Answer:
area of trapezium=½{a+b}h
½(10+12)6
22*3
66cm²
area of rectangle= l*b
6*5
30cm²
area of unshaded portion= area of trapezium - area of rectangle
(66-30)cm²
36cm²
Area of shaded part is 30cm² and area of unshaded part is 36cm² for the given figure
Area of Trapezium and Area of RectangleThe given figure is a rectangle inside a trapezium.
The rectangle is the shaded part while the trapezium is the sum of the shaded and the unshaded part of the figure.
We know that Area of rectangle is given by
A = L x B
where L=Length of rectangle
B=Breadth of rectangle
Given rectangle has L=6cm and B=5cm
Area of rectangle = L x B
= 6 x 5
= 30cm²
which also gives the area of shaded part of the given figure.
Now, area of trapezium
=Height(h)*{(Length of smaller side(a) + length of longer side(b)) ÷ 2}
=h*{(a+b) ÷ 2}
=6*{(10+12) ÷ 2)
= 66cm²
which gives the area of trapezium.
Area of unshaded part = Area of trapezium - Area of rectangle
= 66 - 30
= 36cm²
Hence, area of shaded part is 30cm² and area of unshaded part is 36cm² for the given figure.
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Find tan θ if sec θ = square root of ten divided by three and sin θ < 0.
-3
3
negative one divided by three
negative square root of ten
Answer:
\( - \frac{1}{3} \)
Step-by-step explanation:
The answer is -1/3
A motor racing circuit has length 5 5/6 miles
A straight section of the circuit has length 1 1/4 miles
What fraction of the section is the straight section
Give your answer in it's simplest form
Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire station receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are under 3 minutes?
Find the z-table here.
6.68%
10.56%
89.44%
93.32%
Answer:
b.10.56
pls mark brainliest thx
help just answer youll get 100 just answer all the questions
for the first question, you get 576
for the second one you get 0.1875
Your work or words should justify your answer (explain how you know). As a math teacher, Josie frequently makes photocopies of fun activities for her students to do. When the copies come out of the copy machine, they form a stack. This table shows the relationship between the number of copies in the stack, x, and the height (in millimeters) of the stack, y. x (copies) y (millimeters) According to the values in the table, do x and y have a proportional relationship? yes no
Answer:
Yes, because by dividing x by his equivalent y, you find a constant of proportionality being 10.
x / y = 10
Step-by-step explanation:
20 / 2 = 10
50 / 5 =10
60 / 6 = 10
70 / 7 = 10
A credit card company would like to estimate the proportion of their customers who have at least $10,000 in credit card debt.
They select a random sample of 50 of their customers and find that 42 of them have at least $10,000 in credit card debt.
They would like to construct a 95% confidence interval for the true proportion of their customers who have at least $10,000 in credit card debt.
Random condition:
10% condition:
Large counts condition:
Are the conditions for inference met?
Answer:
Random condition: met
10% condition: met
Large counts condition: not met
Are the conditions for inference met: no
Divide 7/15 by 3/5 =
A. 7/9
B. 21/75
C. 75/21
D. 7/25
Answer:
a
Step-by-step explanation:
7/15. /3/5=7/15*5/3 =7/9
Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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What is the image of ( − 8 , 0 ) after a dilation by a scale factor of 1/4 centered at the origin?
Step-by-step explanation:
it is then simply scanned (multiplied).
the new point is
(-8 × 1/4, 0 × 1/4) = (-2, 0)
hi! Can someone please help me out? Thank you so much :) I’ll give brainly. Question is in image
Answer:
d) 189.3 in²
Step-by-step explanation:
Area of rectangle is,
→ w × l
→ 10 × 15
→ 150 in²
Area of semi circle is,
→ (1/2)πr²
→ (1/2) × 3.14 × (5)²
→ 1.57 × 25
→ 39.3 in²
Now the total area will be,
→ 150 + 39
→ 189.3 in²
Thus, total area is 189.3 in².
Suppose the random variable X has mean 10 and variance 3. Find an upper bound for the probability: P (X > 15).
Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25
what is a variance?The variance is the difference between the numbers in a set of data, to put it simply. Each number's variability is a statistical statistic that indicates how far off from the mean and from each other number in the set it is.
Here,
Given : mean = 10
varience = 3
Using chebyshevs inequality we have
P(|X-u| ≥ k)≤ \(\sigma^{2}\)/\(k^{2}\)
hence we can have,
=> P(X>15) ≤ 3/\(5^{2}\)
=> P(X>15) ≤ 3/25
Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25
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The solution to | x-1 | =5x+2
x-1=5x+2= x-5x=2+1= -4x=3 = x=-3/4
Write a system of equations for this word problem. DO NOT SOLVE IT
Tickets to the movie theater are $5.50 for children
and $7.00 for adults. On Saturday, 1,250 people
attended the movie theater (adults and children)
The movie theater received $7,979 in ticket sales.
How many children and how many adults
attended the theater on Saturday?
Put answer here⬇️
Equation
TOPIC—
# of tickets—
$ earned—
PLEASE HELP ASAP
A system of equations for this word problem is
x + y = 1,2505.5x + 7y = 7,979.What is a system of equations?A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.
A system of equations is also called simultaneous equations.
The cost of movie theater tickets per child = $5.50
The cost of movie theater tickets per adult = $7.00
The total attendees on Saturday = 1,250
The total ticket sales = $7,979
Let the number of children who attended = x
Let the number of adults who attended = y
Equations:x + y = 1,250... Equation 1
5.5x + 7y = 7,979... Equation 2
Multiply Equation 1 by 5.5:
5.5x + 5.5y = 6,875... Equation 3
Subtract Equation 3 from Equation 2:
5.5x + 7y = 7,979
-
5.5x + 5.5y = 6,875
1.5y = 1,104
y = 736
x = 1,250 - y
x = 1,250 - 736
x = 514
Thus, we can conclude that 514 children and 736 adults attended the movie theater on Saturday.
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Which scatterplot shows a linear association?
Answer:
Scatterplot c shows a linear association.
Multiply and write the product as one power
Answer:
2⁸ and 2²⁴
Step-by-step explanation:
Pic attached..
How to convert from vertex to standard y=2(x-2)^2 -2 to standard
The quadratic equation in standard form is:
\(y = 2x^2 - 8x + 6\)
How to convert from vertex form to standard?
Here we have the quadratic equation:
\(y = 2*(x - 2)^2 - 2\)
Here we need to expand the right side, remember:
\((a + b)^2 = a^2 + 2ab + b^2\)
Using that, we get:
\(y = 2*(x - 2)^2 - 2 = 2*(x^2 - 4x + 4) - 2\\\\y = 2x^2 - 8x + 8 - 2\\\\y = 2x^2 - 8x + 6\)
This is the quadratic equation in standard form.
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Determine how long it will take for a principal amount of $1,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded.
A.
5.33 years
B.
6.32 years
C.
11.25 years
D.
14.33 years
c is incorrect
⅓t = 15 solution is 30?
Answer: yes
Step-by-step explanation:
\(y = \frac{ \sqrt{3x} }{1 + e^{2x} } \)
how would one differentiate this?
\(~~~~~~~~y = \dfrac{\sqrt{3x}}{ 1+ e^{2x}}\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx} \left( \dfrac{\sqrt{3x}}{1+ e^{2x}} \right)\\\\\\~~~~~~~~~~~~=\dfrac{(1 + e^{2x} ) \dfrac{d}{dx} \left(\sqrt{3x} \right) - \left(\sqrt{3x} \right)\dfrac{d}{dx}(1+e^{2x})}{\left( 1+ e^{2x} \right)^2}~~~~~~~~~~~~;[\text{Quotient rule}]\\\\\\~~~~~~~~~~~~=\dfrac{(1+e^{2x}) \cdot \dfrac{1}{2\sqrt{3x}} \cdot 3-\left(\sqrt{3x} \right) \cdot 2 e^{2x}}{(1 + e^{2x})^2}~~~~~~~~~~~~~~~~~~~~;[\text{Chain rule}]\\\\\\\)
\(=\dfrac{\dfrac{\sqrt 3 (1 + e^{2x})}{2\sqrt x} -2e^{2x} \sqrt{3x}}{(1+e^{2x})^2}\\\\\\=\dfrac{\tfrac{\sqrt 3(1 +e^{2x}) - 4x\sqrt 3 e^{2x}}{2\sqrt x}}{(1+e^{2x})^2}\\\\\\=\dfrac{\sqrt 3(1+e^{2x} -4xe^{2x})}{2\sqrt x(1 +e^{2x})^2}\)
Please help label the parts of the graph
The parts of the graph when labelled are :
Origin y - intercept x - intercept x - axis y - axis What are the parts of a graph ?There is the origin which is where the line starts from. The x-axis represents the independent variable, which is the variable that is being manipulated or changed in the experiment.
The y-axis represents the dependent variable, which is the variable that is being measured or observed. A trend line is a line drawn on the graph that shows the overall pattern or trend of the data. The x and y - intercepts are the points where the trend line crosses the x and y - axis.
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The function f(x)=4^x-6 is transformed to function G through a vertical compression by a factor of 1/2. Complete the equation of function G .  enter the correct answer in the box. Substitute  numerical values into the equation for a and k.
g(x) = a(4)^x-k
The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2
How to solve a function?
If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:
g(x) = a(4) raise to the power x-k/2
where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:
f(x) = g(x)/2
Substituting the expression for g(x) into this equation and simplifying, we get:
4raise to the power x - 6 = a(4)raise to the power x-k/2
To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:
f(0) = 4 - 6 = -5
f(1) = 4- 6 = -2
Using the equation g(x)/2 = f(x), we can write:
g(0)/2 = -5
g(1)/2 = -2
Substituting the expression for g(x) into these equations, we get:
a(4) raise to the power -k/2 = -10
a(4) raise to the power 1-k/2 = -4
Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":
(4)raise to the power -k/2 / (4) raise to the power 1-k/2 = -10 / -4
Simplifying this equation, we get:
4.raise to the power(1-k/2) = 5
Taking the logarithm of both sides (with base 4), we get:
1-k/2 = log4(5)
Solving for "k", we get:
k = 2 - 2 log4(5)
Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":
a = -10 / (4) raise to the power -k/2
Substituting the numerical value of "k", we get:
k = 2 - 2 log4(5) ≈ 0.872
a = -10 / (4) raise ti the power -k/2 ≈ 2.323
Therefore, the equation for the transformed function g(x) is:
g(x) = 2.323 (4)raise to the power x-0.872/2
or equivalently:
g(x) = 1.1615 (4) raise to the power -x0.872
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Answer:
g(x) = 1/2 (4)^x - 3
Step-by-step explanation:
A vertical compression by a factor of 1/2
means that the entire function f is multiplied by 1/2:
1/2 f (x) = 1/2 (4^x - 6)
= 1/2 (4)^x - 3
manny has just filled out his deposit ticket for his savings account. he hands it to the teller and the teller hands it back to manny. the teller explains to manny that the deposit ticket cannot be accepted in its current form. what must manny do to the deposit ticket in order for the teller to process the deposit ticket? a deposit ticket. the ticket has not been signed for cash back. the date is december 16. a. manny forgot to sign the deposit ticket for less cash back
The manny must do his signature on the deposit ticket in order to get deposited the cashback ticket.
What is cashback?
Cashback is a type of reward program offered by some retailers and online merchants that gives customers money back for making purchases. It is a way for retailers to reward customers for their loyalty and encourage them to keep coming back to their store. Cashback can be offered in the form of a fixed amount, a percentage of the purchase price, or a combination of both. Cashback rewards may be paid in cash or as credits to the customer's account, and they may be used to purchase additional items from the store or to offset future purchases.
When teller sees the deposit ticket he must have seen that it is not signed by manny hence he returned this to manny now manny just have to do one work that to sign that deposit ticket after that teller will accept that deposit ticket and manny will get his required cashback easily in his bank account
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Answer:
a edge
Step-by-step explanation:
Match to the correct one
Answer:
1. b_ 2. a_ 3. c_ 4. d
Step-by-step explanation:
1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.
Sal has 315 pieces of candy. He would have 3 times as many pieces of candy as joey if he had 18 more pieces. Which equation can be used to find j, the number of pieces of candy joey has?
The equation that can be used to find the number of pieces of candy Joey has is j = (315 - 18) / 3 .
What equation can be used to represent the number of candies that Sal has?
Number of candies Sal has = 3(number of candies that Joey has) + 18
315 = 3(j) + 18
Where j represents the number of candies that Joey has.
What equation can be used to represent the number of candies that Joey has?Given this equation, 315 = 3(j) + 18 , we are to make j the subject of the formula. To do this, take the following steps.
Combine similar terms :
(315 - 18) = 3j
Divide both sides by j
j = (315 - 18) / 3
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Nikhil and Mae work at the same company. Nikhil has been at the company 4 times as long as Mae. Nikhil's time at the company is 8 more than 2 times Mae's time. The following system of equations models the scenario: x = 4y x = 8 + 2y How many years has each person been employed by the company? Nikhil has been with the company for 16 years, while Mae has been there for 4 years. Nikhil has been with the company for 24 years, while Mae has been there for 6 years. Nikhil has been with the company for 20 years, while Mae has been there for 5 years. Nikhil has been with the company for 12 years, while Mae has been there for 3 years
The number of years of employment is A. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.
How to find the years of employment ?The system of equations given is:
x = 4y
x = 8 + 2y
You can solve the system by setting the two expressions for x equal to each other:
4y = 8 + 2y
2y = 8
2y / 2 = 8 / 2
y = 4
Substitute y = 4 into the first equation to solve for x:
x = 4 x 4
= 16
So, Mae (y) has been at the company for 4 years and Nikhil (x) has been at the company for 16 years.
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Which ordered pair is a solution of the equation? 3x + 3y = -x + 5y
Answer:
Undefined
Step-by-step explanation:
Without option choices, I don't know what the answer could potentially be.
I got X=.5y, and while solving for Y, I came up with 4.5y=4.5y
It has been a few years since I have done this, but I believe the answer is undefined.
Write the following numbers in decreasing order: −4; 1 2/3 ; 0.5; −1 3/4 ; 0.03; −1; 1; 0; -103; 54
100 points (plz answer asap)
Answer:
-103; -4; -1 3/4; -1; 0; 0.03; 0.5; 2/3; 1; 54
Decreasing order means from largest to smallest
The ordered list is:
54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103
There are 26 students in Jenna’s class. Jenna brought in 14 cupcakes. Which equation can be used to find the number of cupcakes the class still needs (n) so that everyone will get one?
Answer:
Equation: 26-14=(n)
Step-by-step explanation:
If you rest 14 from 26 that is the number of people that still need one.
(The answer is 12)
11) $ 8,000 is invested in an account that yields 6% interest per year. After how many years will the account be worth 13709.60$ if the interest is compounded monthly?
Answer:
\(\large \boxed{\sf \ \ 9\text{ years} \ \ }\)
Step-by-step explanation:
Hello,
First of all, a few remarks:
>>> 1 year is 12 months, right?
>>> Monthly compounding means that each month we compute the interest and they will be included in the investment for the next month.
>>> 6% is an interest per year, it means that to compute the interest for 1 month we need to compute by 6% multiplied by \(\dfrac{1}{12}\)
Let's do it !
At the beginning, we have:
$8,000
After 1 month, we will have:
\(8000 + 8000\cdot \dfrac{6\%}{12}=8000\cdot (1+ \dfrac{6}{1200})= 8000\cdot (1+ \dfrac{1}{200})\)
After 2 months, we will have:
\(8000\cdot (1+ \dfrac{1}{200})\cdot (1+ \dfrac{1}{200})=8000\cdot \left(1+ \dfrac{1}{200}\right)^2\)
After n months, we will have
\(8000\cdot \left(1+ \dfrac{1}{200}\right)^n=8000\cdot \left(1.005\right)^n\)
We are looking for n such that
\(8000\cdot \left(1.005\right)^n=13709.60\\\\ln(8000)+ n\cdot ln(1.005)=ln(13709.60)\\\\\\n = \dfrac{ln(13709.60)-ln(8000)}{ln(1.005)}=108\)
So, we need 108 months to reach this amount, which means 108/12=9 years.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
\(3x+7=12-2x;1\)
Step-by-step explanation:
\(3x + 7 = 12- 2x \\ 3x + 2x = 12 - 7 \\ 5x = 5 \\ x = \frac{5}{5} \\ x =1\)