Evaluate the expression if p=1/2 and S + 3 1/2
3P+2S+ 6 1/3
Answers
The Value of the expression with p = 1/2 and s = 3 1/2 is 87/6.
To evaluate the expression with p = 1/2 and s = 3 1/2, we substitute these values into the given expression:
3p + 2s + 6 1/3
Substituting p = 1/2 and s = 3 1/2:
3(1/2) + 2(3 1/2) + 6 1/3
We first simplify the expression within parentheses:
3/2 + 2(7/2) + 6 1/3
Next, we perform the multiplication:
3/2 + 14/2 + 6 1/3
The denominators are already the same, so we can add the fractions:
3/2 + 14/2 + 6 1/3 = (3 + 14)/2 + 6 1/3
Now, we need to find a common denominator for the fraction and the whole number:
(3 + 14)/2 + 6 1/3 = 17/2 + 6 1/3
To add the fractions, we need a common denominator of 6:
17/2 + 6 1/3 = 17/2 + 18/3
Now, we can find a common denominator for the fractions:
17/2 + 18/3 = 51/6 + 36/6
Adding the fractions:
51/6 + 36/6 = 87/6
Therefore, the value of the expression with p = 1/2 and s = 3 1/2 is 87/6.
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Related Questions
Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.
Answers
The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.
What is the Surface Area of a Box?The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.
What is the Surface Area of a Box?SA = 2(lw + lh + hw), where:
l = lengthw = widthh = height of the boxThe image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:
The surface area to be covered = surface area of the box - area of the bottom rectangular face
The surface area to be covered = 2(lw + lh + hw) - (l)(w)
l = 26
w = 15
h = 8
Substitute
The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =
The surface area to be covered = 1436 - 390 = 1,046 cm
Area of one tile = 1 cm square
Number of tiles needed = 1,046/1
Number of tiles needed = 1,046 tiles.
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Please answer number number 7 I’ll give brainliest thank you!
Answers
Answer:
b) $41.85
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 45 × 7/100
Discount = 45 x 0.07
You save = $3.15
Final Price = Original Price - Discount
Final Price = 45 - 3.15
Final Price = $41.85
hope this helps and is right. p.s. i really need brainliest :)
Answer:
Step-by-step explanation:
that would be A
What translation rule can be used to describe the result of the composition of (x, y) → (x-9, y
-2) and (x, y) + (x + 1, y-2)?
(x, y) = (x+8, y– 4)
(x, y) = (x – 10, y +0)
(x, y) → (x–8. y - 4)
(x, y) = (x - 4. y - 8)
Answers
Answer: Choice C
\((x,y) \to (x-8,y-4)\)
===================================================
Explanation:
The first translation \((x,y) \to (x-9,y-2)\) has x become x-9. This means we shift 9 units to the left.
The second translation \((x,y) \to (x+1,y-2)\) tells us to shift 1 unit to the right when going from x to x+1.
Combining the "9 units to the left" and "1 unit to the right" will produce an overall shift of "8 units to the left". It might help to draw out a number line to see this.
After combining those two translations, we'll have \(x \to x-8\) which means we'll end up with \((x,y) \to (x-8,y-4)\). The first two translations shift the point down 2 units at a time, so overall we shift down 4 units.
Find the volume please
Answers
Answer:
6 cm³
Step-by-step explanation:
The figure is a triangular prism with a triangular base with side lengths 3 cm, 4 cm, 5 cm. The height of the prism is 1 cm.
The sides measuring 3 cm and 4 cm form a right angle.
V = BH
where B = area of the base, and
H = height of the prism.
The base is a triangle, so B = (1/2)bh,
where b = base of the triangle, and
h = height of the triangle
V = (1/2)bhH
V = (1/2)(3 cm)(4 cm)(1 cm)
V = 6 cm³
Tonya has a 2-page story she wants to expand. She plans to write 3 pages per day until it is done. Which equation best represents the relationship?
Answers
Answer:
D. 60h = m
Step-by-step explanation:
A proportional equation that represents the relationship will be in the form of m = kh
Where,
Constant of proportionality = k = m/h
Using (2, 120),
k = 120/2
k = 60
Substitute k = 60 into m = kh
Thus:
m = 60h
This can also be written as 60h = m
PLEASE HELP ASAP
late assignment
Answers
Number line 1 is the number line for -8 < 4x - 8 < 8,
To solve the inequality -8 < 4x - 8 < 8, we can start by adding 8 to all parts of the inequality:
-8 + 8 < 4x - 8 + 8 < 8 + 8
This simplifies to:
0 < 4x < 16
Next, we divide all parts of the inequality by 4:
0/4 < 4x/4 < 16/4
Which further simplifies to:
0 < x < 4
Therefore, the solution to the inequality is x ∈ (0, 4). This represents all the numbers between 0 and 4 (excluding 0 and 4 themselves).
Thus, Number line 1 is the number line for -8 < 4x - 8 < 8,
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Cam can't figure what to eat. He is going to randomly select a piece of fruit from his pantry. These are 4 apples and 5 bananas in his pantry.
What is P( select and apple)?
Answers
Answer:
4/9
Step-by-step explanation:
Cam has 4 apples and 5 bananas he can choose from. This is a total of 4 + 5 = 9 pieces of fruit.
P(Selecting an apple) = # apples / Total # of choices = 4/9
Answer:
0.44
Step-by-step explanation:
P(select an apple)= 4/9 = 0.44
Khan Academy
What’s is ittttt I neeed helppp
Answers
Answer:
n = 14
Step-by-step explanation:
n+4/-2 = -9
n+4 = 18
n = 14
Answer:
n=14
Step-by-step explanation:
n+4/-2 = -9
n+4 = 18
Hope it helps :3
Note: If p(a) = 0 then (x - a) is a factor of p(x)
given that f(-1), f(-2) are zeros of f(x) find the missing values of these coefficients p, q
f(x) = x³ + px² - qx - 4
After finding the values of the coefficients factor and find the solutions of x1, x2 and x3.
Answers
Answer:
Since f(-1) = 0 and f(-2) = 0, we can set up two equations:
(-1)³ + p(-1)² - q(-1) - 4 = 0
(-2)³ + p(-2)² - q(-2) - 4 = 0
Simplifying each equation, we get:
-1 + p - q - 4 = 0
-8 + 4p - 2q - 4 = 0
Simplifying further, we get:
p - q = 5
2p - q = 6
Solving for p and q, we can add the two equations together to eliminate q:
p - q + 2p - q = 5 + 6
3p - 2q = 11
Then, we can substitute the value of q from the first equation into this equation to solve for p:
3p - 2(q + 5) = 11
3p - 2q - 10 = 11
3p - 2q = 21
3p - 2(5 + p) = 21
p - 10 = 7
p = 17
Substituting this value of p into either equation for q, we get:
q = p - 5 = 12
Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:
-1 | 1 17 -12 -4
|__ -1 -16 28
1 1 12
This gives us the factorization:
f(x) = (x + 1)(x² + x + 12)
To find the solutions, we can use the quadratic formula on the quadratic factor:
x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)
x = (-1 ± sqrt(1 - 48)) / 2
x = (-1 ± sqrt(-47)) / 2
x1 = (-1 + i(sqrt(47))) / 2
x2 = (-1 - i(sqrt(47))) / 2
Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.
Step-by-step explanation:
give me thanks for more! your welcome bud!
Alex and Lara have $21.00. each to spend at a book fair, where all students receive a 35% discount. They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax. To check if he has enough to purchase the book, Alex takes 35% of $28.50 and subtract that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount. Lara takes 65% of the normal purchase price and then computes 110% of the reduced price. Is Alex correct? Is Lara correct? Do they have enough money to purchase the book? explain your answer using complete sentences and show your work.
Answers
To begin, let's find how much the book is including tax and the student discount. Once we find this, we can see if Lara or Alex is correct and if they can afford it.
First, we want to compute the student discount. The student discount is 35%. Thus, we can do 0.65 x 28.50 = 18.525. With 10% tax, we have 18.525 x 1.1 = 20.3775. Which will round up to $20.38.
Now, lets see what Alex did and if he got the same answer. First he takes 35% of $28.50 and subtracts it from the normal price.
.35 x 28.50 = 9.975
28.50 - 9.975 = 18.525
Then he takes 10% of this number and adds it back.
.10 x 18.525 = 1.8525
18.525 + 1.8525 = 20.3775
Alex has the correct answer.
Next, we will see if Lara computed it correctly.
First she takes 65% of the normal price.
0.65 x 28.50 = 18.525
Then she computes 110% of the reduced price.
18.525 x 1.10 = 20.3775
Lara also gets the correct answer.
So, do they have enough money to purchase the book?
YES:
$20.38 < $21
Is Alex correct?
YES
Is Lara correct?
YES
Although they used different methods to get the answer, they both got the right one!
I need help quickly
Answers
Using L'hopital we can see that the limit is equal to 1/22
How to solve the limit?Here we want to take the limit of x tending to zero for x/sin(22x)
Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:
y = x
y' = 1
And for:
y = sin(22x)
y' = 22*cos(22x)
Now taking the limit we will get:
\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)
That is the value of the limit.
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Meredith drives 5 miles to the northeast, then 15 miles to the southeast, then 25 miles to the
southwest, then 35 miles to the northwest, and finally 20 miles to the northeast. How many miles is
Meredith from where she started?
Answers
Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.
Answers
a) The distance from point P to the pole is: 6.2 m
b) The height of the Pole is: 6.2 m
How to find the distance and height from angle of elevation?The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.
Now, we are given that:
The angle of elevation of the top of the pole = 45°
Angle of elevation of the top of the pole = 58°.
|PQ|= 10m
a) PR is distance from point P to the pole and using trigonometric ratios, gives us:
PR/sin 58 = 10/sin(180 - 58 - 45)
PR/sin 58 = 10/sin 77
PR = (10 * sin 58)/sin 77
PR = 8.7 m
b) P O can be calculated with trigonometric ratios as:
P O = PR * cos 45
P O = 8.7 * 0.7071
P O = 6.2 m
Now, the two sides of the isosceles triangle formed are equal and as such:
R O = P O
Thus, height of pole R O = 6.2 m
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2/3 of a cup of batter can make 5/6 of a batch of pancakes. How many cups of water are needed to make one batch of pancakes?
Answers
Answer:
1 11/12 cups of water
\((f) = ex + 6\)
use the chain rule and the oppropriate rule to differniate each following function
Answers
The differentiation of the given function f(x) = eˣ+6 is eˣ
What is differentiation?The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given is function f(x) = eˣ+6, we need to find the derivative of this function,
f(x) = eˣ+6
f'(x) = d / dx (eˣ+6)
= d(eˣ)/dx + d(6)/dx
Since, 6 is a constant and derivative of a constant is zero,
d(eˣ)/dx + d(6)/dx = d(eˣ)/dx + 0
Now, when we differentiate eˣ, we get eˣ itself,
Therefore,
d(eˣ)/dx = eˣ
Therefore, the differentiation of the given function f(x) = eˣ+6 is eˣ
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Find the volume for each figure and round to the nearest hundredth.
Answers
Answer:
9.V=480
10.V=25.1
11.V=377
12.V=160
13.V=179.6
14.V=452.4
Step-by-step explanation:
9.V=l*w*h
V=10*8*6
V=480
10.V=pi*1^2*8
V=8pi
V=25.1
11.V=1/3pi*6^2*10
V=1/3pi*36*10
V=1/3pi *360
V=120pi
V=377
12.V=l*w*h/3
V=10*8*6/3
V=480/3
V=160
13.V=4/3pi*3.5^3
V=4/3pi *42.875
V=171.5/3pi
V=179.6
14.V=2/3pi*6^3
V=2/3pi*216
V=432/3pi
V=144pi
V=452.4
Which of the following is the equation of the function f(x) graphed above? A. ƒ(x) = x(x − 2)²(x − 1)(x + 1) B. f(x) = (x - 2) (x − 1)(x + 1) c. f(x)= x(x - 2)²(x − 1)(x + 1) + 1)² D. f(x) = (x - 2)²(x - 1)(x - 1)^ E
Answers
Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 35 weekly reports showed a sample mean of 19.5 customer contacts per week. The population standard deviation was 5.2. Provide a 99% confidence interval for the population mean number of weekly customer contacts for the sales personnel.
Answers
Answer:
The answer is below
Step-by-step explanation:
Given that:
Confidence interval (C) = 99%, mean (μ) = 19.5, standard deviation (σ) = 5.2, sample size (n) = 35
α = 1 - C = 1 - 0.99 = 0.01
α/2 = 0.005
The z score of α/2 (0.005) is the same as the z score 0.495 (0.5 - 0.005) which is equal to 2.576.
The margin of error (E) is given as:
\(E=Z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n} } \\\\E=2.576*\frac{5.2}{\sqrt{35} } \\\\E=2.264\)
The confidence interval = (μ ± E) = (19.5 ± 2.264) = (17.236, 21.764).
The confidence interval is between 17.236 and 21.764.
My friend iis bumped and so am I. Question : graph the function described by the equation y = 2x − 2.
Answers
the graph of the equation y = 2 x - 2 is being obtained.
We are given the equation:
y = 2 x - 2
We need to make the graph of the equation.
We will first find some points on this equation:
x y
0 -2
1 0
2 2
3 4
4 6
5 8
Now, we will plot these points on the graph and join them with a dark line to obtain the graph of the equation y = 2 x - 2.
Therefore, the graph of the equation y = 2 x - 2 is being obtained.
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Suppose that the local tax rate is 6% and you purchase a car for $32,800. How much tax is paid?
Answers
Answer:
Before Tax Price: $32,800.00
Sale Tax: 6.00% or $1,968.00
After Tax Price: $34,768.00
Step-by-step explanation:
Take the precentage of tax and turn it into a decimalMultiply sales tax decimal with the purchased price (Purchase Price x Sales TaxGet your answerAnswer:
$1968
Step-by-step explanation:
Price of car= $32800
Tax= 6%= $32800*0.06= $1968
Suppose a life insurance company sells a
$280,000
1-year term life insurance policy to a
20-year-old
female for
$270.
According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is
0.999544.
Compute and interpret the expected value of this policy to the insurance company.
Answers
Answer:
$142.32, profit on sale of the policy
Step-by-step explanation:
You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.
CostThe insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...
0.000456 × $280,000 = $127.68
ProfitThe company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...
$270 -127.68 = $142.32
The expected value of the policy to the company is $142.32.
This represents its profit from sale of the policy.
__
Additional comment
Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."
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Please awnser asap I will brainlist
Answers
Answer:
True
Step-by-step explanation:
The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4\(\neq\)9, 1\(\neq\)9, 8\(\neq\)9, and 7\(\neq\)9 then 9 is not an element of this set and the statement is true.
A random sample of 41 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $19.55 per car. The population standard deviation is $6.33. Estimate the mean bill for all cars from the drive-thru with 97% confidence.
Answers
Answer:
\(19.55\pm2.145\)
Step-by-step explanation:
We use the equation \(\bar x\pm z^*\sigma/\sqrt n\), where \(\bar x=19.55\), \(\sigma=6.33\), \(n=41\), and \(z^*=2.17\). We obtain \(z^*\) from the z-score of a 0.97 confidence level.
The 97% confidence interval estimate for the mean bill for all cars from the drive-thru is approximately $17.23 to $21.87.
To estimate the mean bill for all cars from the drive-thru with 97% confidence, we can use a confidence interval.
Sample size (n) = 41
Sample mean (x(bar)) = $19.55
Population standard deviation (σ) = $6.33
To calculate the confidence interval, we'll use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
First, we need to calculate the standard error, which is the standard deviation of the sample mean.
Standard Error (SE) = Population Standard Deviation / √(Sample Size)
SE = $6.33 / √(41)
Next, we determine the critical value based on the desired confidence level. Since we want a 97% confidence interval, we need to find the critical value corresponding to a 97% confidence level.
The critical value can be obtained from a standard normal distribution table or by using a calculator. For a 97% confidence level, the critical value is approximately 2.17.
Now, we can calculate the confidence interval:
Confidence Interval = $19.55 ± (2.17 * SE)
Substituting the values:
Confidence Interval = $19.55 ± (2.17 * ($6.33 / √41))
Calculating this, we find:
Confidence Interval ≈ $19.55 ± $2.32
Therefore, the 97% confidence interval estimate for the mean bill for all cars from the drive-thru is approximately $17.23 to $21.87.
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8 feet per second in miles per hour
Answers
Answer:
5.45455
Step-by-step explanation:
Consider two points A(0,0) and B(1, 1) on a Cartesian plane. The equation of the axis of the segment AB is: A. y = 1 2 − B. y = 2 − C. y = 1 − 2 D. y = 1 − E. y = 1 − 2
Answers
So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.
What is slope?
In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.
The slope of the line passing through points A and B can be calculated as follows:
slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1
The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
To find the y-intercept, we can use point A (0,0) and substitute the slope value.
y = mx + b
0 = 1(0) + b
b = 0
Therefore, the equation of the line passing through points A and B is:
y = 1x + 0
Simplifying, we get:
y = x
So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:
y - 0 = 1(x - 0)
y = x
This confirms our earlier answer.
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1. A. What is the formula for the Pythagorean Theorem? (1 point)
B. Find the missing leg of the triangle using the Pythagorean Theorem. Remember that drawings may not be to scale (Round to the nearest tenth).
Show your work. (4 points)
20 ft
18 ft
x
Answers
Answer:
side 1^2 + side 2 ^2 = hypotenuse ^ 2
18^2 + 20^2 = hypotenuse^2
324 + 400 = 724
hypotenuse^2 = 724
hypotenuse = 26.9072480941474
hypotenuse = 26.9
Step-by-step explanation:
The distance between Morristown and Bellington is 4 inches on a map. If the scale on the map is 1 inch = 25 miles, what is the actual distance between the two towns?
Answers
Answer:
Step-by-step explanation:
Ms. Sue please help me, The distance between morristown and bellington is 4 inches on a map. If the scale on the map is 1 inch = 25 miles, what is the actual distance between the two towns?
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answers
Answer:
A
Step-by-step explanation:
A bag of marbles has 12 green marbles, 5 red marbles, 8 blue marbles and 7 yellow marbles. What is the probability of randomly selecting a blue marble?
Answers
Probability = # of desired options / # of total options
Our desired option is blue and there are 9 blue marbles in the bag.
There are 32 total marbles (options) in the bag.
P(blue) = 9 / 32 = 0.28125 = 28.125%
Hope this helps!
6 People fit comfortably in a 3 feet by 3 feet area. Use this value to estimate the size of a
crowd that is 7 yards deep and 18 feet long.
Answers
Answer:
252
Step-by-step explanation:
3*3=9
so 6 people can fit 9feet sqr
7yrd=21feet
21*18=378
378/9=42
42*6=252