Answer:
H) 8, O) 3, W) 1------------------------------
GivenTotal players = 16,Wanted ketchup = 12,Wanted mustard = 7,Wanted ketchup and mustard = 4.Find the numbers of players who ...Wanted only ketchup = 12 - 4 = 8,Wanted only mustard = 7 - 4 = 3,Wanted neither ketchup nor mustard = 16 - (8 + 4 + 3) = 1Solve for x. Show your work, and give exact answers where possible. Otherwise, round to the nearest hundredth.
After solving the value of x is -1/6.
Given:
[tex]25^3^x^+^2[/tex] = 125
[tex]5^{2(3x+2)}[/tex] = [tex]5^3[/tex]
2(3x+2) = 3
6x + 4 = 3
6x = 3-4
6x = -1
divide by 6 on both sides
6x/6 = -1/6
x = -1/6.
Therefore after solving the value of x is -1/6.
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Use point-slope form to write the equation of a line that passes through the
point (20,-10) with slope 13/8.
Answer:
[tex]y+10=\frac{13}{8}(x-20)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
A and B are similar cuboids.
surface area of A: surface area of B = 16:2.
Work out
volume of A: volume of B
For the two similar cuboids A and B,
surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.
As given in the question,
Given : Two similar cuboids A and B,
Let x , y , and z be the length , width and height of cuboid A
And l, b, h be the length , width , and height of cuboid B.
As both the cuboids are similar their sides are in proportion.
k is the constant of proportionality then,
x= kl , y = kb, z = kh
Surface area of A : Surface area of B = 16 :2
⇒2k²(lb +bh +hl) : 2(lb +bh +hl) = 16 : 2
⇒k² = 16 :2
⇒k = 4 : √2
Now volume of A : Volume of B
= xyz : lbh
= k³lbh : lbh
= k³
=( 4 : √2)³
=64 : 2√2
= 64√2 : 4
= 16√2 : 1
Therefore, for the two similar cuboids A and B,
surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.
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Ana runs 3/4 in 6 minutes. Fill in the missing values in the table. Using
the table, find the constant of proportionality. Then write an equation to
represent this relationship. Lessons 2-3 7.AR.4.2
Answer:
In the first one you should write: 6, because the test tells you that in 6 minutes she runs 3/4miles.
So in 12 minutes she runs (3/4miles)*2. (basically 3/4 miles in the first 6 minutes, and other 3/4 miles in the remaining 6munutes).
So in the second space you can write 12, and on the right 2*(3/4), which is... (3/2).
To find the equation:
3/4 = 6
(3/4)*2= 6*2
so we know that in 1 minute we do 1/8miles, and now we have our formula. (1/8)*6=1*6
the formula is: y(miles) =(1/8)*x
in fact is x=6 minutes, y= (1/8)*6, so y=3/4.
What value is equivalent to (8+2) + (6 − 4) × 3?
Answer:
16
Step-by-step explanation:
(8+2) + (6 − 4) × 3
= 10+6
=16
30 POINTS AND WILL GIVE BRAINLIEST
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 41 minutes of calls is $19.26, and the remaining credit after 57 minutes of calls is $17.02. What is the remaining credit after 71 minutes of calls?
I really need help with the steps for this, thank you!!
Answer: The correct answer is $15.06 is remaining after 71 minutes
Step-by-step explanation:
What we need to find out:
The remaining credit after 71 minutes.What we know:
The remaining credit after 41 minutes of calls is $19.26The remaining credit after 57 minutes of calls is $17.02If we convert the minutes (m) and remaining credits (c) to (x,y) data sets, they would look like the following:
x y
41 19.26 (41, 19.26)
57 17.02 (57, 17.02)
Plugging the x, y values into a linear equation, we get:
y - 19.26 = (17.02 - 19.26) / (57 - 41) * (x-41)
Solve the equation for y by adding 19.26 to both sides:
y − 19.26 + 19.26 = −0.14x + 5.74 + 19.26
y = −0.14x + 25
Resulting standard slope-intercept format:
y = −0.14x + 25
Now plug in 71 for the x value (minutes):
y = (-0.14*71) + 25
y = 15.06
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Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|
B.1-41 <1-3/<13<|4|
C. 1211-51> |-7|>1-81
D. 1-41>19> |-31 >|-10|
In actuality, "absolute value" refers to thinking of all numbers as positive and removing all negative signs from front of them (or zero). Symbol for absolute value. -71<181<|9|<1-10| set of absolute values
Explain about the absolute values?Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0.
The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.
The exact distance of an integer or number from zero on a number line is its absolute value. As a result, the absolute value is never negative and is always positive.
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For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.
The types of variation and their constants are;
1) Direct variation with constant of variation as -1/4
2) Direct variation with constant of variation as ³/₂
How to Interpret Mathematical Variations?A variation is defined as a relation that exists between a set of values of one variable and then a set of values of other variables.
In variation, if the variables change proportionately that is they either increase together or decrease together, then they are said to vary directly.
1) We are given the equation;
4y = -x
Now, y is the output while x is the input and so we make y the subject to get; y = -¹/₄x
Now, writing the relationship between y and x as a variation, we will have; y ∝ x
For this to be equal, there has to be a constant of proportionality which means; y = kx
Comparing with our equation tells us that;
This is a direct variation with constant of variation as -1/4
2) We are given the equation;
3x = 2y - 7
Rearranging gives;
2y = 3x + 7
y = ³/₂x + 7
Now, the greater the value of x, the greater the value of y and as such this is also a direct variation with the constant of variation being 3/2.
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HELPP!!! Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
A business owner wants to have the front window of her store painted and is considering two artists for the job. Grace has quoted a flat rate of $99 for the job. Eva's quote is $10 per hour, plus $89 to cover the cost of materials. Depending on how long it takes Eva to paint the window, these two could end up charging the same amount. How much would it cost? How long would Eva have to take? You hav Vide
Answer:
The cost would be $99 with each artist if the job took Eva 1 hour
Step-by-step explanation:
99=10x+89
subtract 89 from both sides
10=10x
1=x
18
8. Carey bought a $2,100 computer system on the installment plan. He made a $400 down
payment, and he has to make monthly payments of $79.50 for the next two years. How much
interest will he pay?
Answer:
$208
Step-by-step explanation:
$79.50 x 24 = 1908
$1908 + 400 = 2308
$2100/2308 = 9%
Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.
What is Interest?Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.
Total number of monthly payments
= 12 months/year x 2 years
= 24 months
and, Monthly payment amount = $79.50
Total amount paid in monthly installments
= Monthly payment amount x Total number of monthly payments
= $79.50 x 24
= $1,908
Next, we can subtract the initial down payment from the total amount paid to find the interest paid:
Total interest paid = Total amount paid - Down payment
= $1,908 - $400
= $1,508
Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.
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jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjkjihhhhhhhhhhhm
Can someone please help me thank you
Answer:
9. 4/5
10. 3/4
11. 1/4
12. 1/8
13. 1/11
14. 1/9
15. 9/10
16. 1/10
Step-by-step explanation:
ur welcome
O Points: 0 of
A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients. After the study was concluded, it
medicine, 7 reacted unfavorably, and 2 were unaffected. If three of the patients are randomly selected, determine the probability that nor
If three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.
In the given question,
A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients.
After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected.
If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable.
Total patient are 24.
The patients reacted favorably to the medicine is 15.
The patients reacted unfavorably to the medicine is 7.
The patients unaffected to the medicine is 2.
Randomly selected patients are 3.
So the probability that none of the patients reacted favorable
P(E) = 9/24 × 8/23 × 7/22
Simplifying
P(E) = 9/3 × 1/23 × 7/22
P(E) = 3 × 1/23 × 7/22
P(E) = 21/506
Hence, if three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.
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The right question is
"A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients. After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected. If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable."
Approximately 72% of persons living in Cape Town who are aged 70 to 84 live in elderly care facilities. If four persons are randomly selected from this population, what is the probability that exactly two of the four live in elderly care facilities?
Select one:
The probability that exactly two of the four live in elderly care facilities is; 0.244
How to solve Binomial Probability Distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula of binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
where;
Px = the probability of exactly x events occurring.
x = the number of expected successful outcomes.
p is probability of success
n is sample size
We are given;
p = 72% = 0.72
n = 4
Thus;
P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)
P(X = 2) = 0.244
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Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
A car manufacturer's sales figures for 2000 to 2008 are shown in the table. Estimate the average rate of change in the number of cars the manufacturer sold between 2002 and 2006.
A.
450 cars per year
B.
225 cars per year
C.
2,900 cars per year
D.
600 cars per year
Answer: In photo below
You're Welcome :)
The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.
What is the average rate of change?The average rate of change shows the slope line over the stated interval.
We can find the average rate of change by dividing the change in y-values by the change in x-values.
Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
The total number of cars sold between 2002 and 2006 = 16,400
The number of cars sold in 2002 = 5,100
The number of cars sold in 2006 = 6,000
The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)
OR:
Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)
Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)
Total change in y-values = 900 (6,000 - 5,100)
Total change in x-values = 4 (2006 - 200)2
Average rate of change = 225 (900/4)
Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.
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Determine which integer(s) from the set S:{−24, 2, 20, 35} will make the inequality five sixths m minus five is less than one half m plus 3 false.
The integer in the set S:{−24, 2, 20, 35} that will make the inequality five-sixths m minus five is less than one-half m plus 3 false is 35
What is inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in inequality aren't always equal. Inequalities imply that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, based on the information we will replace m with 35. This will be illustrated thus:
= 5/6(35 - 5) < 1/2(35 + 3)
= 5/6(30) < 1/2(38)
= 25 < 19
In this case, 25 isn't less than 19. Therefore, 35 is the correct integer.
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A stock’s price fluctuations are approximately normally distributed with a mean of $26.94 and a standard deviation of $3.54. You decide to sell whenever the price reaches its highest 20% of values. What is the highest value you would still hold the stock?
The highest value you would still hold the stock is $23.97
How to determine the highest value you would stock??From the question, the given parameters about the distribution are
Mean value of the set of data = $26.94
Standard deviation value of the set of data = $3.54
Proportion = Highest 20%
This means that the p value is
p = 20%
Express as decimal
p = 0.2
At a p value of 0.2, the z-score is
z = -0.84
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
-0.84 = (x - 26.94)/3.54
Cross multiply in the above equation
So, we have
x - 26.94 = -0.84 * 3.54
Evaluate the products
x - 26.94 = -2.97
Add 26.94 to both sides of the equation
So, we have the following representation
x = 26.94 -2.97
Evaluate the difference
x = 23.97
Hence, the highest value is 23.97
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Math Q 3
A construction crew built 8 1/2 miles of road in 2 1/4 days.
Step-by-step explanation:
1/2 miles in 1/4 day (Given)
Find the distance of the road built in 1 day:
1/4 day = 1/2 miles
4/4 days 1/2 x 4 = 2 miles =
Answer: The rate is 2 miles per day.
the sum of two numbers is 33. the sum of 3 times the larger and 4 times the smaller is 107
The value of the larger number and the smaller number are 25 and 8 respectively.
What is Simultaneous Equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.
They are called simultaneous equations because the equations are solved at the same time.
If the bigger value is represented by x and the smaller value is represented by then
x+y= 33 equation 1
3x+ 4y= 107 equation 2
using Elimination method,
we multiply the coefficients of x by opposite equation
3x+3y=99 equation 3
3x+4y= 107 equation4
subtracting equation 3 from 4
y=107- 99
y= 8
substituting 8 for y in equation 1
x+8= 33
x= 33-8=25
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The weight of substance X is halved per minute. In the beginning, the weight of substance X is 5kg.
(a) Find the weight of substance X after 4 minutes.
(b) After how many minutes will the weight of substance X first go below 0.5kg?
Please give your answer as an integer.
EMERGENCY PLEASE HELPPPP
Answer:
a: 0.3125kg
b: 4
Step-by-step explanation:
for a we simply calculate 5 * 0.5 ^ 4.
we then see that the weight after 4 minutes is smaller than 0.5kg, but if we go back to 3 minutes (by multiplying our solution to a by 2), giving us 0.625kg, which is now bigger than 0.5kg. meaning 4 minutes is the first whole amount that will give us a weight smaller than 0.5kg.
Seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary. Find the measures of these three angles.
The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.
How to find angles of a decagon?A decagon is a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.
Therefore, seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary.
Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.
Therefore,
1440 - 1220 = 220
Let the angles be a, b and c.
Therefore,
a + b + c =220
a + b = 90
b + c = 180
Hence,
a = 220 - 180
a = 40°
b = 90 - 40
b = 50°
c = 180 - 50
c = 130°
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Do the measurements 15,17,22 make up a right triangle? Yes or no explain??
answer me fast
The measurements 15, 17, 22 do not form a right triangle.
In this question, we have the measurements 15, 17, 22
We check whether the measurements 15, 17, 22 is Pythagorean triple.
22^2 = 484
15^2 = 225
17^2 = 289
15^ + 17^2 = 225 + 289
= 514
≠ 484
i.e., 15^ + 17^2 ≠ 22^2
This means, these measurements do not form a right triangle.
Therefore, the measurements 15, 17, 22 do not form a right triangle.
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find the x-intercept of the line y=5/12x+1/6
Answer:
(-2/5,0)
Step-by-step explanation:
if y=0,
5/12 x + 1/6 = 0
5x + 2 = 0
x = -2/5
or, multiply by 6 to get the intercept form:
6y = 5/2 x + 1
-5/2 x + 6y = 1
x/(-2/5) + y/(1/6) = 1
Write the number in 2 equivalent
forms as a fraction, decimal, or
percent.
20
20
What is the equivalent percent?
Step-by-step explanation:
Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.
Pat randomly chooses marbles from an urn without replacement. The urn originally contained 55 red marbles, 30 white marbles, and 15 blue marbles. What is the probability that Pat’s second pick will be a blue marble given that the first pick was a red marble?
The probability that Pat’s second pick will be a blue marble is the fracion 5/3 considering choosing marbles without replacement.
Probability of an event without replacementProbability of an event without replacement simply means once an item is drawn, then we do not replace it back to the sample space before drawing a second item.
For the fact that a red marble was first drawn without replacement with the probability of 55/100, given that there are 55 red marbles and a total of 100 marbles in the Urn.
Hence, there will be 99 samples left for the second draw to be made.
The probability that the second pick will be a blue marble = 15/99.
Therefore, the probability that the second pick is a blue marble after the first pick without replacement is the fraction 5/33 reduced to its lowest term from 15/99.
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The blood types of 200 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type.
If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction
Blood Type Survey Results
Blood Type Number of Patients
A 45
B 65
O 75
AB 15
When a person from this group is selected at random, the probability that this person has type AB blood is 3/40
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:
= Number of AB blood type / Total number of people
= 15 / 200
= 3/40
The probability is 3/40.
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Find the equation in slope intercept
Answer:
y=-1/4x+4
Step-by-step explanation:
The graph starts on 4 so that is your y-intercept
Use slope formula to get the slop (y2-y1 over x2-x1)
Use 2 coordinates for formuls (In your case (0,4) and (4,3))
3-4=-1 4-0=4
slope is -1/4
y= -1/4x+4
I need answer help please
The value of the function f(a+4) is [tex]\frac{7}{a^{2} +8a+11}[/tex]
What is a function?function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable called the dependent variable.
if f(x) = [tex]\frac{7}{x^{2} - 5}[/tex], which means this equation is a function of x,
To find another equation whose function is f(a + 4)
We substitute x for a + 4 in the above equation
f(a+4) = [tex]\frac{7}{(a+4) ^{2} - 5 }[/tex]
expanding [tex](a + 4)^{2}[/tex], and simplifying the denominator, we have
[tex]a^{2}[/tex] +8a + 16 - 5 = [tex]a^{2}[/tex] + 8a + 11
so the simplified form of the new function would be [tex]\frac{7}{a^{2} +8a+11}[/tex]
In conclusion, the function f(a +4) = [tex]\frac{7}{a^{2} +8a+11}[/tex]
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When point F
is reflected in the line y = x, the image is located at F"(-7, 1).
The coordinates of F' when reflected in the line y=x is F'(1,-7)
Given:
When point F is reflected in the line y = x, the image is located at F"(-7, 1).
The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The point is on the line y = x. (y, x).
so the point F"(-7, 1) after reflection changes to:
F'(1,-7)
Hence we get the value of F' as (1,-7).
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Point-slope equation
y-6=3(x - 5)
y- 4 = -9(x+8)
y- 2 = 5x
Slope
-10
2
712
2
Point on
line
(1,4)
(5,-3)
(-7,-7)
The point slope equation and slope of some lines are given below
1) For y - 6 = 3(x - 5), slope = 3
2) For y - 4 = -9(x + 8), slope = -9
3) y - 2 = 5x, slope = 5
4) Point slope equation of line whose slope = -10 and passing through (1, 4)
y - 4 = -10(x - 1)
5) Point slope equation of line whose slope = 2 and passing through (5, -3)
y + 3 = 2(x - 5)
6) Point slope equation of line whose slope = [tex]\frac{1}{2}[/tex] and passing through (-7, -7)
[tex]y +7 = \frac{1}{2}(x +7)\\[/tex]
What is equation of line in point slope form?
The most general form of equation of line in point slope form is given by [tex]y - y_1 = m(x - x_1)[/tex] , [tex](x_1, y_1)[/tex] is a point on the line
Where m is the slope of the line
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
1) y - 6 = 3(x - 5)
y - 6 = 3x - 15
y = 3x - 15 + 6
y = 3x - 9
Slope = 3
If x = 0,
[tex]y = 3 \times 0 -9\\y = -9[/tex]
(0, -9) is a point on the line
2) y - 4 = -9(x + 8)
y - 4 = -9x - 72
y = -9x - 72 + 4
y = -9x - 68
Slope = -9
If x = 0
[tex]y = -9 \times 0 -68\\y = -68[/tex]
(0, -68) is a point on the line
3) y - 2 = 5x
y = 5x + 2
Slope = 5
Putting x = 0
[tex]y = 5 \times 0 + 2\\y = 2[/tex]
(0, 2) is a point on the line
4) Slope = - 10
The line passes through (1, 4)
Point slope equation
y - 4 = -10(x - 1)
5) Slope = 2
The line passes through (5, -3)
Point slope equation
y - (-3) = 2(x - 5)
y + 3 = 2(x - 5)
6) Slope = [tex]\frac{1}{2}[/tex]
The line passes through (5, -3)
Point slope equation
[tex]y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\[/tex]
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