(a) The equation to find the combined area is (34 + 2x) (10 + 2x) = 640.
(b) The width of the roped off area is 3 feet.
(a) Given that,
Length of the rectangular museum = 34 feet
Width of the rectangular museum = 10 feet
Area of a rectangle = Length × Width
Area of the rectangular museum = 34 × 10 = 340 feet²
Combined area = 640 feet²
(34 + 2x) (10 + 2x) = 640, which is the required equation.
(b) Solving the equation,
340 + 20x + 68x + 4x² = 640
4x² + 88x = 300
x² + 22x - 75 = 0
(x - 3) (x + 25) = 0
x = 3 or x = -25
x = -25 is not possible.
So width = 3
Hence the width of the roped off area is 3 feet.
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Determine the area of each face of a cube with the given surface area.
a) 306.6 square meters
b) 450 square inches
Answer:
51.1 m² and 75 in²
Step-by-step explanation:
A cube has 6 congruent square faces
Given the surface area of the cube, that is the combined area of the 6 faces , then
divide the surface area by 6 for area of each face.
(a)
306.6 m² ÷ 6 = 51.1 m²
(b)
450 in² ÷ 6 = 75 in²
a) The area of each face of a cube 306.6 is 51.1 square units.
b) The area of each face of a cube 450 is 75 square units.
a) A cube has 6 faces
Area of each face is (side × side)
Area = side × side
So, total area is equal to 6 times the area of each side.
Area = 6 × (side × side)
Now,
306.6 = 6 (side)²
(side)² = 51.1
Therefore, the area of each face is 51.1 square units.
b) A cube has 6 faces
Area of each face is (side × side)
Area = side × side
So, total area is equal to 6 times the area of each side.
Area = 6 × (side × side)
now,
450 = 6 (side)²
(side)² = 75
Therefore, the area of each face is 75 square units.
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given point O is the center of each circle:
Using the central angle theorem, we can find that the value of the angle:
∠ BOC = 130°.
Define central angle?An inscribed angle is the angle formed inside the circle when two chords intersect it. It can also be defined as the angle made by two specific points at a given location on a circle. Instead, an inscribed angle is defined by two circle chords that share an endpoint.
In the given question,
O is the centre of the circle.
OC, OD, OE, OA and OB are all radius of the circle.
AC and BD are the diameters of the circle.
As BD intersects AC and the angles are given as:
∠COD = 50°
∠DOE = 60°
So, ∠ AOE = 180 - 50 - 60
= 70°
Similarly, ∠AOB = 50°.
Now, ∠ BOC = 360° - 50° - 60° - 70° - 50°
= 130°
Therefore, ∠ BOC = 130°.
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The wheels on Karin's bike are 64 inches in circumference. How many times do the wheels rotate if Karin rides 300 yards?
Answer: 169 times
Step-by-step explanation:
Circumference : 64inches
Distance: 300 yards
We know that 1 yard is 36 inches.
300yd*36 = 10800inches
10800/64 = 168.75 but rounding up makes it 169 times.
A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the variance to be 1.69. She thinks the mean is 7.6 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.14 at the 98% level of confidence
The minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.
The standard deviation is given as (σ) = 1.69.
The mean number of dresses given (μ) = 7.6.
Margin of error given (M.E.) = 0.14.
Confidence level given = 98%.
Z-Score corresponding to 98% confidence interval (Z) = 2.33.
We are asked to find the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval.
We assume the size of the sample to be n.
By the formula of Margin of Error:
M.E. = Z*(σ/√n).
Substituting the values, we get:
0.14 = 2.33*(1.69/√n),
or, √n = 2.33*1.69/0.14 = 28.126429,
or, n = 791.096 ≈ 791 (As sample size needs to be a whole number).
Thus, the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.
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Please help due tonight
Answer:
n = 13
Step-by-step explanation:
1. (9n-8) and (6n-7) combined equal 180 degrees, and we can translate that into an equation and then solve it: \(9n - 8 + 6n- 7 = 180\)
2. (Solving)
Step 1: Simplify both sides of the equation.
\((9n+6n)+(-8-7) = 180\) \(15n-15=180\)Step 2: Add 15 to both sides.
\(15n-15+15 = 180+15\) \(15n = 195\)Step 3: Divide both sides by 15.
\(\frac{15n}{15} = \frac{195}{15}\) \(n = 13\)Therefore, n = 13.
I need to double check a answer. For measure 1 and 3 I got 117, is that right? But for measure 2 I got 63 which is wrong but I have no idea how to solve it, please help me. Also the options are
27,63,73,117
Answer:
All are 63
Step-by-step explanation:
m∠1 = 180 - 117 = 63 (linear pair)
m∠2 = 63 (alternate interior angle with ∠1)
m∠3 = m∠1 = 63 (isosceles triangle property)
Hope it helps :)
Please mark my answer as the brainliest
Please help! Asap thanks!
The function value is 5/2 when x is 0 and value of function is 4 when x =-3.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=|1-x|/2 + 2
We need to find the value of function when x is 0 and when x is -3.
Plug in value x =0
f(0)=|1-0|/2+2
=1/2+2
f(0)=5/2
Now we have to find the function when x is -3
f(-3)=|1+3|/2+2
=4
Hence, the function value is 5/2 when x is 0 and value of function is 4 when x =-3.
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suppose that the only currency was 3-dollar bills and 10-dollar bills. show that every amount greater than 17 dollars could be made from a combination of these bills.
To show that every amount greater than 17 dollars can be made from a combination of 3-dollar and 10-dollar bills, we can use a technique called "proof by induction."
First, let's check the base case: can we make 18 dollars using only 3-dollar and 10-dollar bills? Yes, we can use two 3-dollar bills and one 10-dollar bill: 3 + 3 + 10 = 16.
Now, let's assume that we can make any amount greater than n dollars using only 3-dollar and 10-dollar bills. We want to prove that we can make any amount greater than n+1 dollars as well.
To do this, we can consider two cases:
1. The amount we want to make includes at least one 10-dollar bill. In this case, we can subtract 10 dollars from the amount and use our induction hypothesis to make the remaining amount using only 3-dollar and 10-dollar bills. Then we add the 10-dollar bill back in, and we have made the original amount.
2. The amount we want to make does not include any 10-dollar bills. In this case, we can use our induction hypothesis to make the amount n-7 using only 3-dollar and 10-dollar bills (since 10 - 3 = 7). Then we add a 10-dollar bill and a 3-dollar bill to get n+3, and we can add another 3-dollar bill to get n+6. Finally, we add one more 3-dollar bill to get n+9, which is greater than n+1.
Therefore, we have shown that any amount greater than 17 dollars can be made from a combination of 3-dollar and 10-dollar bills using proof by induction.
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Use the integral test to determine whether each of the following series converges or diverges. For each, fill in the integrated and the value of the integral. Enter diverges if the integral diverges. Then indicate the convergence of the sum.
(a) [infinity]∑n=116n∑n=1[infinity]16n
(b) [infinity]∑n=1n+4n2+8n+4
The series diverges with an integral of 1/ln(16) and the series converges with an integral of 1/4 and a sum of 1/2.
We can use the integral test to determine the convergence of the series ∑n=1∞ 1/6n. The integral of the function f(x) = 1/6x is:
\(∫f(x) dx = (1/6) ln(x) + C\)
Using the limits of integration from 1 to ∞, we get:
∫1∞ f(x) dx = (1/6) ln(∞) - (1/6) ln(1) = ∞
Since the integral diverges, the series also diverges.
We can use the integral test to determine the convergence of the series ∑n=1∞ \((n+4)/(n^2+8n+4\)). The integral of the function f(x) = \((x+4)/(x^2+8x+4)\) is:
∫f(x) dx = (1/2) ln(x^2 + 8x + 4) + 3 ln|x + 4| + C
Using the limits of integration from 1 to ∞, we get:
∫1∞ f(x) dx = (1/2) ln(∞) + 3 ln(∞ + 4) - (1/2) ln(13) - 3 ln(5) = ∞
Since the integral diverges, the series also diverges.
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a class has 50 students 18 are female and 32 are male. if a representative will be chosen in their class what is the probability of having a male or female
Answer:
64% male
36% female
Step-by-step explanation:
We know
A class has 50 students, 18 female, and 32 male.
If a representative is chosen in their class, what is the probability of having a male?
32 divided by 50, times 100 = 64%
So, 64% that the representative is male.
If a representative is chosen for their class, what is the probability of having a female?
18 divided by 50, times 100 = 36%
So, 36% that the representative is female.
Lunch is 7.95 the tax is 10% what’s the total cost
Answer: ($)8.75
Step-by-step explanation:
To calculate the tax, simply do 10%(0.1)*7.95 to get 0.795, rounding up to 0.80(money typically rounds up).
To calculate the total cost, simply do 7.95+0.80 to get 8.75.
Hope it helps <3
How many inch in 10 cm?
Answer: 3.93701
Step-by-step explanation:
Answer:
10 cm to inches is 3 15/16 inches, or in decimal, is 3.9370 inches
Step-by-step explanation:
.
Clarissa needs a $2,500 loan in order to buy a car. Which loan option would allow her to pay the least amount of interest?
Answer:
mortgage
Step-by-step explanation:
are loans distributed by banks to allow consumers to buy homes they can't pay for upfront. A mortgage is tied to your home, meaning you risk foreclosure if you fall behind on payments. Mortgages have among the lowest interest rates of all loans.
Answer:
An 18-month loan with a 4.75% annual simple interest rate
Step-by-step explanation:
What is the equation of this line? PLEASE HURRYYY!!!!!!
What is 7 1/2 divided by 3/4
Answer:
10
Step-by-step explanation:
7 1/2 = 7.5
3/4 = 0.75
7.5 ÷ 0.75 = 10
Check work:
0.75 x 10 = 7.5
if the expression 3x+2 is equal to 15 for some value of x, then what is the value of 9x+5
How can I solve this problem?
a) The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price
b) The down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.
Given,
The purchase price for the studio apartment = $200,000
The down payment they paid = $60,000
a) We have to find the percentage of down payment to purchase price.
Here,
Percentage = (down payment x 100) / purchase price
= (60,000 x 100) / 200,000
= 60/2
= 30
That is,
The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price.
b) We have to find the percentage to purchase price if the down payment is $90,000
Here,
Percentage = (down payment x 100) / purchase price
= (90,000 x 100) / 200,000
= 90/2
= 45
That is,
The down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.
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LaTeX: \left(3x^2\:-\:1\right)+\left(3x^2\:-x^3\right)( 3 x 2 − 1 ) + ( 3 x 2 − x 3 )
Answer:
I wanted to simplify since u didn't specify what u wanted: -x^3 + 6x^2 -1
Step-by-step explanation:
I assume this is what you typed: (3x^2 - 1) + (3x^2 - x^3)
-x^3 + 6x^2 -1
Answer:
-x³+6x²-1
Step-by-step explanation: Hope it helps
just before a referendum on a school budget, a local newspaper polls 377 voters to predict whether the budget will pass. suppose the budget has the support of 54% of the voters. what is the probability that the newspapers sample will lead it to predict defeat?
The probability that the newspapers sample will lead it to predict defeat is 92.36%.
To solve this problem, we need to use the binomial distribution formula.
Let's define the following:
X: number of voters in the sample who do not support the budget (i.e., the sample leads to a prediction of defeat).
n: sample size, which is 377.
p: proportion of voters who support the budget, which is 0.54 (since 54% support it, 46% do not support it).
The probability of the sample leading to a prediction of defeat is:
P(X = k) = (n choose a) * pᵃ * (1-p)ⁿ⁻ᵃ
where (n choose a) = n! / (a! * (n-a)!) is the binomial coefficient.
We want to find P(X >= 189), which means that at least 189 voters in the sample do not support the budget.
P(X >= 189) = 1 - P(X < 189)
To calculate P(X < 189), we can use a normal approximation to the binomial distribution, since n is large and p is not too close to 0 or 1.
The mean of the binomial distribution is mu = n * p = 377 * 0.54 = 203.58
The standard deviation is sigma = √(n * p * (1-p)) = √(377 * 0.54 * 0.46) = 10.20
We can standardize X using the z-score formula:
z = (X - mu) / sigma
P(X < 189) = P(z < (189 - 203.58) / 10.20) = P(z < -1.43)
Using a standard normal table or calculator, we can find that P(z < -1.43) = 0.0764.
Therefore, P(X >= 189) = 1 - P(X < 189) = 1 - 0.0764 = 0.9236.
So the probability that the newspaper's sample will lead it to predict defeat is approximately 0.9236, or 92.36%.
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HELP!! I WILL NAME BRAINLIEST!If f(x) = (x + 7), which of the following is g(x) based on the translation?
g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x - 9)2
g(x) = (x - 5)2
Answer:
g(x) = (x + 5)2
Step-by-step explanation:
:)
please help me find the HCF of this
Answer: a
Step-by-step explanation:
\(a^{2}=a \cdot a\\a^{2}+ab=a(a+b)\)
Therefore, the HCF is a.
Answer:
a
Step-by-step explanation:
Factorizing both terms :
a² = a × aa² + ab = a × (a + b)The HCF of the terms is a.
Find the measure of angle a and B. Round to the nearest degree.
The measure of angle A and angle B are 32° and 58° respectively.
What is the measure of anglw A and B?The figures in the image are right-triangle.
To find the measure of angle A and B, we use the trigonometric ratio.
For angle A:
Angle θ = ?
Opposite to angle θ = 8
Hypotensue = 15
Note that: sine = opposite / hypotensue
sinθ = 8 / 15
Take th sine inverse
θ = sin⁻¹( 8/15 )
θ = 32°
Angle A = 32°
For angle B:
Angle B = ?
Adjacent to angle B = 8
Hypotensue = 15
Note that: cosine = adjacent / hypotensue
cosB = 8/15
Take th cosine inverse
B = cos⁻¹( 8/15 )
B = 58°
Therefore, angle B measures 58 degrees.
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Compare / Contrast Exponential Equations
1.) 2 (1/5)x-5
2.) y=4x
The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows
y = 2 (1/5)^x - 5 y = 4^x
Initial value: 2 1
base function: 1/5 = decay function 4 = growth function
Translation: 5 units down no transformation
What is a decay function?
A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.
It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.
Decay function are exponential functions with the base function as
0 < k < 1This is the opposite of growth function which has values greater than 1
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I need help with finding the surface area of the prism
Answer:May be 12
Step-by-step explanation:
Answer: The surface area of the rectangular prism is 114 cm^2.
Step-by-step explanation:
1) Formula: A = 2wl + 2lh + 2hw
( W=width, l= length, h=height)
2) Plug it in: A=2(3)(8) + 2(8)(3) + 2(3)(3)
3) A= 2( 24) + 2(24) + 2(9)
4) A= 48+ 48+ 18= 114
BRAINLIEST ANSWER IF CORRECT
What value of x shows removeable discontinuity?
Answer:
\(option \: c. \: is \: correct.\)
Step-by-step explanation:
\(the \: value \: of \: x \: that \: shows \\ removeable \: discontinuity \: is \: \to \: 2.\)
if a shirt costs $22. Quien give the person $88 how many shsirts is quien getting?
Answer:
Quien is getting 4 shirts
Step-by-step explanation:
22x=88
-----------
22 22
x=4
BRAINLIEST WOULD BE NICE :)
Violet buys a dresser at a yard sale for $40. She decides to sell it online for a profit. If Violet wants to sell the dresser for at least $65, what is the smallest markup she can make to theoriginal price of the dresser?A. 60%B. 62.5%C. 65%D. 66.7%
Consider that the dresser costs $40 to Violet. So the cost price C is $40.
She wants to sell the dresser for at least %65,
Then the selling price S must be greater than or equal to $65,
\(S\ge65\)Since there is no discount or any overhead expense, the selling price is the same as the marked price M,
\(M\ge65\)Then the minimum marked price will be $65.
Therefore, option (C) is the correct choice (but the % symbol should not be there).
Hazel and Tom travel the same 18 km route.
Hazel starts at 9. 00 am and walks at a constant speed of 4. 8 km/h
Tom starts at 9. 39 am and runs at a constant speed.
Tom overtakes Hazel at 10. 15 am
At what time does Tom finish the route?
Answer:
11:27 am.
Step-by-step explanation:
The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked
1.25 * 4.8
= 6 km.
So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes
= 0.6 hrs.
So, Tom's speed is 6/0.6 = 10 km/hr.
,
and Tom will take 18/10 = 1.8 hours to finish the route,
= 1 hr 48 minutes
So he finishes the route at
9:39 + 1:48
= 11:27 am.
What are some advantages of using a debit card as opposed to cash?
(select all that apply.)
debit cards can be set up to provide a revolving line of credit.
debit cards can be replaced if they are lost.
debit cards can help track spending carefully and accurately.
o debit cards can provide monthly interest payments.
The some advantages of using a debit card as opposed to cash are debit cards can be replaced if they are lost and debit cards can provide monthly interest payments. So the option a and d is correct.
When a consumer uses a debit card to make purchases, the money is taken directly out of their checking account rather than being borrowed from a bank or card provider.
There is no revolving line of credit associated with a debit card.
You can usually request and receive a new debit card approximately two to three working days. When the debit card is claimed missing, the issue of a new duplicate card may be authorized. The bank might, however, charge a fee for providing the new card.
Another type of borrowing is the EMI for a debit card, which carries interest. Currently, annual interest rates are between 12 and 16 percent.
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Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and
C(-4,9). The triangle is transformed using the rule (x,y) -> (2x.y-3) to create triangle
A'B'C'. Select all possible answers for the vertices of triangle A'B'C'.
a. (14,3)
b. (9,3)
c. (-6,10)
d. (-8,6)
e. (-6,2)
The coordinates of the vertices of the triangle A'B'C' are (14, 3), (- 6, 2) and (- 8, 6), respectively. (Correct choices: A, E, D)
What are the coordinates of the vertices of a traingle after using transformation rule?
In this question we find the locations of the three vertices of the triangle, each of which has to be transformed by using a non-rigid transformation rule, that is, a transformation rule that does not conserve the original form of the triangle. We are asked to determine the possible coordinates associated with the triangle A'B'C.
If we know that A(x, y) = (7, 6), B(x, y) = (- 3, 5) and C(x, y) = (- 4, 9), then the coordinates of the vertices of the triangle A'B'C' are:
A'(x, y) = (2 · 7, 6 - 3)
A'(x, y) = (14, 3)
B'(x, y) = (2 · (- 3), 5 - 3)
B'(x, y) = (- 6, 2)
C'(x, y) = (2 · (- 4), 9 - 3)
C'(x, y) = (- 8, 6)
The coordinates of the vertices of the triangle A'B'C' are (14, 3), (- 6, 2) and (- 8, 6), respectively. (Correct choices: A, E, D)
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