We have been given that Lucia is making invisibility potions. Each potion requires 2 eyes of newt. We are asked to find the number of invisibility potions that Lucia can make with 16 eyes of newt.
We will use proportions to find the number of potions that Lucia can make with 16 eyes of newt as:
[tex]\frac{\text{Invisibility potions}}{\text{Number of Newt eyes}}=\frac{1}{2}[/tex]
[tex]\frac{\text{Invisibility potions}}{16}=\frac{1}{2}[/tex]
[tex]\frac{\text{Invisibility potions}}{16}\times 16=\frac{1}{2}\times 16[/tex]
[tex]\text{Invisibility potions}=8[/tex]
Therefore, Lucia can make 8 invisibility potions with 16 eyes of newt.
Perry sells TVs at an electronics store. He makes a 15% commission for every TV he sells. How much would he have to sell a single TV for to make a $72 commission?
Answer:
$480
Step-by-step explanation:
Perry makes 15% commission for each TV he sells.
How much would he have to sell a TV to get $72
First of all, let's call the unknown variable x
So 15% of x= $72
Mathematically, this would be represented as 15/100 * x= 72
15/100x= 72
Breaking down further,
15/100 can be broken down to 3/20
3/20x= 72
So to find the value of x, we divide both sides by 3/20
x= 72 ÷ 3/20
x= 72 * 20/3 (using the law of indices)
x= 1440/3
x= $480 dollars.
So, Perry would have to sell a TV for $480 to make a $72 commission.
Alexis is knitting a blanket 6 meters long. Every 3 decimeter, she changes the color of the yarn to make stripes. How many stripes will the blanket have?
Answer:
There are 20 color strips in the blanket.
Step-by-step explanation:
We are given the following in the question:
Length of blanket = 6 meter
A new color strip is added every 3 decimetres
We have to find the number of color strips in the blanket.
1 decimetre = 0.1 meter
Number of color strips =
[tex]=\dfrac{\text{Length of blanket}}{\text{Color strip every 3 decimeter}}\\\\=\dfrac{6}{3\times 0.1}\\\\=20[/tex]
Thus, there are 20 color strips in the blanket.
The diagonal of a rectangle is 25 in. The width is 15 inches. What is the length
Answer:
a= 20
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
The diagonal is the hypotenuse and the length and width are the legs
a^2 + 15^2 =25^2
a^2 +225 = 625
Subtract 225 from each side
a^2+225-255=625-225
a^2 = 400
Take the square root of each side
sqrt(a^2) =sqrt(400)
a = 20
Megan's quiz scores for the quarter are 85%, 99%, 98%, and 87%. What would Megan have to score
on the fifth quiz to have an overall average of 93%?
Answer:
96%
because if you add all of them up then add 96 then divid by 5 you get 93 which is the average.
hope this helps :)
At the bulk food store, Stacey bought 7 pounds of nuts. She used 8 ounces of nuts in a recipe and then put the rest of the nuts into small bags to use for snacks. If each small bag contained 4 ounces of nuts, how many small bags of nuts did Stacey make
Stacey made 26 small bags of nuts.
To solve this problem, let's first convert all measurements to the same unit, ounces, so we can compare them easily.
Stacey bought 7 pounds of nuts. Since 1 pound is equal to 16 ounces, 7 pounds would be 7×16=112 ounces.
She used 8 ounces of nuts in a recipe.
So, the amount of nuts she had left after using them in the recipe would be 112−8=104 ounces.
Now, if each small bag contains 4 ounces of nuts, we can find out how many small bags she made by dividing the remaining nuts by the amount in each bag:
[tex]\begin{aligned}& \text { Number of small bags }=\frac{\text { Remaining nuts }}{\text { Nuts per bag }}=\frac{104 \text { ounces }}{4 \text { ounces per bag }} \\& =\frac{104}{4} \\& =26\end{aligned}[/tex]
So, Stacey made 26 small bags of nuts.
scientific notation for 778,330,000?
Answer:
7.7833 × 108
Step-by-step explanation:
Answer:
7.78×10∧8
Step-by-step explanation:
PLEASE ANSWER THIS QUICKLY!! I WILL GIVE BRAINLIEST!!!
The monthly demand for a company's sports caps varies directly as the amount spent on advertising and inversely as the square of the price per cap. At $15 per cap, when $2750 is spent each week on ads, the demand is 330 caps. When advertising is increased to $3250, what price yields a demand of 330 caps? (Round your answer to the nearest cent.)
I think it's $16.432 but I'm not sure.
The price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that at $15 per cap , $2750 is spent each week on ads , and demand is 330 caps.
So , we can find how much money earn if cost is $15 per cap.
As 330 is the demand , then total earning is :
= 330 × 15
= $ 4950
Out of this , $2750 is spent per week on ads. So , total profit is :
= 4950 - 2750
= $ 2200
Now , If advertising is increased to $3250 then , money more spent on ads is :
= 3250 - 2750
= 500
So , total earning will be :
= 3250 + 2200
= 5450
And price per cap for demand of 330 caps will be :
= 5450 ÷ 330
= 16.51 per cap
Therefore , the price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.
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A line with a slope of -2 passes through the point (4, 7).
What is an equation for this line in point-slope form? ( the brackets are blanks, fill in the blanks)
y - 7 = [ ] (x - [ ])
Answer:
y-7= -2 (x-4)
Step-by-step explanation:
We can use the point slope formula, since we have a point, and a slope
[tex]y-y_{1} =m(x-x_{1})[/tex]
m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point
We know -2 is the slope, 7 is the y coordinate, and 4 is the x coordinate, so we can substitute them in
y-7= -2 (x-4)
Since we don't need to solve, this is the answer. The first bracket is -2, and the second is 4
Point-slope form: y - y₁ = m(x - x₁)
(m is the slope, (x₁, y₁) is the point you are given that's on the line)
You know:
m = -2
(x₁, y₁) = (4, 7) So plug it into the equation
y - y₁ = m(x - x₁)
y - 7 = -2(x - 4)
[so the first bracket is -2, the second bracket is 4]
A bag contains 100 cubes that are black, yellow, and white. A student randomly selects a cube without looking and replaces it in the bag. If the student selected 9 black cubes, 4 yellow cubes, and 7 white cubes, which of the options below show a reasonable estimate for the total number of a certain cube in the bag? Select all that apply.
A) 45 black cubes
B) 20 yellow cubes
C) 70 white cubes
D) 90 black cubes
E) 35 white cubes
Answer:
The answer is..
A) 45 black cubes
B) 20 yellow cubes
E) 35 white cubes
Step-by-step explanation:
Final answer:
To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. The estimates for the total number of a certain cube in the bag are 45 black cubes and 20 yellow cubes.
Explanation:
To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. In this case, the proportion of black cubes to the total number of cubes is 9/20. So, if there are 100 cubes in total, we can estimate that there are approximately 45 black cubes in the bag. Similarly, the proportion of yellow cubes to the total number of cubes is 4/20, so we can estimate that there are approximately 20 yellow cubes in the bag. However, the proportion of white cubes to the total number of cubes is 7/20, which is less than the proportion of yellow cubes. Therefore, we cannot estimate that there are 70 white cubes in the bag. The estimates for the total number of a certain cube in the bag are A) 45 black cubes and B) 20 yellow cubes.
What’s the dependent probability of this?
"A spinner has an equal chance of landing on each of its six numbered regions. You spin twice. The first spin lands in region one and the second spin lands in region three"
i believe the answer is independant.
if i'm wrong, please tell me so i can fix my mistake =)
Final answer:
The probability of a spinner, with equal chances of landing on any of its six regions, landing on Region 1 first and then on Region 3 in a second spin is 1/36, reflecting independent events.
Explanation:
The question concerns the concept of dependent probability, which involves calculating the likelihood of a sequence of events where the outcome of one event affects the outcome of another.
Since the spinner has an equal chance of landing on each of its six numbered regions, the probability of the first spin landing in region one is 1/6.
However, the second spin is independent of the first, making the probability of landing in region three also 1/6. Since these are independent events, the combined probability of both events happening in sequence is the product of their probabilities, which is 1/6 x 1/6 = 1/36.
The time t required to empty a tank varies inversly as the rate r of pumping. If a pump can empty a tank in 35 min at the rate of 800kL per minute, how long will it atake the pump to empty the same tanks at the rate of 1400kL per minute?
Answer: It will take the pump 20 min
Step-by-step explanation: Please see the attachments below
Robin and Evelyn are playing a target game. The object
of the game is to get an object as close to the center as
possible. Each player's score is the number of
centimeters away from the center. Robin's mean is 107,
and Evelyn's mean is 138. Compare the means. Explain
what this comparison indicates in the context of the data.
Who is winning the game? Why?
Answer:
The mean is all the numbers added together divided by the number of numbers. Greater the numbers the greater the mean. Since the goal of the game is to have as few centimeters away as possible the lowest number (107 or Robin) is winning
Step-by-step explanation:
Answer:
Evelyn has the greater mean. It indicates that, on average, her objects landed farther away from the center than Robin’s. This difference means that Robin is winning the game.
Step-by-step explanation:
this is the answer on the curst platform
Lily goes to gym once every 8 days. Ann goes once every 12 days and Taylor comes once every 16 days. This Wednesday all of them were in the gym. How many days after this Wednesday will all of them meet at the gym again and what day of the week will it be?
Step-by-step explanation:
Lily goes to gym once every 8 days.
Such that she will visit on 8, 16 , 24, 32 , 40, 48th days
Ann goes once every 12 days
Such that she will visit on 12, 24, 36, 48, 60th days ....
Taylor comes once every 16 days
Such that she will visit on 16, 32, 48, 64th days....
Comparing the common days on which they will visit again after wednesday,
it will be after 48 days, (i.e) after 6 weeks and 5 days, it will be tuesday
Answer:
48 days
Step-by-step explanation:
LCM of 8, 12, 16 is 48.
136 / 286 Marks
78%
Daisy measured the heights of 20 plants.
The table gives some information about the heights (h in cm) of the plants.
Height of plants (h) Frequency
0< < 10
10 <n< 20
4
20 <h<30
30 <h <40
2
40 <h <50
50 <h < 60
3
|
By using the midpoints of each group, work out an estimate
for the mean height of a plant.
Will will
be
acer
The mean point of the each group can be calculated using midpoint and mean formula. The mean is sum of all the term divided by number of term.
The mean height of a plant is 30.5.
Given:
The height of plant and frequency is given in table.
Refer the attached table for the calculation of mid point and frequency of midpoint.
Now we have ,
[tex]\rm {Sum \:of\: frequencies} = 20[/tex]
[tex]{\rm Sum \:of\: frequency\: \times midpoint\: product} = 610[/tex]
Calculate the mean of height of a plant.
[tex]\rm Mean=\dfrac{610}{20}\\\rm Mean=30.5[/tex]
Thus, the mean height of a plant is 30.5.
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To estimate the mean height of 20 plants, using midpoints and frequencies, the calculation yields approximately 13.89 cm. This provides a representative value based on the distribution of heights within specified intervals.
To estimate the mean height of the plants using the midpoints of each group, we'll calculate the midpoints for each interval and then find the weighted average.
1. Midpoint for 0 < h < 10:
- Midpoint = (0 + 10)/2 = 5
2. Midpoint for 10 < h < 20:
- Midpoint = (10 + 20)/2 = 15
3. Midpoint for 20 < h < 30:
- Midpoint = (20 + 30)/2 = 25
4. Midpoint for 30 < h < 40:
- Midpoint = (30 + 40)/2 = 35
5. Midpoint for 40 < h < 50:
- Midpoint = (40 + 50)/2 = 45\)
6. Midpoint for 50 < h < 60:
- Midpoint = (50 + 60)/2 = 55
Now, calculate the weighted average using the frequencies:
[tex]\[ \text{Mean height} = \frac{\sum (\text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}} \]\[ \text{Mean height} = \frac{(5 \times 4) + (15 \times 2) + (25 \times 3) + (35 \times 0) + (45 \times 0) + (55 \times 0)}{4 + 2 + 3 + 0 + 0 + 0} \]\[ \text{Mean height} = \frac{20 + 30 + 75}{9} \]\[ \text{Mean height} = \frac{125}{9} \][/tex]
Therefore, the estimate for the mean height of a plant is approximately 13.89 cm.
help QUICK please and thank youuu :))
Step 1: Simplify both sides of the equation.
28 = −7 /2 x
Step 2: Flip the equation.
−7 /2 x = 28
Step 3: Multiply both sides by 2/(-7).
( 2 /−7 )*( −7 /2 x) = ( 2 /−7 )*(28)
x=−8
Answer:
x=−8
[tex]28 = - \frac{7}{2} x \\ x = 28 \div ( - \frac{7}{2} ) \\ x = 28 \times ( - \frac{ 2 }{7} ) \\ x = - 8[/tex]
Let's chek
[tex] - 8 \times ( - \frac{7}{2} ) = \frac{8 \times 7}{2} \\ = 28[/tex]
Answer:
[tex]x = - 8[/tex]
What is a possible measure of an angle that has a terminal side in Quadrant III and makes a 60degree angle with the x -axis
Answer:
[tex]240^\circ[/tex]
Step-by-step explanation:
See the attached picture. One possible angle measure is [tex]60^\circ+180^\circ=240^\circ[/tex]
The possible measure of an angle with terminal side in 3rd quadrant and making an angle of 60°with the X-axis is 240°.
What is the terminal side of an angle?When the vertex of an angle is at the origin and one ray is on the positive x-axis, it is said to be in standard position. The ray on the x-axis is known as the starting side, while the ray on the y-axis is known as the terminal side.
The question is shown in the figure below:
The angle made with X - axis = 60°
Angle is lying in 3rd quadrant
If we start moving in the anticlockwise direction then the measure of the total angle will be 180° + 60° = 240°.
Hence, the total angle for an angle lying in 3rd quadrant is 240°.
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A conical perfume bottle has a radius of 3.4 centimeters and a height of 4.8 centimeters . Using 3.14 for pi, approximately how much perfume can the bottle hold ?
Answer:
58.077 cubic cm
Step-by-step explanation:
Given that:
height : 4.8 cm radius: 3.4 cmAs we know that, the volume of a conical perfume bottle is as following:
V = (1/3) * π * r² * h
So perfume can the bottle hold is:
V = (1/3) * 3.14 * 3.4² * 4.8 = 58.077 cubic cm
Hope it will find you well
Answer:
[tex]V \approx 58.107\,cm^{3}[/tex]
Step-by-step explanation:
The volume of a cone is:
[tex]V = \frac{1}{3}\pi\cdot r^{2}\cdot h[/tex]
Where:
[tex]r[/tex] - Radius, in centimeters.
[tex]h[/tex] - Height, in centimeters.
The volume of liquid that bottle can hold is:
[tex]V = \frac{1}{3}\pi \cdot (3.4\,in)^{2}\cdot (4.8\,cm)[/tex]
[tex]V \approx 58.107\,cm^{3}[/tex]
a circle is centered on point B. Points a, c and d lie on its circumference.
if angle ADC measures 23°, what does angle ABC measure?
Answer:
[tex]m\angle ABC=46^o[/tex]
Step-by-step explanation:
step 1
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m\angle ADC=\frac{1}{2}(arc\ AC)[/tex]
we have
[tex]m\angle ADC=23^o[/tex]
so
[tex]23^o=\frac{1}{2}(arc\ AC)\\arc\ AC=46^o[/tex]
step 2
we know that
Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it
so
[tex]m\angle ABC=arc\ AC[/tex] ----> by central angle
therefore
[tex]m\angle ABC=46^o[/tex]
Solomon is 3D printing chess pieces. The table gives the amount of time needed to print certain numbers of
pieces.
Pieces
Print time (minutes)
16
32
128
512
What does 16 mean in this situation?
Answer:
A= It takes Solomon 16 minutes to print each chess piece.
Step-by-step explanation: Its the first one
The number 16 in this scenario signifies the amount of 3D printed chess pieces. The number indicates the quantity Solomon can print within a particular span of time.
Explanation:In this given context, 16 refers to the number of 3D printed chess pieces. This is a common type of mathematical problem dealing with ratios or rates. Here, the table suggests a ratio that compares the number of pieces printed to the time it takes to print them. Therefore, 16 essentially represents the quantity of chess pieces that Solomon can print using his 3D printer within a certain amount of time.
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Why x and 4x -10 are factors of the expression x(4x - 10)3 rather than terms of the expression.what are the terms of the factor 4x - 10?
Answer:
4x-10Step-by-step explanation:
A "term" is a (signed) number, variable, or product of numbers and variables, separated from other terms by + or - signs. That is, it is the largest such product that includes any given number or variable.
A "factor" is a piece of a product. It is multiplied by other factors to form a product. It can be a (signed) number or variable or some expression.
One way to think of it is that terms are delimited (separated) by + or - signs. Factors are delimited by × or / signs.
__
The terms of 4x -10 are "4x" and "-10".
_____
The sign typically goes with the term. That is, an expression is a sum of terms.
2/3=z/15 what is z?
Please help
Answer:
z=10 because 3x5=15 and you do the same to the other number.
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
To get from 3 to 15 you multiply by 5 so if you multiply 2 by 5 you get 10
2) A pharmacist has 60 ml of an 8% alcohol solution. How much water should be evaporated so that the solution that remains is 10% alcohol?
Answer:
let water evaporated be x ml
...
acid 8% ------60 ml
...
final quantity = 10% ----(60-x)
..
60*8 = 10(60-x)
480=600-10x
10x=600-480
10x= 120
/10
x=12 ml should be evaporated.
Step-by-step explanation:
(3x2 - 4x +8)+(-x2 – 2x – 8)
Hey there,
The question given is as follows:
(3x² - 4x + 8) + (-x² - 2x - 8)When we add polynomials we add like terms (e.x. we add 3x² with -x²) and combine the two to make one polynomial. When we add the two polynomials given above:
2x² - 6x + 0So our answer to the problem would be 2x² - 6x.
Hope I helped,
Amna
The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association
Answer:
The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Step-by-step explanation:
We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.
The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.
Let X = time for this event for boys in secondary school
SO, X ~ Normal([tex]\mu=460,\sigma^{2} =40^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 460 seconds
[tex]\sigma[/tex] = standard deviation = 40 seconds
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;
P(X > x) = 0.10 {where x is the required time which boy need to beat}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-460}{40}[/tex] ) = 0.10
P(Z > [tex]\frac{x-460}{40}[/tex] ) = 0.10
So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;
[tex]\frac{x-460}{40} =1.2816[/tex]
[tex]{x-460}{} =1.2816\times 40[/tex]
[tex]x[/tex] = 460 + 51.264 = 511.264 seconds
Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
30+30-2 hi brainly people and I
Answer:
58
Step-by-step explanation:
Order of operations.
Additions and subtractions, in the order they appear, from left to right.
30 + 30 - 2 =
= 60 - 2
= 58
What is the radius and diameter of the following circle?
7 cm
Diameter =
-
Answer:
Radius =
Diameter =
Answer:
Diameter = 7cm
Radius = 3.5cm
Step-by-step explanation:
The diameter is the distance across the circle; shown as 7cm.
The radius is half the distance of the diameter, or half the distance across the circle.
Answer:
Radius = 3.5
Diameter = 7
Step-by-step explanation:
Radius = half of diameter
Diameter is the 7 cm you see on the image.
D'Naisa mixed her favorite shade of orange paint. She had 111 gallon of orange paint and added 222 quarts of yellow paint and 333 pints of red paint. How many quarts of paint did D'Naisa mix?
Answer:
7.5 Quarts
Step-by-step explanation:
D'Naisa mixed the following:
1 gallon of orange paint2 quarts of yellow paint3 pints of red paint.We are to determine in total, the number of quarts of paint that she mixed. this is done by converting each of the volume to quart.
1 gallon of orange paint
1 gallon = 4 QuartsOrange Paint=4 Quarts3 pints of red paint.
1 pint =0.5 quart3 Pints =3 X 0.5 Quart=1.5 Quart of red paintTherefore,
Total Volume of Paint Mixed in quart= Volume of Orange+Yellow+Red
=4+2+1.5
=7.5 Quarts
There are about 31{,}500{,}00031,500,00031, comma, 500, comma, 000 seconds in a year.
Choose the best approximation of the number of seconds in a year.
The closest approximation to the number of seconds in a year is [tex]3\times10^7[/tex], which is option B.
There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. So, to find the number of seconds in a day, you would multiply these values together:
[tex]\[60 \text{ seconds/minute} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86,400 \text{ seconds/day}.\][/tex]
In a year, there are typically 365 days. So, to find the total number of seconds in a year, you would multiply the number of seconds in a day by the number of days in a year:
[tex]\[86,400 \text{ seconds/day} \times 365 \text{ days/year} = 31,536,000 \text{ seconds/year}.\][/tex]
Since [tex]\(31,536,000\)[/tex] is closest to [tex]\(3 \times 10^7\)[/tex], the best approximation among the given options is B) [tex]\(3 \times 10^7\).[/tex]
Complete Question:
There are about 31,500,000 seconds in a year ?
Choose the best approximation of the number of seconds in a year
A) 3x[tex]10^6[/tex]
B) [tex]\(3 \times 10^7\).[/tex]
A letter is selected from the word EXAMINATIONS. What is the probability that the letter selected is N?
Answer:
2/1
then simplify it
= 1/6
The probability of selecting the letter 'N' from the word EXAMINATIONS is 1/6 or approximately 16.67%.
The word EXAMINATIONS consists of 12 letters, and the letter 'N' appears twice in this word. The probability of selecting an 'N' from the word is calculated by dividing the number of occurrences of 'N' by the total number of letters in the word. Therefore, the probability is 2/12, which simplifies to 1/6.
To express this mathematically, the probability P of selecting 'N' from EXAMINATIONS is given by P = n/N, where n is the number of times the event 'selecting N' occurs, and N is the total number of possible outcomes (total letters in the word).
So, P = 2/12 = 1/6. Therefore, the probability of selecting 'N' is approximately 0.1667, or 16.67%.
find the missing side length
please help :)
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
So we know that triangle ABC and QRS are similar.
There is a theorem that states that corresponding sides of similar triangles are proportional.
This means that we can set up a proportion to find the missing side of the triangle.
3/7=6/n
Cross multiply.
3*n=7*6
3n=42
Divide both sides by 3.
n=14