Answer:
Step-by-step explanation:
The idea here is to be able to write and then solve the equation needed for this. In words, this is what you are looking to solve: "The active ingredinet is 45% of the mass of the pill". Putting those words into an equation:
active ingredient = .45 (mass of pill). Since our active ingredient is 35 mg:
325 = .45m and divide by .45:
m = 722.2 mg
A customer goes to a bank and gets change for a $100 bill. The change is to be in $1, $5, and $10 bills. There were four times as many $5 bills as $10 bills. If there are 25 bills in all, how many are $5 bills?
Answer:
12
Step-by-step explanation:
x = number of $1 bills
y = number of $5 bills
z = number of $10 bills
We know that:
x + y + z = 25 (total amount of bills)
x + 5y + 10z = 100 (total amount of money)
y = 4z (Given)
Substitute the third equation into the first one.
x + 4z + z = 25
x = 25 - 5z
Put this into the second equation.
(25 - 5z) + 5 (4z) + 10z = 100
Simplify and solve.
25 - 5z + 20z + 10z = 100
25z + 25 = 100
25z = 75
z = 3
Substitute this into y = 4z
y = 4 * 3
y = 12
So, there are 12 $5 bills.
Answer:
12 $5 bills
Step-by-step explanation:
Represent the number of each kind of bill by x, y and z: there are x $1 bills, y $5 bills and z $10 bills.
According to the problem statement,
x + y + z = 25 and y = 4z (or z = y/4). Also, the values of the bills add up to $100:
($1)x + ($5)y + ($10)z = $100. Eliminate z by typing y/4 in its place:
x + y + (y/4) = 25 and
x + 5y + 10(y/4) = 100
Doing this has reduced the number of variables to two: x and y. Combining like terms in both equations, we get:
1x + (5/4)y = 25 and
1x + (30/4)y =100
Subtracting the 1st equation from the 2nd, we get:
(25/4)y = 75, or
(4/25)(25/4)y = (4/25)(75) , or y = 12.
If y = 12, z = 12/4, or 3.
Then x + 12 + 3 = 25 coins in all; therefore, x = 15 = 25, and x = 10
There are 10-$1 bills, 12-$5 bills and 3-$10 bills.
Enter in the missing numbers to create equivalent ratios. HELPPPPPPPPPPPPPPPPPPPP
Select all number combinations that COULD make a triangle
4 cm, 5 cm, 7 cm
5 cm, 6 cm, 11 cm
2 cm, 9 cm, 10 cm
3cm, 4 cm, 10 cm
Answer:
2 cm, 9 cm, 10 cm
Step-by-step explanation:
To know if a combination is a triangle all you have to do is see if the combinations add up to 180
(2)(9)(10)=180 therefore it is a triangle.
All the other angles do not add up to 180 so they can't be triangles!!
(4)(10)(3) =120
(5)(6)(11) =330
(4)(5)(7) =140
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Answer:
A.
Step-by-step explanation:
It's the closest one to the answer, The answer I got is - 4;2
Pls help
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Answer:
d po yung answer
Step-by-step explanation:
sana makatulong
Need help like Right now
larry runs his heater when the temperature, t is no more than 70f
A- t<70
B- t>70
C t ≤ 70
D t ≥ 70
Answer:
its d i think bc i had that on my quizz
Step-by-step explanation:
slope of a line that goes through points (-8,0) and (0,6)
Answer:
3/4
Step-by-step explanation:
slope = rise / run
slope = ∆y/∆x
slope = (y2 - y1) / (x2 - x1)
slope = (6 - 0) / ( 0 - -8)
slope = 6/8
slope = 3/4
Kevin and Doreen each made a fruit salad. The amounts of ingredients they have are shown. Kevin used all of the strawberries, blueberries, and melon to make his fruit salad. Doreen made 2 cups of fruit salad containing all of the bananas, peaches and apples. How much fruit salad did Kevin make? How much more fruit salad did Doreen make than Kevin?
Answer:
The first thing you should do for this case is to graph the data you have in the statement to see the relationship between grapes and blueberries.
The function represented by the table is
y = 0.25x
Then, as Mandie is making 15 glasses of fruit salad, we have:
y + x = 15
We have two equations and two unknowns that we must solve.
y = 0.25x
y + x = 15
Resolving
For x:
0.25x + x = 15
1.25x = 15
x = 15 / 1.25 = 12
For y:
y = 0.25x = 0.25 (12) = 3
Answer
The ratio of grapes to blueberries she should use is 12: 3
A line that includes the point (1,8) has a gradient of 2. What is its equation in
gradient-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Submit
ere to search
O
acer
Answer:
y=2x+6
Step-by-step explanation: y=mx+b
substitute in known values y=2x+b gradient is 2 (given)
substitute in coordinate values (1,8) 8=2(1)+b
solve for B 8=2+b
-2 -2
6=b
therefore the answer is y=2x+6
Find the surface area of the cube.
5.5 yd
5.5 yd
5.5 yd
The surface area is
square yards.
HELPPPPPP
Answer:181.5
Step-by-step explanation:
5.5*5.5*6
multiply by six because there are six side
Suppose a call center receives 4000 calls on average during their Friday evening shift. Next Friday several people have put in for time off, so the center will be staffed by 178 call center employees. When working continuously, the average call center employee can handle 22 calls per evening shift (with a standard deviation of 5 calls). Assuming the center receives its expected 4000 calls next Friday, what is the probability that the center will have enough employees to handle this call volume
Answer:
The probability that the center will have enough employees to handle this call volume is 0.2764
Step-by-step explanation:
Probability is defined as the ratio of favorable outcomes to the total number of outcomes.
Here the total mean expected number of outcomes=u = 4000
The favorable expected outcomes are = x= 22* 178= 3916
The standard deviation= σ= 5
The random variable X =178 has normal distribution with mean 4000/22 and standard deviation 5
So z= x-u/σ
Z= (3916-4000)/22/5
z= -0.764
From the table of areas under normal curve
P ( x= 3916)= P( -0.764 ≤ Z≤ 0)
P ( x= 3916)= 0.2764
The probability that the center will have enough employees to handle this call volume is 0.2764
large pies cost $5 and small pots cost $2. If $45 pies were sold for $120 how many small pies were sold
Answer:
I'm assuming that's supposed to just be 45, not $45
Step-by-step explanation:
35 small pies were sold
10 large pies = $50
35 small pies = $70
50 + 70 = 120
5x - 2y = 15
2x + 4y = 12
Select the solution to the system from the options below:
Answer:
7/2, 5/4
Step-by-step explanation:
Answer:
x = 7/2 and y = 5/4
Step-by-step explanation:
2(5x - 2y = 15)
2x + 4y = 12
10x - 4y = 30
2x + 4y = 12 (add)
-----------------
12x = 42
x = [tex]\frac{42}{12}[/tex] = [tex]\frac{7}{2}[/tex]
2x + 4y = 12 (subsitute)
2([tex]\frac{7}{2}[/tex]) + 4y = 12
7 + 4y = 12
4y = 5
y = [tex]\frac{5}{4}[/tex]
10
1 point
Solve the system of linear equations. Check your solution.
2x+y = 3
X-y= 3
Solution type your answer...
type your answer...
Answer:
x = 2, y = -1.
Step-by-step explanation:
2x + y = 3
x - y = 3
Adding the 2 equations eliminates y:
3x = 6
x = 2.
Substitute for x in the first equation:
2(2) + y = 3
y = 3 - 4
y = -1.
Check the results by substitution in equation 2:
2 - (-1)
= 2 + 1 = 3 .
Checks OK.
Solve for x in the triangle below. Round your answer to the nearest tenth. Help please
Step-by-step explanation:
sin theta =p/h
sin 42=x/13
0.66×13=x
x=8.69
stay safe healthy and happy.Help pls.......asap i have 2 minuets
Answer:
It would be 3 1/2!
Step-by-step explanation:
Because it is X by Y (Usually) AKA bottom row to side row so, it is in the middle of 3 and 4 so it would be 3 1/2!
Answer:
( 3, 3.5) or 3 1/2
Step-by-step explanation:
The cordinate is ( 3, 3.5) but if it has a fraction form like your question had all you want to do is convert 3.5 into a fraction. 3.5 into a fraction is 3 1/2 the 0.5 becomes 1/2 and the 3 is a 3. So the answer is 3 1/2 or ( 3, 3.5).
If the band sells 100 series A ticket and 13000 series B tickets they will earn $865000. Write an equation to represent this situation.
Answer:
100x + 13000y = 865000
Step-by-step explanation:
x = Series A price
y = Series B price
you buy rice at $0.71 a pound a batch requires 4 pounds or rice how much is one batch
Answer:
$2.84 for one batch
Step-by-step explanation:
$0.71 x 4 = $2.84
Answer:
$2.84 for one batch
Step-by-step explanation:
I know this how you ask? $0.71 x 4 = $2.84
HELP
What is the equation of the trend line in the scatter plot ?
Factor completely: 5x2 - 2x
what percent of 160 is 56?
Answer:
35%
Step-by-step explanation:
[tex] \frac{56}{160} = \frac{7}{20} = 0.35 = 35\%[/tex]
Write ONLY your numeric answer. You do not need the degree symbol.
B
E
310
D
с
Find mZDEC.
Answer:
118
Step-by-step explanation:
All angles inside a triangle add up to 180. D and C is the same. 31 x 2 = 62
180 - 62 = 118
The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 16 and 4, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a bell-shaped distribution. Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the distribution.
A) between 12 and 20 hours per week
B) between 8 and 24 hours per weelk
C) between4 and 28 hours per week
D) less than 12 and more than 20 hours per week
Answer:
B) between 8 and 24 hours per week
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 16, standard deviation of 4.
Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the distribution.
Within 2 standard deviations of the mean, so:
16 - 4*2 = 16 - 8 = 8 hours per week.
16 + 4*2 = 16 + 8 = 24 hours per week.
This means that the correcgt answer is given by option B.
Use what you know about triangles to classify this triangle.
a triangle with three equal angles and three equal sides
Question 1 options:
Acute isosceles triangle
Obtuse scalene triangle
Equiangular triangle
Obtuse isosceles triangle
Answer: C equilateral triangle
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
i did the test :)
plot 7/8 and 2 1/4 on a number line
The given fractions are plotted on number line as given below.
What is number line?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
The given fractions are 7/8 and [tex]2\frac{1}{4}[/tex].
To plot fractions on the number line, follow the steps given below:
Step 1: Draw a number line of a suitable length.
Step 2: If the given fraction is a proper fraction, then mark points 0 and 1 on the number line. Or, if it is an improper fraction, then first convert it into a mixed fraction, and then mark two integers between those the given fraction lies.
Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.
Step 4: Starting from the left point, count forward the number of parts shown by the numerator.
Step 5: Mark the point on the line.
Hence, the given fractions are plotted on number line as given below.
Learn more about the number line here:
https://brainly.com/question/13425491.
#SPJ2
Simplify the expression
6:3x4
Answer:
8
Step-by-step explanation:
6:3=2
six divided by three equals four (hence the ratio)
2*4=8
two times four equals eight.
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Answer:
Interest earned = $32.835
Step-by-step explanation:
Given the following data;
Principal = $275
Number of times = 0.5
Interest rate = 2.9% = 0.029
Time = 4 years
To find the interest earned, we would use the compound interest formula;
[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
A is the future value.
P is the principal or starting amount.
r is annual interest rate.
n is the number of times the interest is compounded in a year.
t is the number of years for the compound interest.
Substituting into the equation, we have;
[tex] A = 275(1 + \frac{0.029}{0.5})^{0.5*4}[/tex]
[tex] A = 275(1 + 0.058)^{2}[/tex]
[tex] A = 275(1.058)^{2}[/tex]
[tex] A = 275(1.1194)[/tex]
A = $307.835
Interest earned = 307.835 - 275
Interest earned = $32.835
Ten years ago, Scott bought a board game for $30. That board game has now increased it's value by 83%.
100
What would be the price of that game now?
Answer:54.9
Step-by-step explanation:
What is the value of x?
A) Impossible to determine
B)62°
C)56°
D)76°