Orly will produce 30/x cups of trail mix if she uses x cups of raisins as for every 10 cups of trail mix Orly mixes, she adds 3 cups of raisins.
what is unitary method ?Academic issues involving proportional relationships are typically solved using the unitary method. It entails first determining the significance of one unit, which may then be used to determine the value of a set of units, or the opposite. For instance, if the cost of one item is $5, increasing 10 by $5 would provide the cost of ten products, or $50. On the other hand, if the total price of 5 goods is $30, you may calculate the price of 1 item by taking $30 and dividing it by 5 to go and get $6. The unitary technique can be used to solve a broad variety of proportional issues, including those involving time, space, speed, and some other physical factors.
given
For every 10 cups of trail mix Orly mixes, she adds 3 cups of raisins.
If she uses x cups of raisins, we can build up a proportion to determine how many cups of trail mix she will produce:
3/10 = x/c
And c is the quantity of cups she will create for the trail mix.
To find c, we can cross-multiply:
10 * 3 = x * c
30 = x * c
c = 30/x
Orly will produce 30/x cups of trail mix if she uses x cups of raisins as for every 10 cups of trail mix Orly mixes, she adds 3 cups of raisins.
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In 2012, the population of a city was 5.51 million. The exponential growth rate was 3.82% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
helppppppp
Answer:
a) To find the exponential growth function, we can use the formula:
P(t) = P0 * e^(rt)
Where:
P(t) = the population at time t
P0 = the initial population (in this case, 5.51 million)
e = the mathematical constant e (approximately 2.71828)
r = the annual growth rate (in decimal form)
t = the number of years
Substituting the given values, we have:
P(t) = 5.51 * e^(0.0382t)
b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:
P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million
Therefore, the estimated population of the city in 2018 is approximately 6.93 million.
c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:
10 = 5.51 * e^(0.0382t)
e^(0.0382t) = 10/5.51
0.0382t = ln(10/5.51)
t ≈ 11.7 years
Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.
d) To find the doubling time, we can use the formula:
T = ln(2) / r
Where:
T = the doubling time
ln = the natural logarithm
2 = the factor by which the population grows (i.e., doubling)
r = the annual growth rate (in decimal form)
Substituting the given value of r, we have:
T = ln(2) / 0.0382 ≈ 18.1 years
Therefore, the doubling time for the population of the city is approximately 18.1 years.
The most important of the Shinto gods is the sun goddess who gave light to the world, named ______.
Amaterasu
Susanoo
Tsukyomi
Izanagi
Answer: Amaterasu
Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.
A partial table of nutrients and Daily Values (DVS)
based on a 2000-calorie diet is provided. The Sodium row and the Vitamin D row are completed, and each % of the DV is calculated.
Compare each amount with the amount on the given nutrition label. Now use the amount of
saturated fat on the nutrition label to calculate its
% of DV, X. Use the saturated fat amount on the nutrition label
to calculate the %DV for saturated fat.
Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
What is the explanation for the above response?To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.
From the label, we see that the serving size contains 3.5g of saturated fat.
To calculate the %DV for saturated fat, we use the equation:
%DV = (amount of nutrient per serving / DV) x 100%
Plugging in the values for saturated fat, we get:
%DV = (3.5g / 19g) x 100%
%DV = 0.1842 x 100%
%DV ≈ 18%
Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
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The table shows the age distribution of members of a gym. A member of gym is chosen at random. What is the probability that the person is: a) 21 or more b) 55 or less c) not in the 21 to 35 age group
The probability that the selected member is 21 or more is 88%.
The probability that the selected member is 55 or less is 86%.
The probability that the selected member is not in the 21 to 35 age group is 58%.
Finding probabilities:The basic probability formula of dividing the number of favorable outcomes by the total number of outcomes.
In this case, we are given the percentage of members in each age group, and we need to find the probability of selecting a member with a certain age range.
Here we have
The table shows the age distribution of members of a gym.
Age - Under 21 21 -35 36 - 55 Over 55
percentage 12 42 32 14
a) To find the probability that the selected member is 21 or more,
Add the percentage of members who are 21-35, 36-55, and over 55 since all of these age groups are 21 or more.
Probability (21 or more)
= Percentage (21-35) + Percentage (36-55) + Percentage (Over 55)
= 42% + 32% + 14%
= 88%
b) To find the probability that the selected member is 55 or less,
Add the percentage of members who are under 21, 21-35, and 36-55 since all of these age groups are 55 or less.
Probability (55 or less)
= Percentage (Under 21) + Percentage (21-35) + Percentage (36-55)
= 12% + 42% + 32%
= 86%
c) To find the probability that the selected member is not in the 21 to 35 age group,
Add the percentage of members who are under 21, 36-55, and over 55 since all of these age groups are not in the 21 to 35 age group.
Probability (not in the 21 to 35 age group)
= Percentage (Under 21) + Percentage (36-55) + Percentage (Over 55)
= 12% + 32% + 14%
= 58%
Therefore,
The probability that the selected member is 21 or more is 88%.
The probability that the selected member is 55 or less is 86%.
The probability that the selected member is not in the 21 to 35 age group is 58%.
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how did slugger mcfist get a black eye
Find any solution(s) (refer to attachment) of and select the correct statement.
A. The equation has no solution.
B. The equation has two solutions.
C. The equation has one solution.
D. The equation has one solution and one extraneous solution.
If a population of yeast cells grows from 5 to 160 in a period of five hours, what is the rate of growth
Answer:
The population of yeast cells is growing at a rate of approximately 46.41% per hour.
Step-by-step explanation:
To find the rate of growth of the yeast population, we can use the exponential growth formula:
P(t) = P₀ * e^(kt)
where P(t) is the population size at time t, P₀ is the initial population size, k is the growth rate constant, and t is the time elapsed.
In this case, the initial population size P₀ is 5, the final population size P(5) is 160, and the time elapsed t is 5 hours. We want to find the growth rate constant k.
Plugging in the values, we get:
160 = 5 * e^(5k)
Divide by 5:
32 = e^(5k)
Now, take the natural logarithm (ln) of both sides to isolate k:
ln(32) = ln(e^(5k))
Using the property that ln(a^b) = b * ln(a):
ln(32) = 5k * ln(e)
Since ln(e) = 1:
ln(32) = 5k
Now, divide by 5:
k = (ln(32)) / 5 ≈ 0.4641 (rounded to four decimal places)
So, the growth rate constant k is approximately 0.4641 per hour.
To express the rate of growth as a percentage, multiply the growth rate constant by 100:
0.4641 * 100 ≈ 46.41%
The population of yeast cells is growing at a rate of approximately 46.41% per hour.
The rate of growth of the yeast cells is 31 cells per hour.
Explanation:The rate of growth of the yeast cells can be calculated by finding the average rate of change in the population over the given time period.
In this case, the population increased from 5 to 160 in 5 hours, so the average rate of growth can be calculated as (160 - 5) / 5 = 31. The rate of growth of the yeast cells is 31 cells per hour.
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The mean starting salary for nurses is 67,694 dollars nationally. The standard deviation is approximately
10,333 dollars. Assume that the starting salary is normally distributed.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
a) State the random variable.
rv X a randomly selected nurse
b) Find the probability that a randomly selected nurse has a starting salary of 78371.8 dollars or more.
c) Find the probability that a randomly selected nurse has a starting salary of 91407.1 dollars or less.
d) Find the probability that a randomly selected nurse has a starting salary between 78371.8 and 91407.1
dollars.
e) Find the probability that randomly selected nurse has a starting salary that is at most 41861.5 dollars.
f) is a starting salary of 41861.5 dollars unusually low for a randomly selected nurse?
Why or why not?
Select an answer
g) What starting salary do 65% of all nurses have more than?
Round your answer to two decimal places in the first box.
Put the correct units in the second box.
Therefore, 65% of all nurses have a starting salary of more than $71,725.31.
Random variable: X, the starting salary of a randomly selected nurse.
b) P(X ≥ 78371.8) = 1 - P(X < 78371.8)
Using the Z-score formula:
z = (X - μ) / σ = (78371.8 - 67694) / 10333 ≈ 1.03
Looking up the probability in the standard normal table or using a calculator, we get:
P (Z ≥ 1.03) ≈ 0.1492
Therefore, P (X ≥ 78371.8) ≈ 0.1492.
c) P (X ≤ 91407.1)
Using the Z-score formula:
z = (X - μ) / σ = (91407.1 - 67694) / 10333 ≈ 2.30
Looking up the probability in the standard normal table or using a calculator, we get:
P(Z ≤ 2.30) ≈ 0.9893
Therefore, P (X ≤ 91407.1) ≈ 0.9893.
d) P (78371.8 < X < 91407.1) = P(X < 91407.1) - P(X < 78371.8)
Using the Z-score formula:
z1 = (78371.8 - 67694) / 10333 ≈ 1.03
z2 = (91407.1 - 67694) / 10333 ≈ 2.30
Looking up the probabilities in the standard normal table or using a calculator, we get:
P(Z < 1.03) ≈ 0.8498
P(Z < 2.30) ≈ 0.9893
Therefore, P (78371.8 < X < 91407.1) ≈ 0.9893 - 0.8498 ≈ 0.1395.
e) P (X ≤ 41861.5)
Using the Z-score formula:
z = (41861.5 - 67694) / 10333 ≈ -2.50
Looking up the probability in the standard normal table or using a calculator, we get:
P (Z ≤ -2.50) ≈ 0.0062
Therefore, P (X ≤ 41861.5) ≈ 0.0062.
f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse, because it is more than 3 standard deviations below the mean. A salary this low would be in the bottom 0.62% of all nurse salaries.
g) To find the starting salary that 65% of all nurses have more than, we need to find the z-score that corresponds to the 65th percentile, and then use the Z-score formula to solve for X.
Using a standard normal table or calculator, we find that the z-score corresponding to the 65th percentile is approximately 0.3853.
Using the Z-score formula:
z = (X - μ) / σ
Substituting μ = 67694, σ = 10333, and z = 0.3853, we get:
0.3853 = (X - 67694) / 10333
Solving for X, we get:
X = 10333(0.3853) + 67694 ≈ 71725.31
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Evaluate (2-5i)(p+q)(i) when p=2 and q=5i
Answer:
29i
Step-by-step explanation:
While multiplying complex numbers we should remember that i^2=−1.
As p=2 and q=5i,
(2−5i)(p+q)i
= (2−5i)(2+5i)i
= (2×2+2×5i−5i×2−5i×5i)×i
= (4+10i−10i−25×i2)×i
= (4+10i−10i−25×(−1))×i
= (4+25)×i
=29i
A pianist plans to play 3 pieces at a recital from her repertoire of 25 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?
There are 13,800 different recital programs possible.
What is permutation?
In mathematics, a permutation is an arrangement of objects in a specific order. In other words, a permutation is a way of selecting a certain number of objects from a larger set and arranging them in a particular order.
The pianist has 25 choices for the first piece, then 24 choices for the second piece (since one piece has already been played), and 23 choices for the third piece (since two pieces have already been played). Therefore, the number of different recital programs possible is:
25 x 24 x 23 = 13,800
There are 13,800 different recital programs possible.
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Part A Select the location of -2 and -9 on the number line. Select the places on the number line to plot the points. -10 20 10 Part B Use mathematical symbols to write an inequality that compares -2 and -9. Explain how the number line can be used to show that your inequality is correct. Enter your inequality and your explanation in the space provided. 109 10 - Math symbols + px C 1 1 0 ▷ Relations ▸ Geometry X . 00 1.1 0.8
It should be noted that to select the location of -2 and -9 on the number line, the steps are given below.
What are the steps?Draw a number line with zero in the center and a positive direction to the right and a negative direction to the left.
Find the position of -9 by counting 9 units to the left of zero on the number line. Mark this point with a dot or a cross.
Find the position of -2 by counting 2 units to the left of zero on the number line. Mark this point with a dot or a cross.
Label the points as -9 and -2 to indicate their values.
Your number line should now have two marked points at positions -9 and -2.
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What is the product of the binomials below? (d-1)(d+2)(d-3)
The product of the binomial (d-1)(d+2)(d-3) is d³-2d²-5d+6.
What are binomials?A binomial is an expression with two terms. For example 3x+4 is an example of binomial and also 3x²+3x is also an example of binomial.
To find the product of (d-1)(d+2)(d-3) , we multiply the three binomial together to give us a polynomial expression.
(d-1)(d+2) = d(d+2) -1( d+2)
= d²+2d-d-2
= d²+d-2
now solving (d²+d-2)(d-3)
= d( d²+d-2) -3(d²+d-2)
= d³+d²-2d-3d²-3d+6
collect like terms
= d³+d²-3d²-2d-3d+6
= d³-2d²-5d+6
therefore the product of (d-1)(d+2)(d-3) is d³-2d²-5d+6
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14. The local credit union is offering a special student checking account. The monthly cost of the account is $15. The first 10 checks are free, and each additional check costs $0.75. You search
the Internet and find a bank that offers a student checking account with no monthly charge. The first 10 checks are free, but each additional check costs $2.50.
a. Assume that you will be writing more than 10 checks a month. Let n represent the number of checks written in a month. Write a function rule for the cost c of each account in terms of n.
b. Write an inequality to determine what number of checks in the bank account would be more expensive than the credit union account.
c. Solve the inequality in part b.
Answer: a. c(n) = 15 + 0.75(n - 10)
b. 15 + 0.75(n - 10) = 2.50(n - 10)=
Simplifying and solving for n, we get:
n = 50
c. n > 50
Step-by-step explanation:
a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:
c(n) = 15 + 0.75(n - 10)
The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
The cost c of the bank account in terms of the number of checks written n can be expressed as:
c(n) = 2.50(n - 10)
The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:
15 + 0.75(n - 10) = 2.50(n - 10)
Simplifying and solving for n, we get:
n = 50
So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.
c. The solution to the inequality is:
n > 50
This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.
a. (10 points) The number of brownies sold by a bakery on a random day is a random variable with a mean value of 38 and a standard deviation of 6. What is the probability that the total number of brownies sold for a random sample of 56 days is less than 2070? Explain. b. (10 Points) Let X₁, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means µ4 7.4 pounds and μ₁ = 3.6, μ₂ = 0.9, µ3 = 1.8, μ4 µ2 variances o² = 0 = 0 = 0 = 1. Find P (2X₁ + 1X₂ + 3X3 + 1X4 ≤ 17.6). -
a. The probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.
b. The probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6
Explain probability
Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will definitely occur. Probability is a fundamental concept in mathematics and is used in many fields, including statistics, science, and finance.
According to the given information
a. The total number of brownies sold for a random sample of 56 days, Y, is a normal random variable with mean µ_Y = 56µ_X = 5638 = 2128 and standard deviation σ_Y = √(56)*σ_X = √(56)*6 = 25.21.
We want to find P(Y < 2070). Standardizing Y, we get:
Z = (Y - µ_Y) / σ_Y = (2070 - 2128) / 25.21 = -2.31
Using a standard normal distribution table or calculator, we can find that P(Z < -2.31) is approximately 0.0107. Therefore, the probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.
b. 2X₁ + X₂ + 3X₃ + X₄ is also a normal random variable with mean 2µ₁ + µ₂ + 3µ₃ + µ₄ = 2(3.6) + 0.9 + 3(1.8) + 7.4 = 18.5 and variance 4o² + o² + 9o² + o² = 14o².
We want to find P(2X₁ + X₂ + 3X₃ + X₄ ≤ 17.6). Standardizing the variable, we get:
Z = (17.6 - 18.5) / √(14o²) = -0.5735 / √(o²)
To find P(Z ≤ -0.5735 / √(o²)), we need to know the value of o². If o² = 1, then P(Z ≤ -0.5735) = 0.2831. If o² is a different value, we would need to adjust accordingly.
Therefore, the probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6
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Given this equation what is the value of x at the indicated point?(image)
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
The equation [tex]y=\frac{7}{2}x+3[/tex] tells us that, to find y, we must multiply x by [tex]\frac{7}{2}[/tex] and then add 3. Here, we are given the y value. We simply must plug in y and solve for x.
We are given: the equation [tex]y=\frac{7}{2}x+3[/tex], and [tex]y=-4[/tex]
So, we have:
[tex]y=\frac{7}{2}x+3 =\\\\-4 =\frac{7}{2}x+3[/tex]
Solve for the variable x.
[tex]-4=\frac{7}{2}x+3=\\\\\\-7 = \frac{7}{2}x =\\-14 = 7x=\\-2 = x[/tex]
Therefore, when y is equal to -4, x is equal to -2.
LOOK AT THE PHOTO PLS
The next entry on the long division would be 0.054, and 0.0054
How to perform long divisionLong division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:
Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.
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List the sample space for rolling a fair 12-sided die.
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
S = {1}
S = {12}
The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
What is sample space?Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.
In the given question,
The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.
Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.
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Determine the effective tax rate for a taxable income of $115,500. Round theginal answer to the nearest hundredth
A) 18.71%
B) 17.20%
C) 24.10%
D) 24.75%
The effective tax rate for a taxable income of $115,500 is A) 18.71%
How to calculate the taxThe introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).
Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,
= 18%
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From a group of 10 people, you randomly select 3 of them.
What is the probability that they are the 3 oldest people in the group?
Give your answer as a fraction
The probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.
What is fraction?
A fraction is a method of representing a part of a whole or a ratio of two numbers. It is a number that is written in the form of one integer (the numerator) over another integer (the denominator), separated by a line or slash.
The probability of selecting the 3 oldest people in a group of 10 people depends on the assumption that all 10 people are distinct individuals and that the selection process is truly random.
The total number of ways to select 3 people from a group of 10 people is given by the combination formula:
C(10, 3) = 10! / (3! * 7!) = 120
This means that there are 120 possible ways to select a group of 3 people from a group of 10 people.
Since we are interested in selecting the 3 oldest people, we assume that the 3 oldest people are identified and we only need to select them from the group of 10 people. There is only 1 way to select the 3 oldest people out of the group of 10 people.
Therefore, the probability of selecting the 3 oldest people in a group of 10 people is:
P = Number of ways to select the 3 oldest people / Total number of ways to select 3 people from a group of 10 people
P = 1 / 120
P = 0.0083
So, the probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.
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Naya has a pitcher that contains 3 cups of salted lassi, a yogurt drink with sait and sites. She pours 6 fluid ounces of lassi into each glass. If she uses all of the lassi, how many glasses does Naya use?
A. 2
B. 4
C. 16
D. 18
After 6 fluid ounces , Naya uses 4 glasses as a result.
Define ounces?A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce . A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce
In Naya's pitcher, there are three glasses of salted lassi.
She fills each glass with six fluid ounces of lassi.
By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.
8 fluid ounces make constitute a cup.
Consequently, 3 cups equal 24 fluid ounces (3 x 8).
24 divided by 6 results in:
4 glasses are equal to 24/6.
Naya uses four glasses as a result.
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I need help pleaseee
According to the factor form of the quadratic equation 4 · x² - 484, x = - 11 and x = 11 are the lesser x and the greater x of the expression.
How to determine the zeros of a quadratic equation
Herein we find a quadratic equation of the form a² · x² - b², whose factor form is introduced below by means of algebra properties:
a² · x² - b² = a² · (x² - b² / a²) = a² · (x - b / a) · (x + b / a)
Where - b /a is the lesser x and + b / a is the greater x.
If we know that a² = 4 and b² = 484, then the roots of the quadratic equation are:
4 · x² - 484 = 4 · (x - 11) · (x + 11)
The lesser x and the greater x are - 11 and 11, respectively.
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HELP RAAHHHH
1. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 4 feet with an intal upward velocity of 72 feet per second
The T-shirt is caught 42 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
2. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 3 feet with an intal upward velocity of 80 feet per second
The T-shirt is caught 36 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
Answer:
1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:
h(t) = -16t^2 + 72t + 4
To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:
t = -b/2a = -72/(2(-16)) = 2.25 seconds
To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):
h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet
The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.
2. Using the same kinematic equation as before, we have:
h(t) = -16t^2 + 80t + 3
To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:
t = -b/2a = -80/(2(-16)) = 2.5 seconds
To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):
h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet
The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.
Step-by-step explanation:
Problem 6: Find the surface area and round to the nearest tenth.
Therefore, the surface area of the prism is approximately 557.2 square feet when rounded to the nearest tenth.
What is surface area of prism?The surface area of a prism is the total area of all its faces, including the bases. The formula for finding the surface area of a prism depends on the shape of its base. For a right prism, the surface area can be found by adding the area of the two bases to the lateral area, which is the sum of the areas of all the rectangular faces of the prism.
Here,
To find the surface area of the prism, we need to find the area of each of the six rectangular faces that make up the prism, and then add them together. The two triangular faces are congruent, so we can find the area of one and double it to get the total area of the two.
The area of a triangle is given by:
Area = (1/2) x base x height
For the given triangles, the base is 9 ft and the height is 8 ft (for one triangle) and 10 ft (for the other triangle), so the areas are:
Area1 = (1/2) x 9 ft x 8 ft
= 36 ft²
Area2 = (1/2) x 9 ft x 10 ft
= 45 ft²
The total area of the two triangles is:
TotalArea = 2 x (Area1 + Area2)
= 2 x (36 ft² + 45 ft²)
= 162 ft²
Now, we need to find the area of the four rectangular faces. Each face is a rectangle with a length of 13 ft and a height of 7.6 ft, so the area of each face is:
AreaRect = length x height
= 13 ft x 7.6 ft
= 98.8 ft²
The total area of the four rectangular faces is:
TotalRectArea = 4 x AreaRect
= 4 x 98.8 ft²
= 395.2 ft²
To find the total surface area of the prism, we add the area of the two triangles to the area of the four rectangular faces:
TotalSA = TotalRectArea + TotalArea
= 395.2 ft² + 162 ft²
= 557.2 ft²
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Use the box plot showing the ages of those who watch the television show 'The Code" to answer the question that follows.
Which value is the best approximation for the range in ages for the middle 50% of viewers?
A) 10
B) 15
C) 20
D) 45
The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.
What is interqurtile range?The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.
What is Range?Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.
According to the given information:
A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).
To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.
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solve the equation for y
7y+2y=81
Before we begin we must know:
¿What is an equation?An equation is an algebraic equality in which letters (unknowns) with unknown value appear. The degree of an equation is given by the largest exponent of the unknown. To solve an equation is to determine the value or values of the unknowns that transform the equation into an identity.
Solving the equation, we will first add what is in the first, I mean:
[tex]\implies \sf 7y + 2y[/tex]Now we must convert to a fraction, first we will put the greater number on top and the smaller number below.
[tex] \boxed{ \sf y \implies \frac{81}{9} }[/tex]Now the last thing we should do is divide both numbers by nine (9), and we will have the following:
[tex] \boxed{ \sf y = \frac{81}{9} \implies 9}[/tex]∴ The result of our equation is y = 9
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how to solve 3(x+6) = x + 8 + x
the solution to the equation is x = -10.use the distributive property of multiplication over addition to simplify the left-hand side of the equation
what is distributive property ?
The distributive property is a mathematical property that is used to simplify expressions that involve multiplication and addition or subtraction. It states that when you multiply a number (or variable) by a sum or difference,
In the given question,
To solve the equation 3(x+6) = x + 8 + x, you can use the distributive property of multiplication over addition to simplify the left-hand side of the equation, and then combine like terms on both sides of the equation.
Here are the steps:
Distribute the 3 on the left-hand side of the equation:
3(x+6) = 3x + 18
Combine the two x terms on the right-hand side of the equation:
3x + 18 = 2x + 8
Subtract 2x from both sides of the equation:
3x - 2x + 18 = 2x - 2x + 8
Simplifying this expression gives:
x + 18 = 8
Finally, subtract 18 from both sides of the equation:
x + 18 - 18 = 8 - 18
Simplifying this expression gives:
x = -10
Therefore, the solution to the equation 3(x+6) = x + 8 + x is x = -10.
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The distance from Cory's home to the library is 2 6 mile. Which point is at 2 6 on the number line?
As a result, the point on the number line that represents 10 miles would be much more to the right and outside the bounds of the image.
What is the example's line number?The line number 10.12, for instance, refers to page 10, line 12. The part of the line number to the left of the period is referred to as the "page" or "part," and the part to the right is referred to as the "line."
What is number line defined simply?A number line is a representation of numbers along a straight line. It acts as a template for grouping and contrasting numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
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Question:
The distance from Cory's home to the library is mile. Which point is at on the number line?
A. Point A
B. Point B
C. Point C
D. Point D
In 1997, a city had a population of 230,000 people. Each year since, the population has grown by 6.3%.
Let t be the number of years since 1997. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
Answer:
y = 0.028t + 230,000 Step-by-step explanation: We know t = number of years since the start of the study y = be the city's population Each year the population
Step-by-step explanation:
5
The edge of a cube-shaped box measures 1 foot long. Three students each
made an observation about the box.
• Grace said that the perimeter of each face is 48 inches long.
• Maddy said that the area of each face is 144 square inches.
• Elena said that the volume of the box is 3 cubic feet.
Whose observations are correct?
A Grace, Maddy, and Elena
B Elena and Grace
C Grace and Maddy
D Elena and Maddy
The only observations that are correct are Grace's and Maddy's. The answer is Option C.
Whose observations are correct among Grace, Maddy and Elena?We can start by finding the perimeter, area, and volume of one face of the cube, and then see which observation is correct.
The perimeter of one face of the cube is 4 times the length of one edge, which is:
= 4 × 12 inches
= 48 inches. So Grace's observation is correct.
The area of one face of the cube is the length of one edge squared, which is:
= 12 inches × 12 inches
= 144 square inches. So Maddy's observation is also correct.
The volume of the cube is the length of one edge cubed, which is:
= 1 foot × 1 foot × 1 foot
= 1 cubic foot. So Elena's observation is not correct.
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Charlie invests $325 in an account that pays 8% simple interest for 15 years.
Use the simple interest formula, I = P ∙ r ∙ t, to answer the following questions.
How much interest will Charlie’s initial investment earn over the 15-year period?
How much money does Charlie have after the 15 years?
Answer: To answer these questions using the simple interest formula, we need to know the values of P (the principal or initial investment), r (the interest rate), and t (the time period in years).
In this case, P = $325, r = 0.08 (8% expressed as a decimal), and t = 15.
Using the simple interest formula, I = P ∙ r ∙ t, we can calculate:
I = $325 ∙ 0.08 ∙ 15 = $390
Therefore, Charlie's initial investment will earn $390 in interest over the 15-year period.
To calculate how much money Charlie will have after the 15 years, we need to add the interest earned to the initial investment.
The total amount of money that Charlie will have after the 15 years is:
Total amount = Initial investment + Interest earned
Total amount = $325 + $390
Total amount = $715
Therefore, Charlie will have $715 after 15 years.
Step-by-step explanation: