Match each function formula with the corresponding transformation of the parent function y = –x 2 – 1. 1. y = –x2 – 1 Translated right by 1 unit 2. y = –(x – 1)2 – 1 Reflected across the x-axis 3. y = x2 + 1 Translated down by 1 unit 4. y = –x2 Reflected across the y-axis 5. y = –(x + 1)2 – 1 Translated left by 1 unit 6. y = –x2 – 2 Translated up by 1 unit
Answers
Answer:
1. f₁(x)=-x²+2x-2
2. f₂(x)=-x²+6x-10
3. f₃(x)=-x²-2
4. f₄(x)=-x²+10x-26
5. f₅(x)=-x²-2x-2
6. f₆(x)=-x²
Step-by-step explanation:
1. we have that f(x) is translated right by 1 unit , also
according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2
2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)
y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10
3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)
y+2 = -(x)² ⇒ y=-x²-2
4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)
y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26
5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)
y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2
6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)
y+0 = -(x+0)² ⇒ y=-x²
Related Questions
the area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height. What are the base and the height of the triangle
Answers
Answer: height = 10 feet
Base = 24 feet
Step-by-step explanation:
Let h represent the height of the triangular flower bed.
Let b represent the base of the triangular flower bed
The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
The area of a triangular flower bed in the park has an area of 120 square feet. This means that
1/2 × bh = 120
bh = 120 × 2
bh = 240- - - - - - - - - - - - - - - 1
The base is 4 feet longer than twice the height. This means that
b = 2h + 4
Substituting b = 2h + 4 into equation 1, it becomes
h(2h + 4) = 240
2h² + 4h = 240
2h² + 4h - 240 = 0
Dividing through by 2, it becomes
h² + 2h - 120 = 0
h² + 12h - 10h - 120 = 0
h(h + 12) - 10(h + 12) = 0
h - 10 = 0 or h + 12 = 0
h = 10 or h = - 12
Since the height cannot be negative, then h = 10
Substituting h = 10 into equation 1, it becomes
10b = 240
b = 240/10
y = 24
The answers are : (a) The height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet[/tex]. (b) The base [tex]\( b \)[/tex] of the triangular flower bed is [tex]24 \ feet[/tex]
Let's denote the height of the triangular flower bed as [tex]\( h \)[/tex] feet.
According to the problem, the base of the triangle is [tex]4\ feet[/tex] longer than twice the height. Therefore, the base [tex]\( b \)[/tex] can be expressed as:
[tex]\[ b = 2h + 4 \][/tex]
The formula for the area [tex]\( A \)[/tex] of a triangle is given by
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Given that the area [tex]\( A \)[/tex] of the triangular flower bed is [tex]120\ square\ feet[/tex], we can write the equation:
[tex]\[ \frac{1}{2} \times b \times h = 120 \][/tex]
Substituting [tex]\( b = 2h + 4 \)[/tex] into the area equation:
[tex]\[ \frac{1}{2} \times (2h + 4) \times h = 120 \][/tex]
Now, solve for [tex]\( h \)[/tex]
[tex]\[ (2h + 4) \times h = 240 \][/tex]
[tex]\[ 2h^2 + 4h = 240 \][/tex]
[tex]\[ 2h^2 + 4h - 240 = 0 \][/tex]
Divide the entire equation by [tex]2[/tex] to simplify:
[tex]\[ h^2 + 2h - 120 = 0 \][/tex]
Now, solve this quadratic equation using the quadratic formula, [tex]h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 2 \), and \( c = -120 \)[/tex]
[tex]\[ h = \frac{-2 \pm \sqrt{(2)^2 - 4 \times 1 \times (-120)}}{2 \times 1} \][/tex]
[tex]\[ h = \frac{-2 \pm \sqrt{4 + 480}}{2} \][/tex]
[tex]\[ h = \frac{-2 \pm \sqrt{484}}{2} \][/tex]
[tex]\[ h = \frac{-2 \pm 22}{2} \][/tex]
The solutions for [tex]\( h \)[/tex] are:
[tex]\[ h = \frac{20}{2} = 10 \][/tex]
[tex]\[ h = \frac{-24}{2} = -12 \][/tex]
So, the height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet.[/tex]
Now, calculate the base [tex]\( b \)[/tex]
[tex]\[ b = 2h + 4 \][/tex]
[tex]\[ b = 2 \times 10 + 4 \][/tex]
[tex]\[ b = 20 + 4 \][/tex]
[tex]\[ b = 24 \][/tex]
The complete Question is
The area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height.
a. What is the base of the triangle ?
b. What is the height of the triangle ?
Having some trouble with this...pls help (in fraction form)
Answers
Answer:
[tex]\frac{17}{6}[/tex] or [tex]2\frac{5}{6}[/tex]
Step-by-step explanation:
1.Find the Least Common Denominator (LCD)
LCD = 6
2.Make the denominators the same as the LCD.
[tex]2+\frac{1*3}{2*3} + \frac{1*2}{3*2}[/tex]
3.Simplify. Denominators are now the same
[tex]2+\frac{3}{6} + \frac{2}{6}[/tex]
4. Join the denominators
[tex]2+\frac{3+2}{6}[/tex]
5.Simplify
[tex]2\frac{5}{6}[/tex] = [tex]\frac{17}{6}[/tex]
Answer:
1 1/3
Step-by-step explanation:
Given function:
2y+xx= 1/3y= 1/2Rewrite:
2·1/2+1/3Find the solution:
[tex]2[/tex]·[tex]1/2=1[/tex] [tex]1+\frac{1}{3}=1\frac{1}{3}[/tex]Therefore, 2y+x=1 1/3..
HL Theorem
ASA Postulate
SSS Postulate
SAS Postulate
Answers
Answer:
HL theorem.
Step-by-step explanation:
This states that if the hypotenuse (H) and one leg (L) of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
Answer:
ASA Postulate
Step-by-step explanation:
[tex] In \:\triangle QTS \:\&\:\triangle SRQ\\\\
QT || SR\\\\
\angle QTS \cong \angle SRQ... (each\: 90°)\\\\
TS \cong QR.... (given) \\\\
\angle QST \cong \angle SQR.. (alternate\:\angle s) \\\\
\therefore \triangle QTS \cong \triangle SRQ\\.. (By \: ASA \: Postulate) [/tex]
RHS Postulate can also be applied to prove both the triangles as congruent.
The voters of the city passed an ordinance to increase their sales tax by ¼ percent. The proceeds of the sales tax are to be used for culture and recreation. In the governmental activities journal, how would the ¼ percent sales tax revenue be recorded?
Answers
Answer:
General Revenue Sales Tax
Step-by-step explanation:
The ¼ percent would be recorded as general revenue sales tax in government activities journal.
This is because the revenue from the tax are categorised as the revenues generated from payrolls (which are imposed on employers), income and profits taxes, social security contributions, taxes levied on goods and services.
Options:
Program Revenue-Culture and Recreation-Sales Tax.
Program Revenue-Culture and Recreation-Operating Grants and Contributions.
General Revenue-Sales Tax.
General Revenue-Culture and Recreation-Sales Tax.
Answer:
General Revenue - Sales Tax
Step-by-step explanation:
General revenue is the income that is generated by the state which may be used to serve any administrative purpose by the state, and tax revenue is the income that is generated by the state through taxation.
Since the sales tax is a way of generating income by the state, it should be recorded as sales tax under general revenue.
Please assist me with these story problems.
Answers
Answer:
4. 16
5. $88
6. $687.50
Step-by-step explanation:
4. Let n represent the number.
An expression representing the number multiplied by 0.9 and 6.3 subtracted from the product is ...
0.9n -6.3
We want that result to be 4.5, so we have the equation ...
0.9n -6.3 = 4.5
Since all of the coefficients are divisible by 0.9, we can divide by 0.9 to get ...
n -7 = 9
Adding 7 gives ...
n = 16
The number is 16.
_____
5. For a problem like this, I like to work it backward. If Craig got an extra $18, then everyone's share was $32 -18 = $14. That was the share from a 5-way split, so the amount the friends split evenly was 5×$14 = $70. The total they started with must have been $70 +18 = $88.
The amount they split unevenly was $88. The amount they split evenly, after setting aside $18 for Craig's parents, was $70.
__
It is a bit tricky to write one equation for the amount the friends started with before they did any splits. Call that amount A. Then after setting aside $18, they split (A-18) five ways. Each of those splits was then (A-18)/5. When the $18 was added to one of those, the result was the $32 that Craig got. So, we have ...
(A -18)/5 +18 = 32
and the solution process is similar to the "working backward" description above: subtract 18, multiply by 5, add back 18.
(A -18)/5 = 14
A -18 = 70
A = 88 . . . . . . . . the amount the friends split unevenly
_____
6. Let P represent the original price of the laptop. We're told the price after all of the discounts was 500, so we have ...
P -50 -(0.20P) = 500
0.80P = 550 . . . . . add 50, collect terms
P = 687.50 . . . . . . . divide by the coefficient of P
The original price was $687.50.
Can someone please explain this problem to me idk what I am doing wrong and can you draw the problem for me thanks
Answers
Answer:
you're not doing anything wrong
Step-by-step explanation:
In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.
__
Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.
As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.
__
This is a good one to discuss with your teacher.
Bonita Industries sells radios for $50 per unit. The fixed costs are $645000 and the variable costs are 60% of the selling price. As a result of new automated equipment, it is anticipated that fixed costs will increase by $215000 and variable costs will be 50% of the selling price. The new break-even point in units is:
Answers
Answer:
The new break even point in units = 34400 units
Step-by-step explanation:
Fixed cost ( F ) = $ 645000
Selling price ( s )= $ 50
Variable Cost ( v ) = [tex]\frac{60}{100}[/tex] × 50 = 30
Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F}{s - v}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{50 - 30}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{20}[/tex]
⇒ [tex]x_{BEP}[/tex] = 32250 units
Now the new fixed cost ( [tex]F_{1}[/tex] ) = $ 645000 + $ 215000 = $ 860000
Selling price ( s )= $ 50
Variable Cost ( v ) = [tex]\frac{50}{100}[/tex] × 50 = $ 25
Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F_{1} }{s - v}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{860000}{50 - 25}[/tex]
⇒ [tex]x_{BEP}[/tex] = 34400 units
Therefore, The new break even point in units = 34400 units
plz help i really need it
Answers
Answer:
y=\frac{1}{8}x+4
Step-by-step explanation:
first, we can quickly get rid of options 1 and 2, since the y-intercept is not -4, but +4.
this leaves us with options 3 and 4.
we can rule out option3, since the slope is not 4, but 1/8.
hope this helps :)
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage ofthe total variation that can be explained by the linear relationship between the two variables. r = 0.885 (x = weight of male, y = waist size of male)
Answers
Answer:
Step-by-step explanation:
The coefficient of determination = [tex]r^{2}[/tex] = [tex]0.885^{2}[/tex] = 0.7832
It means about 78% variation in waist size of males can be explained by their weight and about 23% can not be explained.
HRLP HELP HELP!!!!! nearest foot
Answers
The horizontal distance the plane has covered is 3940 feet
Explanation:
The plane makes an angle 10° with the ground when it took off from the field.
We need to find the horizontal distance the plane when it has flown 4000 feet.
The length of the hypotenuse is 4000 feet.
Let the horizontal distance be x.
We shall find the value of x using the cosine formula.
The formula is given by
[tex]cos \theta=\frac{adj}{hyp}[/tex]
Substituting the values, we have,
[tex]cos \ 10^{\circ}=\frac{x}{4000}[/tex]
Substituting the value for cos 10°, we get,
[tex]0.985=\frac{x}{4000}[/tex]
Multiplying both sides of the equation by 4000, we get,
[tex]0.985\times 4000=x[/tex]
Simplifying, we get,
[tex]3940=x[/tex]
Thus, the horizontal distance the plane has covered is 3940 feet
George is 3 time as old as chun. Chun is 1/2 as old as elizabeth. Waneta is 4/7 as old as elizabeth. Waneta is 8 years old. How many years old is george
Answers
Answer:
21 years old.
Step-by-step explanation:
Given:
Waneta is 8 years old
Waneta is 4/7 as old as Elizabeth.
Chun is 1/2 as old as Elizabeth.
George is 3 time as old as Chun.
Question asked:
How many years old is George ?
Solution:
Let age of Elizabeth = [tex]x[/tex] years
Waneta is 4/7 as old as Elizabeth. ( given )
Age of Waneta = [tex]\frac{4}{7} \ of \ Elizabeth[/tex]
[tex]8=\frac{4}{7} \times x\\\\8=\frac{4}{7}x[/tex]
By cross multiplication:
[tex]4x=56[/tex]
By dividing both sides by 4
[tex]x=14\\[/tex]
Age of Elizabeth = [tex]x[/tex] = 14 years
Chun is 1/2 as old as Elizabeth. ( given )
Age of Chun = [tex]\frac{1}{2} \ of \ Elizabeth\\[/tex]
= [tex]\frac{1}{2} \times14= 7\ years[/tex]
George is 3 time as old as Chun. ( given )
Age of George = [tex]3\ times \ of \ Chun\\[/tex]
[tex]=3\times7=21\ years[/tex]
Therefore, George is 21 years old.
i can't fail this class plz helppppppp
Which of the following are ordered pairs for the equation y = -1/3x - 6?
(0,-6) (3,-7) (-3,5)
(0,-6) (3,-7) (-3,-5)
(0,-6) (3,7) (-3,-5)
(0,6) (3,7) (-3,-5)
Answers
Answer:
2nd option (B)
Step-by-step explanation:
(0,-6) works
(3,-7) works
(-3,-5) works
This means the answer is B
An election with 8 candidates has a 2-stage voting process. In the first stage, voters choose 1 candidate from all 8 names on the ballot. The 3 candidates who receive the most votes in the first round will appear on the second ballot. Due to time constraints, a print shop must prepare ballots for the second ballot in advance of the first-stage results.
How many different ballots must the shop prepare?
Answers
Answer:
56
Step-by-step explanation:
8C3 = 56
On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0).
What is the range of the function on the graph?
all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to –3
Answers
Answer:
All numbers greater than or equal to -3.
Step-by-step explanation:
Just took the edge test.
Answer:
yeah. its d
Step-by-step explanation:
edge test 2020
Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four.
Answers
[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .
Step-by-step explanation:
We need to Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four. Which is equivalent to [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] :
[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex]
⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{44}[/tex]
⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{16(3)} - \sqrt{9(6)}[/tex]
⇒ [tex]7\sqrt{3}- 4\sqrt{6} + 4\sqrt{(3)} - 3\sqrt{(6)}[/tex]
⇒ [tex]11\sqrt{3}- 4\sqrt{6}- 3\sqrt{(6)}[/tex]
⇒ [tex]11\sqrt{3}- 7\sqrt{6}[/tex]
[tex]\sqrt{3} = 1.732 , \sqrt{6} = 2.449[/tex]
⇒ [tex]11(1.723)- 7(2.449)[/tex]
⇒ [tex]1.909[/tex]
Therefore, [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .
Answer:
11√3 - 7√6
Step-by-step explanation:
I took the test and got it right.
Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water. How many fluid ounces of soap should he use? (1 cup 5 8 fl oz)
Answers
Answer: 28 fl oz
Step-by-step explanation:
84 fl oz. = 10.5 cups of water
10.5/3=3.5*8=28
why 3.5 times 8 is to get the exact amount of fluid ounces
Answer: he would need 14 fluid ounces of concentrated soap.
Step-by-step explanation:
The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water.
1 cup = 8 fluid ounces
Converting 3 cups of water to fluid ounces, it becomes
3 cups = 3 × 8 = 24 fluid ounces
Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. This means that the amount of concentrated soap that he would use is
(84 × 4)/24 = 336/24 = 14 fluid ounces of concentrated soap
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places. A. 0.250 B. 0.994 C. 0.500 D. 0.006 Click to select your answer.
Answers
Answer:
(D) 0.006
Step-by-step explanation:
Total number of cards :52
Please note that, all cards have a the possibility of appearing 4 times.
Hence total possible number of a '2' is 4 cards and so it is also for a '10'
Having this Understanding, let's solve the question properly.
The probability that the FIRST CARD is 2 = 4/52
Probability that the second card without replacement is a 10 = 4 / 51
P( 1st two and 2nd four)
4/52 * 4/51 = 4/663
= 0.0060332
Rounding to 3 decimal places = 0.006
Find v × w if v = 3i + 8j – 6k and w = –4i – 2j – 3k.
Answers
Answer:
[tex]vXw =-36i+33j+26k[/tex]
Step-by-step explanation:
v = 3i + 8j – 6k
w = –4i – 2j – 3k
The cross product
[tex]v X w=\left|\begin{array}{ccc}i&j&k\\3&8&-6\\-4&-2&-3\end{array}\right|[/tex]
[tex]=i\left|\begin{array}{cc}8&-6\\-2&-3\end{array}\right|-j\left|\begin{array}{cc}3&-6\\-4&-3\end{array}\right|+k\left|\begin{array}{cc}3&8\\-4&-2\end{array}\right|\\[/tex]
[tex]=i(-24-12)-j(-9-24)+k(-6+32)\\vXw =-36i+33j+26k[/tex]
Factor the expression. 100k^3 – 75k^2 + 120k – 90
5(5k^2 + 6)(4k – 3)
(25k^2 – 6)(20k + 3)
5(5k^2 – 6)(4k + 3)
(5k^2 + 30)(4k – 15)
Answers
For this case we must factor the following expression:
[tex]100k ^ 3-75k ^ 2 + 120k-90[/tex]
We take common factor 5:
[tex]5 (20k ^ 3-15k ^ 2 + 24k-18) =[/tex]
We have two groups within the parentheses:
Group 1: [tex]20k ^ 3-15k ^ 2[/tex]
Group 2: [tex]24k-18[/tex]
We factor each group:
Group 1: [tex]6 (4k-3)[/tex]
Group 2: [tex]5k ^ 2 (4k-3)[/tex]
Rewriting we have:
[tex]5 (5k ^ 2 (4k-3) +6 (4k-3)) =\\5 ((5k ^ 2 + 6) (4k-3))[/tex]
Answer:
[tex]5 (5k ^ 2 + 6) (4k-3)[/tex]
plz dont skip me help me
In which quadrant would point (12, 18) be located?
Quadrant IV
Quadrant II
Quadrant I
Quadrant III
Answers
Answer:
it's Quadrant 1 because both of he cordnates
Step-by-step explanation:
Please help. And show how you got your answer so I know how to do it.
Answers
Answer:
9. (x, y) = (6√3, 3)
10. (x, y) = (14, 14√2)
11. (x, y) = (2√6, 3√2)
12. (x, y) = (6, 2)
Step-by-step explanation:
Because you have memorized a short table of trig functions, you know that the ratio of side lengths of a 30°-60°-90° triangle is 1 : √3 : 2, and the ratio of side lengths of a 45°-45°-90° triangle is 1 : 1 : √2.
In each case, we compare the given side ratios to the known ratios for the kind of triangle we have. Then we multiply the triangle ratios by a scale factor that makes the given number match the corresponding ratio value. Matching the other ratio values, we can determine the values of the variables.
__
9. Using the side ratios for the 30-60-90 triangle, you have
6 : x : y+9 = 1 : √3 : 2
Multiplied by 6, the ratios on the right are ...
6 : x : y+9 = 6 : 6√3 : 12
x = 6√3
y +9 = 12
y = 3
__
10. Using the side ratios for the 45-45-90 triangle:
14 : x : y = 1 : 1 : √2
Multiplying the ratios on the right by 14, we have ...
14 : x : y = 14 : 14 : 14√2
x = 14
y = 14√2
__
11. Again using the 30-60-90 ratios:
√6 : y : x = 1 : √3 : 2
Multiplying the ratios on the right by √6, we have ...
√6 : y : x = √6 : 3√2 : 2√6
y = 3√2
x = 2√6
__
12. Again, using the 45-45-90 ratios:
x : 3y : 6√2 = 1 : 1 : √2
Multiplying the ratios on the right by 6, we have ...
x : 3y : 6√2 = 6 : 6 : 6√2
x = 6
3y = 6
y = 2
Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses but cannot work more than 30 hours per week in order to attend classes. Write a system of inequalities that models this situation where p represents the hours he works at the pizzeria and b represents the hours he works at the bookstore.
Answers
Answer: The system of inequalities that models this situation are
p + b ≤ 30
12.5p + 9.5b ≥ 300
Step-by-step explanation:
Let p represent the number of hours he works at the pizzeria.
Let b represent the number of hours he works at the bookstore.
He cannot work more than 30 hours per week in order to attend classes. This means that
p + b ≤ 30
Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses. This means that
12.5p + 9.5b ≥ 300
School D has 880 boys to 200 girls The ratio of girls to all students is 5 to 27 22/27 of all students are boys idk how to get from 880 to 27 and do a proportion
Answers
Answer:
(i)Ratio of the Number of Girls in the School to the Total Population
=5:27
(ii)Ratio of the Number of Boys in the School to the Total Population=22:27
Step-by-step explanation:
Below is the steps on how the given ratio are derived
If the school has 880 boys and 200 girls
Total Population of the School=880+200=1080
Ratio of Girls to all Student is 5:27
Now, this is derived from this:
Ratio of the Number of Girls in the School to the Total Population
=200:1080[tex]=\frac{200}{1080} =\frac{5}{27}[/tex]
Which in reduced form is 5:27
You can do likewise for boys
Ratio of the Number of Boys in the School to the Total Population=880:1080[tex]=\frac{880}{1080} =\frac{22}{27}[/tex]
Which in reduced form is 22:27
Christopher's back yard is in the shape of a trapezoid. The bases of his back yard are 30 and 40 feet long. The area of his back yard is 525 square feet. Write and solve an equation to find the height of Christopher's back yard.
Answers
Answer:
15 feet
Step-by-step explanation:
525 = ½(30+40)h
525 = 35h
h = 525/35
h = 15 feet
2)
What are the relative minimum and relative maximum values over the interval -3,3] for
the function shown in the graph? (4 points)
Minimum:
Maximum:
Answers
Answer:
minimum: -9maximum: -6Step-by-step explanation:
For a point to be a relative extreme, there must be points on both sides that are not as extreme. That is, the ends of the interval may be extreme values, but do not qualify as relative extrema, since there are not points on both sides.
In the interval [-3, 3], the relative extrema are the turning points.
The relative minimum is at y = -9 on the y-axis.
The relative maxima are at y = -6, between 1 and 2 on either side of the y-axis.
Answer:
minimum: -9
maximum: -6
Step-by-step explanation:
Brenda invests $4500 in a savings account earning 5.5% interest compounded quarterly. What will the account balance be after 7 years?
Answers
Answer: The account balance will be $6596 after 7 years.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $4500
r = 5.5% = 5.5/100 = 0.055
n = 4 because it was compounded 4 times in a year.
t = 7 years
Therefore,.
A = 4500(1 + 0.055/4)^4 × 7
A = 4500(1 + 0.01375)^28
A = 4500(1.01375)^28
A = $6596
TRUE OR FALSE. if the slopes of two lines are negative reciprocals, the lines are perpendicular
Answers
Answer:
TRUE
Step-by-step explanation:
Kelly uses 8.7 paints of blue paint and white paint to paint her bedroom walls. 1 4 of this amount is blue paint, and the rest is white paint. How many paints of white paint did she use to paint her bedroom walls
Answers
Answer: she used 6.525 pints of white paint.
Step-by-step explanation:
Kelly uses 8.7 paints of blue paint and white paint to paint her bedroom walls. If 1/4 of this amount is blue paint, it means that the amount of blue paint that she used in painting her bedroom walls is
1/4 × 8.7 = 2.175 pints of blue paint.
Since the rest of the paint is white, it means that the pints of white paint that she used to paint her bedroom walls is
8.7 - 2.175 = 6.525 pints of white paint
Answer:
she uses 6.525 pints of paint
Step-by-step explanation:
An ice cream shop serves small and large scoops of ice cream. Each scoop is sphere-shaped. Each small scoop has a diameter of approximately 6 centimeters. Each large scoop has a diameter of approximately 10 centimeters What is the difference, in cubic centimeters, between a large scoop of ice cream and a small scoop of ice cream? Round your answer to the nearest tenth.
Answers
The difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.
Explanation:To find the difference in volume between a large scoop and a small scoop of ice cream, we need to calculate the volume of each scoop and then subtract the volume of the small scoop from the volume of the large scoop.
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Since the diameter of the small scoop is 6 cm, the radius is 3 cm. Plugging this into the formula, we get V = (4/3)π(3 cm)³. Evaluating this expression, we find that the volume of the small scoop is approximately 113.1 cm³.
Similarly, the diameter of the large scoop is 10 cm, so the radius is 5 cm. Using the same formula, we find that the volume of the large scoop is approximately 523.6 cm³.
To find the difference in volume, we subtract the volume of the small scoop from the volume of the large scoop: 523.6 cm³ - 113.1 cm³ = 410.5 cm³. Therefore, the difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.
Learn more about Volume here:https://brainly.com/question/21623450
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The final answer is 410.5 cubic centimeters.
1. Calculate the volume of a small scoop:
- Given the diameter of the small scoop, [tex]\( d_{\text{small}} = 6 \) cm[/tex].
- Radius of small scoop, [tex]\( r_{\text{small}} = \frac{d_{\text{small}}}{2} = \frac{6}{2} = 3 \)[/tex] cm.
- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \).[/tex]
- Substitute the radius into the volume formula: [tex]\( V_{\text{small}} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) \)[/tex].
- Calculate:
[tex]\( V_{\text{small}} = 36 \pi \)[/tex] cubic centimeters.
2. Calculate the volume of a large scoop:
- Given the diameter of the large scoop,[tex]\( d_{\text{large}} = 10 \) cm[/tex].
- Radius of large scoop, [tex]\( r_{\text{large}} = \frac{d_{\text{large}}}{2} = \frac{10}{2} = 5 \) cm[/tex].
- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].
- Substitute the radius into the volume formula:
[tex]\( V_{\text{large}} = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) \)[/tex].
- Calculate:
[tex]\( V_{\text{large}} = 166.7 \pi \)[/tex] cubic centimeters.
3. Find the difference:
- Difference in volume: [tex]\( V_{\text{large}} - V_{\text{small}} = 166.7 \pi - 36 \pi \)[/tex].
- Calculate: [tex]\( V_{\text{large}} - V_{\text{small}} = 130.7 \pi \)[/tex].
- Approximate [tex]\( \pi \)[/tex] to 3.14.
- [tex]\( 130.7 \times 3.14 = 410.498 \)[/tex].
- Rounded to the nearest tenth, the difference is approximately 410.5 cubic centimeters.
The idea in Exercise 3.51 generalizes to give a new formula for the expected value of any nonnegative integer-valued random variable. Show that if the random variable X takes only nonnegative integers as its values then E(X) = X[infinity] k=1 P(X ≥ k). This holds even when E(X) = [infinity], in which case the sum on the right-hand side is infinite. Hint. Write P(X ≥ k) as P[infinity] i=k P(X = i) in the sum, and then switch the order of the two summations.
Answers
Final answer:
The question asks to demonstrate that for a nonnegative integer-valued random variable X, the expected value E(X) equals the summation over all k of the probability P(X ≥ k). This is shown by expressing P(X ≥ k) as an infinite sum, switching the order of summation, and counting each probability P(X = i) exactly i times.
Explanation:
The student's question pertains to the calculation of the expected value (E(X)) of a nonnegative integer-valued random variable. Specifically, the question asks to show that for such a random variable X, the expected value can be expressed as E(X) = ∑₋∞ k=1 P(X ≥ k). To demonstrate this, we begin with the definition of expected value:
E(X) = μ = ∑ xP(x).
Next, we unpack P(X ≥ k) by writing it as an infinite sum of probabilities for all integers i starting from k:
P(X ≥ k) = ∑₋∞ i=k P(X = i).
To find the expected value, we consider the sum of all such probabilities over all k:
∑₋∞ k=1 P(X ≥ k) = ∑₋∞ k=1 ∑₋∞ i=k P(X = i).
We then switch the order of summation, so that we first sum over all possible values of i and then for each i, we sum over the corresponding k that contributes to P(X = i):
E(X) = ∑₋∞ i=1 P(X = i) ∑₉ i k=1.
By doing this, we count each P(X = i) exactly i times, which leads us to the initial definition of expected value, thus proving the given formula.