Final Answer:
Pill 1 is more cost-effective, meeting or exceeding daily requirements for vitamins A, B1, and C with lower cost (30¢) compared to pill 2 (60¢). It provides 480 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C with fewer pills, making it the optimal choice.
Step-by-step explanation:
The patient's daily requirements are 420 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C. Let's evaluate the contribution of each pill to these requirements.
Pill 1 provides 120 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C.
Pill 2 provides 60 IU of vitamin A, 1 mg of vitamin B7, and 15 mg of vitamin C.
To meet the vitamin A requirement, the patient can take 4 pills of type 1 (4 * 120 IU = 480 IU), while it would take 7 pills of type 2 (7 * 60 IU = 420 IU). So, pill 1 is more efficient for meeting the vitamin A requirement.
For vitamin B1, both pills contribute 1 mg each, and since the requirement is 5 mg, the patient needs to take 5 pills of either type.
For vitamin C, the patient needs 60 mg. Pill 1 provides 10 mg per pill, so 6 pills are needed (6 * 10 mg = 60 mg). Pill 2 provides 15 mg per pill, so 4 pills are needed (4 * 15 mg = 60 mg).
Considering the cost, pill 1 costs 30¢, and pill 2 costs 60¢. Since both pills are equally effective in meeting the B1 requirement and pill 1 is more efficient for vitamin A and equally efficient for vitamin C, the patient should choose pill 1 due to its lower cost.
The red shape has been translated into the blue shape. The translation is
A) (x', y') = (x, y - 6)
B) (x', y') = (x - 6, y)
C) (x', y') = (x - 4, y - 4)
D) (x', y') = (x - 6, y - 6)
Flippin Middle School spends $11 for every workbook it buys. At most how many workbooks can Flippin Middle school buy if it has $44 to spend?
Answer:
4
Step-by-step explanation:
4 because 11x4=44
Flippin Middle School can buy at most 4 workbooks if it has $44 to spend.
To determine the maximum number of workbooks that Flippin Middle School can buy with $44, we need to divide the total amount of money available by the cost of each workbook.
Let's denote the number of workbooks that can be bought as [tex]\( W \)[/tex], and we know that each workbook costs $11. Therefore, the total cost for [tex]\( W \)[/tex] workbooks would be [tex]\( 11W \)[/tex].
Given that the school has $44 to spend, we can set up the following inequality to find the maximum number of workbooks that can be purchased:
[tex]\[ 11W \leq 44 \][/tex]
Now, we divide both sides of the inequality by 11 to solve for [tex]\( W \)[/tex]:
[tex]\[ W \leq \frac{44}{11} \][/tex]
[tex]\[ W \leq 4 \][/tex]
Since [tex]\( W \)[/tex] must be a whole number because one cannot buy a fraction of a workbook, the maximum number of workbooks that Flippin Middle School can buy is 4.
Is it rational or irrational
which of the following is a solution of the inequality y-5≥8
Answer:
See below
Step-by-step explanation:
Given: y-5≥8
Add 5 to both sides: y≥13
So any real number that is equal to 13 or above will be a solution for y.
Answer:
y>=13
Step-by-step explanation:
Let's solve the given question
y-5>=8
Add 5 to both sides
y>=8+5
y>=13
Note the >= will change only if that other side is negative
But since it is positive,it still remains
y>=13
write this polynomial in standard form- (5a+2)(a+4)
Answer:
5a²+22a+8
Step-by-step explanation:
(5a+2)(a+4)
5a² + 20a + 2a + 8
5a² + 22a + 8
Answer:
if minus is part of the question:
-(5a^2+22a+8)=-5a^2-22a-8
if not then:5a^2+22a+8____ a tip: make the question clear next time...good luck!
A circular playground for a daycare center is to be covered with square tiles that are 9 inches on each side. The circle has a
diameter of 12 ft. The tiles are packaged in boxes of 25 tiles. How many boxes of tiles are needed?
Answer:
9 boxes
Step-by-step explanation:
If the diameter is 12 ft then the radius is 6 ft
6ft=72 inches,Area of circle=pi*72^2,5184*pi square inches
Area covered by a box of tiles=9^2*25
number of boxes needed:5184*pi/81*25=8.0425 boxes
9 boxes.
Graphic DesignWorks employed three different salespeople last year. Person
1 earned $3500 in the first quarter, person 2 earned $7500 in the first quarter,
and person 3 earned $8000 in the first quarter. What are the maximum FUTA
deductions for the first quarter?
O
A. $217.00
O
B. $961.00
O
O
C. $1085.00
D. $1178.00
Answer:
$1085.00
Step-by-step explanation:
The maximum FUTA deductions for the first quarter is $1050.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
The Federal Unemployment Tax Act (FUTA) tax rate is 6% of the first $7,000 paid to each employee per year.
So,
For person 1:
The FUTA tax is 6% of $3500 = $210.
For person 2:
The FUTA tax is 6% of $7000 = $420
Since the FUTA tax is limited to $7000 of wages per employee per year.
For person 3:
The FUTA tax is 6% of $7000 = $420.
Since the FUTA tax is limited to $7000 of wages per employee per year.
The maximum FUTA deduction would be the sum of the FUTA tax for each employee.
= $210 + $420 + $420
= $1050.
Therefore,
The maximum FUTA deductions for the first quarter is $1050.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ5
What is the missing constant term in the perfect square that starts with x^2+10x
Answer:
25.
Step-by-step explanation:
If an expression is
[tex]x^2+bx[/tex]
then we have to add [tex](\frac{b}{2})^2[/tex], to make it perfect quare.
The given expression is
[tex]x^2+10x[/tex]
Here, b=10.
[tex](\frac{b}{2})^2=(\frac{10}{2})^2=5^2=25[/tex]
Now,
[tex]x^2+10x+25=x^2+2x(5)+5^2=(x+5)^2[/tex]
Therefore, we need to add 25 to make it perfect square.
put these fraction into ascending order: 1/5 4/5 7/10
1/5, 7/10, 4/5 you need to change the denomenator
Which formula can be used to find the nth term of the sequence 0.8, 0.72, 0.648
Answer: C
Step-by-step explanation:
Took the test
Answer:
an=0.8x0.9n-1
Step-by-step explanation:
Determine the explicit formula of the following sequence -3,-18,-108...
Answer:
[tex]a_{n}[/tex] = - 3[tex](6)^{n-1}[/tex]
Step-by-step explanation:
Note the common ratio r between consecutive terms, that is
r = - 18 ÷ - 3 = - 108 ÷ - 18 = 6
This indicates the sequence is geometric with n th term ( explicit formula )
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = - 3 and r = 6, thus
[tex]a_{n}[/tex] = - 3[tex](6)^{n-1}[/tex]
I WILL GIVE YOU A BARNLIEST BUT PLEASE PLEASE HELP
Mr. Lopez wrote the equation 32 g + 8 g minus 10 g = 150 on the board. Four students explained how to solve for g.
Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.”
Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.”
Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is 10 and StartFraction 5 Over 7 EndFraction.”
Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.”
Which student’s work is correct?
Alyssa
Rahul
Toni
Wilhem
Answer:
Wilhem is correct.
Answer:
wilhem
Step-by-step explanation:
What number goes on the blank? 2000, 400, 80, 16, _____ . What is the function?: linear, exponential, or neither. Write down the function expression for the sequence. It should be the form "y = ..."
Answer:
2000,400,80,16, = missing answer is 3.2
This is because everything on the linear
declines by dividing y by 5 for x = 3.2 * 5
so for rate of change = 5/3.2 = 1.56
An expression for y = y- 64 = 2 2 8 X - 63. (0,12)
or y = y-5 = - 3x -1
which = 3.2 -5 = -2.8 x 5 = -14
Step-by-step explanation:
9) A rectangular pencil box has internal dimensions of 2 cm by 4 cm by 9 cm. What is the length, to the nearest centimeter, of the longest pencil that will fit into the box?
A) 9 cm B) 11 cm C) 10 cm D) 12 cm
show work for brainlist
Write an expression to represent:
The sum of four and the product of three and a number x
Answer:
4 + 3x
Step-by-step explanation:
What is the length of the dotted line
Answer:
What dotted line. There is no dotted line on here my friend
Step-by-step explanation:
Nick wants to write
thank-you notes to 15 of
his friends. The cards
are sold in packs of 6.
How many does he need
to buy?
Answer:
Nick needs to buy 3 packs.
Step-by-step explanation:
If Nick buys 3 packs he will have 18 cards. If he uses 15 of them he will have 3 left over. If he only bought 2 packs he would be 3 cards short of the amount he really needed.
Answer:
Nick needs to buy 3 packs because if he buys 2 packs he'll have 12 cards which won't be enough. He will have an extra 3 cards remaining.
Place the four problem-solving steps in order.
Look back
Understand
Plan
Solve
SUBMIT
Answer:
understand plan solve look back submit das easy
Step-by-step explanation:
A triangle has a right angle and an acute angle of 51 degree's and X. What is X? (Number Only)
HELP ITS A TEST
Answer:
39°
sum of triangle's interior angles: 180°
180°-90°-51°=39°
What is the range of the function y=4e^x?
Answer:
All real numbers greater than 0
Step-by-step explanation:
A function assigns values. The range of the function will be all real numbers greater than 0.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As we can see in the function x can take up any value from -∞ to +∞. Although the value of eˣ will still be positive for any value of x.
Thus, the range of the function will be all real numbers greater than 0.
Learn more about Function:
https://brainly.com/question/5245372
What is the slope of the line that contains the points (-1,9) and (5,21)
Answer:
2
Step-by-step explanation:
slope of the line is the gradient (m):
m = y2-y1 / x2-x1
m = 21-9 / 5-(-1)
m = 12 / 6
m = 2
Answer:
The correct answer is D. 2
Step-by-step explanation:
I just got it correct.
The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller).
Answer:
(22, 9)
Step-by-step explanation:
The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller). I'll call the two integers a and b.
a - b = 13 a + b² = 103
+b +b
a = 13 + b plug this into the second equation
a + b² = 103
(13+b) + b² = 103 subtract 103 from both sides to get one side equal to zero
-103 -103
b² + b - 90 = 0 what factors (two numbers multiply) to -90 that also add up
to 1? The only two that work are -9 and 10.
(b-9)(b+10) = 0 so b-9 = 0 or b+10 = 0
+9 +9 or -10 -10
b = 9 or b = -10 but both numbers must be positive
b = 9 and a = 13 + b so a = 13 + 9 = 22
(22, 9)
The airline distance from Rome, Italy to Paris, France is 697 miles. The distance from Paris to Berlin,
Germany is 545 miles and the distance from Berlin to Rome is 734 miles. What is the angle formed from
Berlin to Paris to Rome?
Answer:
Angle Rome to Paris = 44.68°
Angle Paris to Berlin = 71.26°
Angle Berlin to Rome = 64.06
Step-by-step explanation:
See attachment for diagram illustration for this.
Let represent distance from Rome to Paris as a, distance from Paris to Berlin as b, and distance from Berlin to Rome as c.
Therefore we say
a = 697miles, b = 545miles, c = 734miles
To find the respectively angle formed from, Berlin to Paris to Rome, we will apply the cosine rule, which states that:
c² = a² + b² - 2abCosC
734² = 697² + 545² - 2(697*545)cosC
2(697*545)cosC = 697² + 545² - 734²
759739 cosC = 244078
cosC = 244078/759739
cosC = 0.3212
C = cos-¹0.3212
C = 71.26°
To get angle B, we will apply the sine rule, which states that:
a/sineA = b/sineB = c/sineC
Therefore we have
545/sineB = 734/sine71.26
= 545/sineB = 734/0.947
= 545/sineB = 734/0.947
= 545/sineB = 775.08
SineB = 545/775.08
B = sine-¹0.7032
B = 44.68°
Angle A = 180 - (B+C) angle in a triangle
A = 180 - (44.68 + 71.26)
A = 180 - 115.94
A = 64.06°
A = 64.06°
B = 44.68°
C = 71.26°
Angle Rome to Paris = 44.68°
Angle Paris to Berlin = 71.26°
Angle Berlin to Rome = 64.06°
Answer:
The Angle formed from Rome to Berlin(R)=44.68 degreesThe Angle formed from Paris to Berlin(P)=71.26 degreesThe Angle formed from Berlin to Paris(B)=64.06 degreesStep-by-step explanation:
The movement of the airplane can be represented using a triangle. In Triangle PRB, we are required to find Angles P, R and B.
Using Law of Cosines
[tex]cos R=\frac{p^2+b^2-r^2}{2pb} \\cos R=\frac{734^2+697^2-545^2}{2*734*697}\\R=arcCos\left(\frac{734^2+697^2-545^2}{2*734*697}\right)\\R=44.68^0[/tex]
Using law of Sines
[tex]\frac{r}{sin R}=\frac{p}{SIn P} \\\frac{545}{sin 44.68}=\frac{734}{Sin P} \\\text{Cross Multiply}\\545 X Sin P=734 X sin 44.68\\Sin P=\frac{734 X sin 44.68}{545} \\P=arcSin\left(\frac{734 X sin 44.68}{545}\right)\\P=71.26^0[/tex]
Now,
P+R+B=180 degrees (Sum of Angles in a Triangle)
[tex]71.26^0+44.68^0+B=180^0\\B=180^0-[71.26^0+44.68^0]\\B=64.06^0[/tex]
The Angle formed from Rome to Berlin(R)=44.68 degreesThe Angle formed from Paris to Berlin(P)=71.26 degreesThe Angle formed from Berlin to Paris(B)=64.06 degreesA scale drawing of a living room is shown below. The scale is 1 : 40.
Answer:
do u need help? where is the image?
Step-by-step explanation:
when typing a question, below is a circle with a plus button, this allows to add an article, picture or a document of your work that you need anything help with. hope this helps!
Ms. Sung budgets a maximum of $320 per month for groceries. She grocery shops 4 times a month. Which inequality can be used to find the possible values of x, the amount she can spend at the grocery store during each shopping trip?
Answer:
Less than or equal to $80
Step-by-step explanation:
If she get $320 a month and shops 4 times a month, you have to find the unit rate. This is so that you know the maximum amount of money she can spend.
320÷4=80
She can't go above $80, but she can spend any amount under $80. Than means the amount she can spend is less than or equal to $80.
The inequality that can be used to find the possible values of x is x≤80.
Maximum budget per month =$320
Number of times Ms Sung goes to a shop a month = 4
Amount spent on each shopping trip = x
What is inequality?Inequality is a statement that equates to two expressions.
So, the amount spent on 4 shopping trips = 4x
The maximum amount she can spend on all trips=$320
This means, [tex]4x\leq 320[/tex]
So, [tex]x\leq 80[/tex]
Hence, the inequality that can be used to find the possible values of x is x≤80.
To get more about inequality visit:
https://brainly.com/question/24372553
Y=3.2x+5 what is the answer for y
Answer:
Step-by-step explanation:
Y = 3.2x + 5 is a linear function with slope 3.2 and y-intercept 5.
For any x value you choose to substitute for x, you'll obtain a unique y value. For example, if we were to substitute -3 for x, we'd get:
f(-3) = y = 3.2(-3) + 5, or y = -9.6 + 5 = -4.6
There is only one y result for each choice of x.
Y=3.2x+5 alone does not have an "answer." Again: You must pick your own x values and for each such value you must calculate y.
The value of a car in each of its first 3 years is: $24,000, $18,000, $13,500. These amounts form a sequence. Which of the following statements best describe this sequence?
Geometric with a common ratio of approximately 1.33
Geometric with a common ratio of 0.75
Arithmetic with a common difference of $6000
Neither arithmetic or geometric
Answer:
The second one
Step-by-step explanation:
Are the ratios 19:15 and 4:3 equivalent?
yes
no
Answer:
No
Step-by-step explanation:
The ratio 19:15 is equivalent to 19/15
19/15=1.26666
The ratio 4:3 is equivalent to 4/3
4/3=1.33333
1.26666 is not equal to 1.3333, so the ratios are not equivalent
Hope this helps! :)
Answer:
no
Step-by-step explanation:
cross multiply to check
19/15 and 4/3
multiply 19 x 3=57
multiply 4 x 15=60
since 57 and 60 aren't equal to each other then the ratios aren't equivalent
How many different ways can 7 people sit in seats labeled A – G? *
1 point
7 ways
5040 ways
14 ways
720 ways
The seats are arranged in 5040 ways, if 7 people sit in seats labeled A, B, C, D, E, F, G.
Step-by-step explanation:
The given is,
7 people sit in seats labeled A, B, C, D, E, F, G.
Step: 1
No.of people = 7
No. of seats labeled = 7
Formula to calculate the number of ways to arrange,
[tex]P_{n} = n![/tex]...................................(1)
Where, n - Positive integer
Step: 2
From given, n = 7
Equation (1) becomes,
[tex]P_{7} = 7![/tex]
= 7 × 6 × 5 × 4 × 3 × 2 × 1
= 5040
= 5040 ways
Result:
The seats are arranged in 5040 ways, if 7 people sit in seats labeled A, B, C, D, E, F, G.
Which set of line segments could create a right triangle? (4 points)
Group of answer choices
5, 6, 11
5, 9, 10
5, 13, 18
5, 12, 13
Answer:
5,6,11
Step-by-step explanation:
Answer:
A 5, 6, 11
Step-by-step explanation: