with four equal vertices and parallel sides of equal length.
Given, the sides of the rectangle are 4 and 7.
And in the diagram,
The rectangle overshadowed by the rectangle having the sides 4 and 2.
So, the sides of the shaded rectangle are 4 and (7-2).
So, the area of the rectangle
= length x width
= 4 x (7-2)
= 4 (7-2)
Therefore, the area is 4 (7-2) unit².
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Related Questions
Miles is renting a meeting room at a college. There is a reservation fee of $21 and an additional fee of $4 per hour. He needs to spend no more than $85. What is the possible number of hours for which Miles could rent the meeting room? Use t for the number of hours.
t ≤26.5
t<4
t ≤ 16
t<21.25
Answers
The equation represents that, Miles could rent the meeting room for t ≤ 16 hours.
What is inequality?
The word inequality means a mathematical expression in which the sides are not equal to each other. Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.
The total cost for Miles to rent the meeting room for t hours is given by the equation C = 21 + 4t. We are trying to find the number of hours t for which C is equal to or less than $85.
We can solve this problem by setting up the inequality 21 + 4t ≤ 85 and solving for t.
Subtracting 21 from both sides gives us 4t ≤ 64.
Dividing both sides by 4 gives us t ≤ 16.
Thus, Miles can rent the meeting room for t hours, where t is less than or equal to 16. This means that he can rent the room for 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 hours.
Hence, the equation represents that, Miles could rent the meeting room for t ≤ 16 hours.
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Use the figures to answer the questions.
1. What is the diameter of circle A ?
2. What is the diameter of circle B ?
3. What is the radius of circle A ?
4. What is the radius of circle B?
5. Are the radius and diameter of the two circles proportional? Explain.
6. The circumference of circle Q is 21 centimeters.
a. Write a proportion to find the circumference of circle P
b. What is the circumference of circle P?
Answers
Answer:
1) 12ft
2) 8ft
3) 6 ft
4) 3ft
5)
Answer:
1. 12ft
2. 8ft
3. 6ft
4. 4ft
5. The diameter and radius of the circles are proportional by a factor of 1.5 because 12/8 = 1.5 and if I multiply circle B's radius by a factor of 1.5 I will get the radius of Circle A as is with the diameter.
6.
A- (3/7)(21) = x
B- x approximately equals 9
Step-by-step explanation:
Circumference formula
C= 2(pi)r
z equals circumference of circle q
Q = 7
P = 3
Z = 21
(P/Q)(Z) = x
Therefore (3/7)(21) = 9
We can prove this by using the Circumference formula
C= 2(pi)r
C=2(pi)1.5
C= 3(pi)
C= 9.4247...
Rounded = 9
hope this helps!!
Which statement is correct?
A)The Interquartile Range (IQR) for the Chess Club is equal to the IQR for the Checkers Club.
B)The 3rd Quartile ages for the Chess Club is equal to the 3rd Quartile ages for the Checkers Club.
C)The Median age for the Chess Club members is twice that of the Median age for the Checkers Club members.
D)The Range of the Chess Club members is equal to the Range for the Checkers Club members.
Answers
Answer:
B
Step-by-step explanation:
PLEASE HELP!!!!
A group of friends were hanging out discussing the movies. They discovered that altogether, they went to the movies 30 times last year. Clio went 5 times as often as Alex. Bernice went 2 more times than Alex. How many times did Clio go to the movies last year?
A. 5
B. 10
C. 20
D. 4
Answers
So we have
X 5x and x+2
All toghter 7x+2=30 so alex went there 4 times so clii went 20times
Step-by-step explanation:
30/4=7.4
30/5=6
6/3=2
Alex went to the moves 4 times that year.
Write a polynomial function with
zeros: 4, 5i
PLEASE HELP ASAP ITS DUE TMR
Answers
Answer:
[tex]85 \sqrt{5} [/tex]
Solve for x.
− x/2<−1
Answers
Answer: x>2
Step-by-step explanation:
To solve for x, we want to use inverse operations to isolate x.
[tex]-\frac{x}{2} < -1[/tex] [multiply both sides by -2]
[tex]x > 2[/tex]
A wire of length 15 is cut into two pieces which are then bent into the shape of a circle of radius r and a square of side s . Then the total area enclosed by the circle and square is the following function of s and r If we solve for s in terms of r , we can reexpress this area as the following function of r alone:
Thus we find that to obtain maximal area we should let r= To obtain minimal area we should let r=
Answers
Since s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π). This same r will also maximize the area.
Since the length of 15 is divided between the circumference of the circle and the perimeter of the square,
2πr + 4s = 15 ⇒ s = (15 - 2πr ) / 4
A = πr2 + s2 = πr2 + [ (15 - 2πr ) / 4]2 = πr2 + (225 - 60πr + 4π2r2) / 16
A = π(1 + π/4)r2 - (15/4)πr + 225/16
dA/dr = 2π(1 + π/4)r - (15/4)π = 0 ⇒ r = (15/4)π / [2π(1 + π/4)] = 15 / (8 + 2π)
Since A(r) is concave up, it has a minimum at
r = 15 / (8 + 2π)
Since s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π). This same r will also maximize the area.
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Van is 12 yrs older than john. Two yrs ago. Van was twice as old as john. Find thier present age.
Answers
Answer:
John = 14 ; Van = 26
Step-by-step explanation:
V = 12 + J
V - 2 = 2(J-2)
12 + J - 2 = 2J - 4
J + 10 = 2J - 4
2J - J = 10 + 4
J = 14
V = 12 + 14
V = 26
Given that 58% of all gold dealers believe next year will be a good one to speculate
in South African gold coins, in a simple random sample of 150 dealers, what is the
probability that between 55% and 60% believe that it will be a good year to
speculate?
Answers
The normal distribution is a continuous probability distribution that is symmetrical around the mean. The mean in this case is 58%, and the standard deviation can be calculated using the formula:
standard deviation = sqrt( (p * (1 - p)) / n )
where p is the proportion of all gold dealers who believe that it will be a good year to speculate (58% in this case) and n is the sample size (150 in this case).
Plugging in the given values, we get:
standard deviation = sqrt( (0.58 * (1 - 0.58)) / 150 ) = 0.042
To find the probability that between 55% and 60% of the sample believe that it will be a good year to speculate, you can use a z-score table to find the z-score for 55% and 60%, and then use these z-scores to find the probability.
The z-score for 55% is (55 - 58) / 0.042 = -7.14, and the z-score for 60% is (60 - 58) / 0.042 = 2.38.
Using a z-score table, you can find that the probability of a z-score between -7.14 and 2.38 is approximately 0.45.
Therefore, the probability that between 55% and 60% of a sample of 150 gold dealers believe that it will be a good year to speculate in South African gold coins is approximately 0.45.
6 Find the value of the unknowns in each of the following.
(a) 2(w 2 5 z)+3(2 x -2 -6)=4(4 7 y 3)
Answers
The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.
Given,
To determine the value of the unknowns in the matrix,
A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.
Here,
[tex]2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right][/tex]
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,
2z -18 = 12
z = 15
10 - 6 = 4y
y = 1
Thus, the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.
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Pls answer its for my final
Answers
The equivalent expression is (x + 2√3i) (x - 2√3i).
What is a Polynomial Equation?
The equations formed with variables, exponents and coefficients are called as polynomial equations. It can have different exponents, where the higher one is called the degree of the equation.
Given polynomial is,
x² + 12
We need to find it's equivalent expression for that see the options
Solve the option (a)
(x + 2√3i) (x - 2√3i)
Now, solve this if we get equal to x² + 12 that means that option is answer
x(x - 2√3i) + 2√3i(x - 2√3i)
x² - 2xi√3 + 2xi√3 - 2√3i * 2√3i
x² - 12 i²
we know, i² = -1
so, we get
x² + 12
We get the answer by 1st option. If you solve other options you'll get different answer.
Hence, the equivalent expression is (x + 2√3i) (x - 2√3i).
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Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 970(1.042)*
Answers
The change represents growth and rate of increase is 4.2%
What is an exponential function?Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.
Given that, an exponential function y = 970(1.042)ˣ
When the growth rate is greater than 1, then the function represents a growth.
The general form equation is:
y(x)= a(1+r)ˣ such that r is the growth percent.
So,
1+r = 1.042
r = 0.042
r = 4.2%
Hence, the growth rate is 4.2%
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Write as a logarithmic equation. 2^1/2= square root 2
Answers
Answer:
1
log₂√2 = ------
2
Step-by-step explanation:
I'm assuming the equation looks like this:
2¹⁽² = √2
1
log₂√2 = ------
2
I hope this helps!
The function f(x) is a cubic function and a limited table of values is provided below. Write the equation of the cubic polynomial in standard form.
Answers
The equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
What is a polynomial function?
Polynomial functions are defined for all values of x and have a finite number of roots (x-values at which the function is equal to 0). The roots of a polynomial function can be found by solving the equation f(x) = 0.
By using the given table, we can plot the points on the graph and we can draw a graph
• Fitted coefficients:
a = 9
b = -9
c = -1
d = 1
Then we can prepare the polynomial as
y = 9 - 9x - x² + x³
Now write down in the standard form, we get
f(x) = x³ - x² -9x + 9
Hence, the equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
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Help me thank y very much
Answers
Answer: 1/2
Step-by-step explanation:
Use rise over run. Up 1, over 2.
And so on. Find nice points on the graph to practice slope with!
I Need Help For This TGA
Answers
Comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²
The expressions are given in the question as:
(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²
As per the PEMDAS rule, the required solution would be as:
⇒ (8 + 3² - 2·6)/(7 - 1·2)
⇒ (8 + 9 - 12)/(7 - 2)
⇒ (17- 12)/5
⇒ 5/5
⇒ 1
⇒ (3/4 + 1/8) + 1/8 - 2²
⇒ (6 + 1)/8 + 1/8 - 4
⇒ 7/8 + 1/8 - 4
⇒ (7 + 1)/8 - 4
⇒ 8/8 - 4
⇒ 1 - 4
⇒ -3
Here 1 > -3
Thus, comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².
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Answer:Pemdas
Step-by-step explanation:Comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²
The expressions are given in the question as:
(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²
As per the PEMDAS rule, the required solution would be as:
⇒ (8 + 3² - 2·6)/(7 - 1·2)
⇒ (8 + 9 - 12)/(7 - 2)
⇒ (17- 12)/5
⇒ 5/5
⇒ 1
⇒ (3/4 + 1/8) + 1/8 - 2²
⇒ (6 + 1)/8 + 1/8 - 4
⇒ 7/8 + 1/8 - 4
⇒ (7 + 1)/8 - 4
⇒ 8/8 - 4
⇒ 1 - 4
⇒ -3
Here 1 > -3
Thus, comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².
Which expression is equivalent to (ab7)4?
ab28
ab11
a5b11
a4b28
Answers
The expression that is equivalent to the given expression, (ab⁷)⁴, is a⁴b²⁸. The correct option is the last option a4b28
Writing an equivalent expressionFrom the given information, we are to determine the expression that is equivalent to the given expression
The given expression is
(ab⁷)⁴
To determine the expression that is equivalent to this expression, we will expand the given expression
Expanding the expression
(ab⁷)⁴
Applying the distributive exponent law of indices,
(a)⁴ × (b⁷)⁴
Simplifying
a⁴ × b²⁸
= a⁴b²⁸
Hence, the equivalent expression is a⁴b²⁸
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Answer:
I think it's a4b28
Step-by-step explanation:
Determine whether the statement is always, sometimes, or never true.
When the measure of ∠4 is 120° , the measure of ∠1 is 60°
always true
sometimes true
never true
Answers
Answer:
always true , because 120+60=180
A family of 4 goes out to eat at a restaurant. They buy a family dinner platter that costs $29. Each of the 4 family members also gets a dessert for $3 apiece.
Let the variable x represent the total cost of the meal. Which of the following equations is correct?
Select ALL that apply.
A. x = 3 * 4 + 29
B. x = 3 + 4 + 29
C. x = 41
D. x = 36
Answers
The equations that model the total cost of the meal are:
A. x = 3 * 4 + 29
C. x = 41
Which of the following equations is correct?
We know that the family has 4 members and they buy:
A family dinner platter, which costs $29Each member also gets a dessert, which costs $3 per piece.Then the total cost is the $29 for the dinner plate plus four times the $3 for the dessert, this is:
x = $29 + $4*3
x = $29 + $12
x = $41
Then the correct options are A and C.
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The length of a vegetable garden is 6 feet longer than it’s width if the area of the garden is 55 square feet , find its dimensions.
Answers
Answer:
Width is 5.
Length is 11.
Step-by-step explanation:
Let the width be x.
x = width
The length is 6 feet longer.
x + 6 = length
Area is
length × width
Area is 55 (given)
55 = x(x+6)
Use distributive property.
55 = x^2 + 6x
Set equal to 0 and factor to solve. See image.
We have to toss out a solution that doesn't make sense. A measure of a side of a rectangle cannot be negative.
see image.
5 The graph shows the relationship between the number of hours Teresa spends
knitting and the number of squares she completes for a blanket. Based on the
equivalent ratios shown in the graph, how many hours does it take Teresa to
knit 265 squares? Show your work.
Teresa's Knitting
Completed Squares
60
50
40
30
20
10
0
0
•
●
6
●
8 10 12
Hours Knitting
Answers
It will take 220.8 hour, Teresa to knit 265 squares
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Given that the relationship between the number of hours Teresa spends
knitting and the number of squares she completes for a blanket.
We need to find the hours does it take Teresa to knit 265 squares.
Now Based on the equivalent ratios we have;
Teresa's Knitting /Completed Squares
10/12 = x / 265
Thus, Now cross multiplication we get;
x = 265(10/12)
x = 220.8
The answer is 220.8
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18x=6(z-1) solve for z
Answers
Answer: z=3x+1
Step-by-step explanation:
1. Distribute 6 through the parentheses
18x=6z-6
2. Move the z variable to the left side and x variable to the right
-6z= -6-18x
3. Divide both sides by -6 in order to get z by itself
z=1+3x
4. Reorder the terms using commutative property
z=3x+1
Tisha’s mom wants to make a smoothie using this recipe. How many cups of blueberries will she need if he uses 15 bananas?
Answers
Answer:
5 cups
Step-by-step explanation:
6bananas =2cups
6(2cups)+6(2cups)+3(1cup)= 15 bananas
5cups of blueberries
The weight of 10-week-old male children is distributed given a normal with a standard deviation of 87 grams.
How much data is enough to estimate, with a 95% confidence, the average weight of this population with an error not superior to 15 grams?
Answers
To determine how much data is enough to estimate the average weight of this population with a 95% confidence and an error not superior to 15 grams, we would need to use a statistical sample size calculator or consult a statistical table. Factors that would need to be considered include the desired confidence level, the desired margin of error, and the standard deviation of the population.
Using a sample size calculator, we can input these values and determine the required sample size. For example, with a 95% confidence level, a margin of error of 15 grams, and a standard deviation of 87 grams, the required sample size would be approximately 38 children. This means that we would need to measure the weight of at least 38 male children who are 10 weeks old in order to estimate the average weight of the population with a 95% confidence and an error not superior to 15 grams.
It is important to note that this is just an estimate and the actual sample size may vary depending on the specific characteristics of the population being studied. Additionally, it is always a good idea to consult with a statistician or other expert to ensure that the appropriate sample size is used in any statistical analysis.
How long will it take 15 machines to complete a task given that it takes 9 days for 5 machines to complete the same task?
Answers
Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines.
What are work and time?Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.
Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.
As per the given,
5 machines take 9 days,
5 x 9 = 45 machines day
45/15 = 3 days
Hence "Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines".
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Mary wishes to estimate the mean height of women aged 18-24. She picks a sample of 100
women aged between 18 and 24 and constructs a 99% confidence interval for the
population mean. If she were to repeat this procedure 200 times in total, she would obtain
200 different confidence intervals. How many of these intervals would you expect to
contain the population mean, u? Explain your thinking.
Answers
We would expect 198 of the intervals to contain the mean.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data
Given that Mary wishes to estimate the mean height of women aged 18-24.
picks a sample of 100
Women aged between 18 and 24 and constructs a 99% confidence interval for the population mean.
If Mary were to repeat this procedure 200 times in total, she would obtain
200 different confidence intervals.
A confidence interval of a parameter gives an interval in which the parameter is expected to be found. Because the interval either contains or doesn't contain the parameter, the probability is either 0 or 100%, which is not helpful. A 95% CI says that if we construct 100 intervals, 95% will contain the parameter. That is a true percentage, not a confidence. We don't know which 95, however, since the parameter is still unknown or unknowable.
I would expect 99%×200 or 198 of the intervals to contain the mean.
Hence, would expect 198 of the intervals to contain the mean.
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The table shows the depths (relative to sea level) of several scuba divers.
What is the difference between Oscar's depth and Annabelle's depth? Write your answer as a mixed number in simplest form
Answers
Answer:(-6 5/6)
Step-by-step explanation:
-12.5=-12-1/2
-5 2/3= -5-2/3
=(-12 3/6)-(-5 4/6)
=(-6 5/6)
gimme brainlliest
The manager of a water park collects data on daily high temperature and the number of customers entering the park for 15 summer week days. Based on these data he produces a least regression equation y= -3110+51.2x. One day the high temperature was 93F and 1700 customers entered the park. Which of the following is the residual for this observation?
Answers
Answer: A residual is the difference between the observed value of a dependent variable and the predicted value based on a given model. In this case, the manager of the water park has produced a least squares regression equation of the form y = -3110 + 51.2x, where y is the number of customers entering the park and x is the daily high temperature. This equation can be used to predict the number of customers based on a given temperature.
On the day in question, the high temperature was 93F and 1700 customers entered the park. Using the given equation, we can predict the number of customers that would be expected based on this temperature:
y = -3110 + 51.2x
= -3110 + 51.2 * 93
= -3110 + 4768.6
= 1658.6
The residual for this observation is the difference between the observed value of 1700 and the predicted value of 1658.6, which is 1700 - 1658.6 = 41.4. This is the residual for this observation.
¿Consideras usted que las empresas de servicios pueden incluir todas las cuentas de las empresas comerciales?
Answers
Answer:
Step-by-step explanation:
es posible que desee cambiar a la sección de negocios del sitio web porque es posible que puedan responderle mejor
6 people equally share 1/2 a pan of macaroni and cheesse draw a diagram to represent the situation
Answers
Share of the each person is 1/12. And the above situation can be represented in the given picture.
Fractions and diagrams:Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire.
When we cut a piece of cake from the entire thing in real life, that could be the best example for Fractions.
To represent a fraction in a diagram we choose a closed polygon like a circle, square, etc.
First, divide the polygon into the number of parts as given in the denominator and shade the number of taken parts that are given in the numerator.
Here we have
6 people equally share 1/2 a pan of macaroni and cheese
As we know 1/2 means half
By the given data, Half of the macaroni and cheese is shared by 6 people which means Half of the pan of macaroni and cheese again divided into 6 parts
=> (1/2) ÷ 6 = [tex]\frac{ \frac{1}{2} }{6}[/tex] = [tex]\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]
Therefore,
Share of the each person is 1/12. And the above situation can be represented in the given picture.
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