Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{4x - 36}}}}[/tex]Step-by-step explanation:
[tex] \sf{x + 3x - 36}[/tex]
Here, we have to collect like terms.
_________________________________
▪️What do you mean by like terms ?
⇒Like terms are those which have the same base. While adding or subtracting like terms, we should add or subtract the coefficients of like terms.
_________________________________
Let's add the like terms :
Answer : 4x - 36
Hope I helped!
Best regards!
If tan x° = 6 divided by g and sin x° = 6 divided by h, what is the value of cos x°?
Answer:
adjacent / hypotenuse cos x° = g divided by h is right
Step-by-step explanation:
If [tex]tanx^{o} = \frac{6}{g}[/tex] and [tex]sinx^{o} = \frac{6}{h}[/tex] then [tex]cosx^{o} = \frac{g}{h}[/tex] .
Trigonometric Ratios:By right angled triangle we have,
Trigonometric ratios as
sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex]tanθ = [tex]\frac{opposite}{adjacent}[/tex]Given [tex]sinx^{o} = \frac{6}{h}[/tex] and [tex]tanx^{o} = \frac{6}{g}[/tex]
By comparison, we haveopposite = 6, hypotenuse = h, adjacent = g
Hence, we can write[tex]cosx^{o}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex] [tex]=\frac{g}{h}[/tex]
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A marble is drawn at random from a box containing 10 red, 30 white, 20 blue, and 15 orange marbles. Find the probability that it is (a) orange or red, (b) not red or blue, (c) not blue, (d) white, (e) red, white, or blue
Step-by-step explanation:
given data:
total marbles = 75
red marble = 10
white marble = 30
blue marble = 20
orange marble = 15
solution:
a. Probability of drawing an orange or red
= 15/75 + 10/75
= 1/3
b. probability of not drawing a red or blue
= 1 - 20+10/ 75
= 3/5
c. Not blue
= 1 - p
= 1 - 20/75
= 11/5
d. Probability of drawing a white
= 30/75
= 2/5
e = red, white or blue
= 10/75 + 30/75 + 20/75
= 4/5
Answer:
Step-by-step explanation:4/5
The probability that an online student owns a laptop is 0.82 and the probability that a student owns a desktop is 0.65. If the probability that a student owns both is 0.55, find the probability that a student owns a laptop or a desktop.
Answer:
The probability that a student owns a laptop or a desktop is 92%.
Step-by-step explanation:
We are given that the probability that an online student owns a laptop is 0.82 and the probability that a student owns a desktop is 0.65. The probability that a student owns both is 0.55 .
And we have to find the probability that a student owns a laptop or a desktop.
Let the probability that a student owns a laptop = P(L) = 0.82
The probability that a student owns a desktop = P(D) = 0.65
The probability that a student owns both laptop and desktop = P(L [tex]\bigcap[/tex] D) = 0.55
Now, the probability that a student owns a laptop or a desktop is given by = P(L [tex]\bigcup[/tex] D)
P(L [tex]\bigcup[/tex] D) = P(L) + P(D) - P(L [tex]\bigcap[/tex] D)
= 0.82 + 0.65 - 0.55
= 0.92 or 92%
So, the probability that a student owns a laptop or a desktop is 92%.
Everything in a store is discounted by 25%. What is the sale price of a clock with a regular price of $24.60?
Answer:
$24.35
Step-by-step explanation:
sale price⇒ total price-discount price
s.p=$24.60-25/100 ∴25%⇒25/100
s.p⇒$2460/100-25/100 ∴24.60⇒2460/100
s.p⇒$24.35
⇒$24.35
f(x) = x/2 - 1 find f (12)
Answer:
5
Step-by-step explanation:
Hi,
f(12)= 12/2 -1 = 6 -1 = 5
Thanks
Answer:
5
Step-by-step explanation:
f(x) = x/2 - 1
Let x = 12
f(12) = 12/2 -1
= 6-1
= 5
The Pampered Pet Hotel cares for dogs and cats while their owners are away. The daily fee for boarding a dog at the hotel is different from the fee for boarding a cat. On Tuesday, 11 dogs and 14 cats stayed at the hotel and the hotel earned \$573.25 . On Friday, 22 dogs and 9 cats stayed at the hoteland the hotel earned 790.25How much does it cost per day to board a dog and a cat at the pet hotel?
Step-by-step explanation:
Let the rate of boarding a dog and a cat be x and y respectively.
Now,
11x + 14y = 573.2522x + 9y = 790.25Further solving the two equations :
Y = $ 18.75
X = $ 28.25
A geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term
Answer: the first term is 45
Step-by-step explanation:
Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20
So ar²= 20 and we make this equation i
Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)
Further simplification gives us
3a= a/(1-r)
We simplify Futher by multiplying both sides by (1-r)
3a.(1-r) = a/(1-r).(1-r)
3a(1-r)=a
= 3a-3ar=a
Make 3ar the subject of the formula
3ar= 2a and lets make this equation (ii)
Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²
Ar²/r² = 20/r²
A=20/r²lets make this equation (iii)
Step 4: subtitle a as 20/r² into equation (ii)
Since 3ar=2a
Then 3.(20/r²).r = 2. 20/r²
= (60/r²) .r = 40/r²
60/r = 40/r2
Multiplying both sides by r² gives us
60r = 40
Divide both sides by 20 gives us
= 3r= 2
Divide both sides by 3 gives us
= r = 2/3
Step 5: substitute r for 2/3 in equation i
ar²= 20
a. (2/3)2 = 20
= a.4/9 = 20
= 4a = 180
= a = 180/4
a = 45
(9x - 4x2 + 9) + (-x3 + 4x2 - 3)
Answer:
The solution to the given expression is -x³ + 9x + 6
Step-by-step explanation:
(9x - 4x² + 9) + (-x³ + 4x² - 3)
Since there is a positive sign in front of the second parentheses, then the terms inside will stay the same.
9x - 4x² + 9 - x³ + 4x² - 3
Group terms together that are alike. Also known as like terms.
-x³ + (-4x² + 4x²) + 9x + (9 - 3)'
Combine like terms.
-x³ + 9x + 6
Answer:
- [tex]x^{3\\}[/tex] + 9x + 6
Step-by-step explanation:
First, you need to combine like terms. Like terms, when dealing with exponents can be categorized by their powers.
hIn this case, 9x stands alone, because there is no other coefficient with the power of just x.
9x
Next, we can look at the -4x^2. The other similar coefficient is + 4x^2. We can combine both of those, which will equal out to 0.
Next, you have 9. It can be combined with -3, since none of them have an exponent attached. It will equal 6
9x + 6
We also have a -x^3 left over. There is no like term to combine with it, so we can leave it as is.
Our problem now looks like
9x + 6 - [tex]x^{3}[/tex]
You can rearrange them in the proper order, so it will look like,
- [tex]x^{3}[/tex] + 9x + 6.
And there you have it!
A 16 and 12 km of road music players work with their 214 km of road per week how many weeks will it take to repair a stretch of road
Answer:
i tried to answer but the question made no sense
Step-by-step explanation:
Can someone please help me with this ?
Answer:
x = -2i and 2i (or ±2i)
Step-by-step explanation:
Solve for x:
2x² - 4 = -12
2x² = -8
x² = -4
x = √(-4) = ±2i
Which of the following is the inverse of y=
6^x?
Answer:
y = (ln x) / (ln 6)
Step-by-step explanation:
1. Exchange x and y: x = 6^y
2. Solve for y: Take the natural log of both sides:
ln x = y ln 6
Then: y = (ln x) / (ln 6)
Note: y = (log x) / (log 6) is also correct
part 7: please assist me with these problems
Answer: 10) 40° 11) 9.9
Step-by-step explanation:
[tex]\text{Law of Sines:}\quad \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
10) Given: a = 31, b = 20, A = 84°
[tex]\dfrac{\sin 84^o}{31}=\dfrac{\sin B}{20}\\\\\\\dfrac{20\sin 84^o}{31}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{20\sin 84^o}{31}\bigg)=B\\\\\\39.9^o=B[/tex]
11) Given: a = 18, A = 105°, B = 32°
[tex]\dfrac{\sin 105^o}{18}=\dfrac{\sin 32^o}{b}\\\\\\b=\dfrac{18\sin 32^o}{\sin 105^o}\\\\\\b=9.87[/tex]
At the beginning of the months, a consumer had $437.52 of in his bank account. During he made deposits of $256 and $217.14 of $80 and write checks of $115.98 and $108.90 - What balance left?
Question:
At the beginning of the months, a consumer had $437.52 of in his bank account. During which he made deposits of $80, $256 and $217.14 and write checks of $115.98 and $108.90 - What balance left?
Answer:
The customer's balance is $765.78
Step-by-step explanation:
Given
Start Amount = $437.52
Deposits = $80, $256 and $217.14
Withdrawals (Checks) = $115.98 and $108.90
Required
Determine his balance
We start by calculating the total deposits made by the customer
[tex]Total\ Deposits = \$80 + \$256 + \$217.14[/tex]
[tex]Total\ Deposits = \$553.14[/tex]
Next, we calculate the total withdrawals (checks)
[tex]Total\ Withdrawals = \$115.98 + \$108.90[/tex]
[tex]Total\ Withdrawals = \$224.88[/tex]
At this point, we can now calculate the customer's balance as follows;
[tex]Balance =Start\ Amount + Total\ Deposits - Total\ Withdrawals[/tex]
[tex]Balance = \$437.52+ \$553.14 -\$224.88[/tex]
[tex]Balance = \$765.78[/tex]
Hence, the customer's balance is $765.78
The balance left in the consumer's account is $765.78.
The amount of money in the consumer's account increases with the deposits made and reduces when she writes checks.
The total value of the deposits have to be determined first.
Total value of the deposits = $256 + $217.14 + $80 = $553.14
The value of the checks written has to be determined
$115.98 + $108.90 = $224.88
Add the value of deposit, subtract the value of checks from the beginning balance
$437.52 + $553.14 - $224.88 = $765.78
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At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes?
Answer:
a) Cost of a chicken shawarma wrap?
$10.99
b) Cost of one order of spiced potatoes?
$4.99
Step-by-step explanation:
Cost of a chicken sharwarma wrap = a
Cost of an order of spiced potatoes = b
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3a + 2b = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5a + 4b = $74.91 ................Equation 2
So we have:
3a + 2b = $42.95 .............Equation 1
5a + 4b = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of b in Equation 2
Equation 2 by coefficient of b in Equation 1
3a + 2b= $42.95 .............Equation 1 × 4
5a + 4b = $74.91 ................Equation 2 × 2
12a + 8b = 171.80..............Equation 3
10a + 8b = 149.82..............Equation 4
Subtract Equation 3 from Equation 4
2a = 21.98
a = 21.98/2
a = 10.99
Therefore, a = Cost of Chicken sharwarma wrap = $10.99
Subtitute 10.99 for 9in Equation 1
3a + 2b = $42.95 .............Equation 1
3(10.99) + 2b = 42.95
32.97 + 2b = 42.95
2b = 42.95 - 32.97
2b = 9.98
b = 9.98/2
b = 4.99
b = Cost of an order of spiced potatoes = $4.99
Hence,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
(Hurry, please!) A line passes through the point (8,-1) and has a slope of 5/4. Write an equation in slope intercept form for this line.
Answer:
y = 5/4x -11
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = 5/4 x + b
Substitute the point into the line
-1 = 5/4(8) +b
-1 =10 +b
Subtract 10 from each side
-11 = b
y = 5/4x -11
Answer:
[tex]\huge \boxed{y=\frac{5}{4} x-11}[/tex]
Step-by-step explanation:
The slope-intercept form of a line is written as,
[tex]y=mx+b \\ \\ \\ \sf m= slope \\ \\ b=y -intercept[/tex]
The slope is given.
[tex]\displaystyle y=\frac{5}{4} x+b[/tex]
The line passes through the point (8, -1).
[tex]x=8 \\ \\ y=-1[/tex]
Plugging in the values.
[tex]\displaystyle -1=\frac{5}{4} (8)+b[/tex]
Solving for b or y-intercept of the line.
[tex]\displaystyle -1=\frac{40}{4} +b[/tex]
[tex]-1=10+b[/tex]
[tex]-11=b[/tex]
The y-intercept of the line is -11.
[tex]\displaystyle y=\frac{5}{4} x-11[/tex]
Please help me with this
Answer:
Hey there!
3^-8(3^4)=3^-4
The second option is correct.
Hope this helps :)
What’s the ratio for this rectangle
Answer: 9 to 4
Step-by-step explanation:
Using the grids you can count them to see what the width is.
The width is 9 units and the height is 4 units so the ration will be 9 to 4
The ratio of width of the rectangle to the height of the rectangle is 9 to 4.
A rectangle is a quadrilateral with four sides and four angles. It is a type of geometric shape characterized by its properties, including having opposite sides that are equal in length and all angles measuring 90 degrees (right angles).
In the given rectangle, there are 4 units or boxes in the height.
There are 9 units or boxes which makes width of the rectangle.
Hence, the ratio of width of the rectangle to the height of the rectangle is 9 to 4.
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What's the area of the following triangle?
6 in.
10 in.
16 in.
2
86 in.
14 in.?
30 in.
Answer:
30
Step-by-step explanation:
Formula is 1/2bh
6 times 10 = 60
60 divided by 2 equals 30
Answer:
⇒30 in²
Step-by-step explanation:
area ofΔ⇒1/2×length×width
⇒ 1/2×6 in×10 in
⇒1/2×60in²
⇒30 in²
Determine if 0.292992999299992999992... is rational or irrational
and give a reason for your answer.
Answer:
Irrational
Step-by-step explanation:
Can't be put into a fraction.
If f(x) = 3x + 10x and g(x) = 5x - 3, find (f+ g)(x).
O A. 18x– 3
O B. 3x + 15x - 3
O c. 3x - 5x + 3
O D. 3x + 5x + 3
A florist sells 3 similar bouquets of flowers for $78. What is the cost per bouquet?
Answer:
$26
Step-by-step explanation:
Divide 78 by 3, which will get you 26 dollars per bouquet!
Answer:
Cost per bouquet is $26.
Step-by-step explanation:
You take the total cost of all three bouquets and divide them by the number of bouquets. 78/3 = 26.
Solve for x: 3x+y=5x-y
Answer: x= y
Step-by-step explanation:
3x + y =5x -y Subtract 5x from both sides
-5x -5x
-2x + y = -y Now subtract y from both sides
-y -y
-2x = -2y Now divide both sides by -2
x = y
What’s the Answer
please?
Answer:
Widths are 2, 4, 5
Border or the perimeter of all these rectangles = 16
Perimeter of a rectangle
=> 2 ( L + W)
W = Width
L = Length
Area of a rectangle
=> L x W
First rectangle
Perimeter = 2(L+W)
=> 2 (L + 2) = 16
=> 2L + 4 = 16
=> 2L + 4 - 4 = 16 - 4
=> 2L = 12
=> 2L/2 = 12/2
=> L = 6
Length of the First Rectangle = 6
Area = L x W
=> 6 x 2 = 12
Area of the First Rectangle = 12
Second rectangle
Perimeter = 2( L + W)
=> 2 (L + 4) = 16
=> 2L + 8 = 16
=> 2L + 8 - 8 = 16 - 8
=> 2L = 8
=> 2L/2 = 8/4
=> L = 4
Length of the Second Rectangle = 4
Area = L x W
=> 4 x 4
=> 16
Area of the Second Rectangle = 16
Third Rectangle
Perimeter = 2 (L + W)
=> 2 (L + 5) = 16
=> 2L + 10 = 16
=> 2L + 10 - 10 = 16 - 10
=> 2L = 6
=> 2L / 2 = 6/2
=> L = 3
Length of the Third Rectangle = 3
Area = L x W
=> 3 x 5
=> 15
Area of the Third Rectangle = 15
To find which figure covers more spaces, we need to which figure has more area.
=> Rectangle 2 has the largest area = 16
Every positive number is also a rational number True or false
Answer:
false
Step-by-step explanation:
hope this helps✨
What is the z-score of the value 65 in a population if the population has a mean s = 62 and a standard deviation o = 2.4? A. 1.25 B. 0.9169 C. -1.25 D. 1.009
Answer:
Option A
Step-by-step explanation:
z-score = (value - mean)/std = (65-62)/2.4 = 1.25
Write a ratio for the following description: For every 6 cups of flour in a bread recipe, there are 2 cups of milk. Type your answer in the format: 3:4 with no spaces. Describe a situation that could be modeled with the ratio 4: 1.
Answer:
6:2 or 1:3
Step-by-step explanation:
Not really sure how to explain this, but I hoped this helped!
J(x) = 220/x^3 and j-x)=220/(-x)^3
Answer:
Option (A)
Step-by-step explanation:
If a function 'f' is an odd function,
f(-x) = -f(x)
If a function 'f' is an even function,
f(-x) = f(x)
In this question given function is,
f(x) = [tex]\frac{220}{x^3}[/tex]
To check the given function is odd or even,
f(-x) = [tex]\frac{220}{(-x)^{3} }[/tex]
= [tex]-\frac{200}{x^{3}}[/tex]
Therefore, from the definition of even and odd functions,
Function 'f' is an odd function.
Option (A) will be the correct option.
How many solutions does the system have?
Answer: A
Step-by-step explanation:
There are 2 ways to solve this problem.
Solution 1:
Since we are given two equations, we set them equal to each other to find where they intersect, the solution.
3x+3=-2x+3 [combine like terms]
5x=0 [divide both sides by 5]
x=0
Now that we have x=0, we can plug it into either equation to find the point of intersection.
y=3(0)+3
y=3
We know that the point of intersection is (0,3).
-------------------------------------------------------------------------------------------------------------
Solution 2:
This way of solving the problem doesn't require any calculations. All it requires is an understanding of slope-intercept form equation. From the two equations given, we know that they are linear lines. Linear lines can only intersect once. Knowing this, we know that there can only be exactly one solution.
In part of an agreement between cigarette agencies and the government, levels of nicotine in cigarettes are to be slowly reduced over time. A sample of 40 measurements conducted on one brad of cigarettes 10 years ago yielded an average of 32.9mg per cigarette with a sample standard deviation of 4.4 mg. A study done last month on 30 cigarettes of this brand yielded a sample mean of 30.6mg with sample standard deviation 5.1 mg. What type of test should be used to determine if the levels now are lower than what they were 10 years ago
Answer: INDEPENDENT SAMPLES T-TEST
Step-by-step explanation:
Given that;
sample size n₁ = 40, sample size n₂ = 40
sample mean x₁ = 32.9, sample mean x₂ = 30.6
Standard deviation S₁ = 4.4, Standard deviation S₂ = 5.1
Now
NULL hypothesis H₀ : u₁ = u₂
and Alternative hypothesis H₁ : u₁ > u₂
Therefore based on the information provided above, the type of test that should be used to determine whether the level of nicotine are now lower than what they were 10 years ago is the INDEPENDENT SAMPLES T-TEST
A marketing organization claims that more than 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted
Answer:
there is insufficient evidence to support the claim that more than 10% of the employees are paid minimum wage.
Step-by-step explanation:
Given that:
A marketing organization claims that more than 10% of its employees are paid minimum wage.
The null hypothesis is:
[tex]H_o : p = 10[/tex]
The alternative hypothesis is:
[tex]H_1 : p > 10[/tex]
If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted
i.e Decision Rule: fails to reject the null hypothesis
Then the interpretation of the decision is that, there is insufficient evidence to support the claim that more than 10% of the employees are paid minimum wage.