The number of bacteria present at 5 hours is (b) 148.413
How can the number of bacteria present be described?From the question, we were given,
f(t) = eᵗ
Then f(t) = number of bacterials present at a particular time t.
f(5) = number of bacterial present at 5 hours
So, we have
f(5) = e⁵
f(5) = 148.413
Then this can be written in the whole number as 148 which implies that the second option is correct because using f(t) = eᵗ to describes the growth of a colony of bacteria will provide us with the answer
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 4 feet and a height of 18 feet. Container B has a radius of 5 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty. To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?
The percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.
What is volume of cylinder?[tex]V = r^2h[/tex] , where r is the radius of the cylinder's base, h is its height, and (pi) is a mathematical constant corresponding roughly to 3.14159, gives the volume of a cylinder.
To solve this problem, we need to calculate the volumes of the two containers and then determine how much of Container B is empty after the water from Container A is transferred to it.
The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex] , where r is the radius of the base and h is the height of the cylinder.
Container A has a radius of [tex]4[/tex] feet and a height of 18 feet, so its volume is:
[tex]V(A) = \pi (4^{2} )(18) = 288\pi[/tex] cubic feet
Container B has a radius of 5 feet and a height of 15 feet, so its volume is:
[tex]V(B) = \pi (5)^2(15) = 375\pi[/tex] cubic feet
When the water from Container A is transferred to Container B, the volume of water in Container B will be:
V(water in [tex]B) = V(A) = 288\pi[/tex] cubic feet
The total volume of Container B is 375π cubic feet, so the volume that is empty after the transfer is:
V(empty in [tex]B) = V(B) - V(water in B) = 375\pi - 288\pi = 87\pi[/tex] cubic feet
To find the percentage of Container B that is empty, we need to divide the volume that is empty by the total volume of Container B and then multiply by 100:
Percent empty [tex]= (V(empty in B) / V(B)) \times 100[/tex]
[tex]= (87\pi / 375\pi) \times 100[/tex]
[tex]= 23.2[/tex]%
Therefore, the percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.
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Please help me with this
There is higher variability of y with large values of x.
There is a non linear relation between x and y.
How to explain the variabilityWe observe from figure b that for lower values of x the residuals are negative and as the values of x increases the residuals become positive but are distributed very close to the zero line.
Again for the extremely high values of x the residuals become negative following a decreasing non linear trend. Hence, from the residual plot we can conclude that the relation between x and y is a non linear one. Hence, the correct option is fourth option i.e, There is a non linear relation between x and y.
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Models that represent z+9=14 ASAP
To represent z+9=14, we can start by subtracting 9 from both sides of the equation:
z + 9 - 9 = 14 - 9
Simplifying the left side of the equation gives:
z = 5
Therefore, the solution to the equation z+9=14 is z=5.
Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here.
Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6
Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21
Create and interpret a 98% confidence interval for the difference in the placebo and the new drug. (10 points)
A: The data provides convincing evidence, at α=0.02 level, that the glucose drug is effective in reducing mean glucose level.
B: The 98% confidence interval for the difference in mean reduction of glucose level between placebo and drug groups is 3.5 to 13.7 mg/dL, supporting the effectiveness of the glucose drug
A: To test whether the glucose drug is effective in producing a reduction in mean glucose level, we will use a two-sample t-test with equal variances assuming normality of the differences.
Let μA be the true mean reduction in glucose level for the placebo group and μB be the true mean reduction in glucose level for the glucose drug group. The null hypothesis is H0: μA - μB = 0, and the alternative hypothesis is Ha: μA - μB < 0
Using the given data, the sample mean reduction for the placebo group is 9.7 mg/dL and for the glucose drug group is 18.3 mg/dL. The pooled sample standard deviation is 8.064 mg/dL, and the t-statistic is calculated to be:
t = (xB - xA) / (sP × √(1/nA + 1/nB))
= (18.3 - 9.7) / (8.064 × √(1/10 + 1/10))
= 2.551
where xA and xB are the sample means, sP is the pooled sample standard deviation, and nA and nB are the sample sizes.
B: To create a 98% confidence interval for the difference in the placebo and the new drug, we will use the formula:
CI = (xB - xA) ± tα/2,sP × √(1/nA + 1/nB)
where xA and xB are the sample means, sP is the pooled sample standard deviation, nA and nB are the sample sizes, and tα/2,sP is the t-value corresponding to a 98% confidence level with 18 degrees of freedom.
Using the values from Part A, we have:
CI = (18.3 - 9.7) ± 2.101 × 8.064 × √(1/10 + 1/10)
= 8.6 ± 5.103
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The correct question is:
Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here.
Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6
Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21
Part A: Do the data provide convincing evidence, at the α = 0.02 level, that the glucose drug is effective in producing a reduction in mean glucose level?
Part B: Create and interpret a 98% confidence interval for the difference in the placebo and the new drug.
HELPPPPPPPPPP... please help i don't get this whatsoever and my teacher doesn't really help. i dont get none of it at all. please help asap !
Answer:
I can tell
Step-by-step explanation:
Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)
a ups dispatcher sends a delivery truck to 10 different locations. if the truck stops at each location only once, how many different routes are possible
Therefore, there are 3,628,800 different routes possible for the delivery truck to visit all 10 locations only once.
What is factorial notation?Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by an exclamation mark (!) placed after the number. Factorial notation is often used in combinatorics to calculate the number of possible permutations and combinations of a set of objects.
Here,
The number of different routes possible for the delivery truck can be calculated using factorial notation.
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
This simplifies to:
10! = 3,628,800
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help pls im failing 100 POINTS IF U HELP
Answer: 44%, 26%, less likely
Step-by-step explanation:
just do the math!!
Help please
Condense to a single logarithm is possible
In(6x^9)-In(x^2)
The logarithm expression can be simplified to:
In(6x^9)-In(x^2) =7·ln(6x)
How to write this as a single logarithm?There are some logarithm properties we can use here.
log(a) - log(b) = log(a/b)
log(a^n) = n*log(a)
(these obviously also apply to the natural logarithm)
Now let's look at our expression, it says that:
In(6x^9)-In(x^2)
Using the first rule, we can rewrite this as.
In(6x^9)-In(x^2) = ln(6x^9/x^2)
Now solving the quotient in the argument:
ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)
That is the expresison simplified.
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Marisol is making bracelets and rings to sell at a craft fair She plans to sell each bracelet for $6 and each ring for $8. The craft fair committee charges a $25 fee to sell at the fair, and it costs Marisol $2 to make a bracelet and $4 to make a ring. If Marisol wants to sell at least $600 in jewelry and spend less than $300 for supplies and the fee, which system of inequalities represents the situation? Let b represent the number of bracelets and r represent the number of rings.
The equation that represent the number of bracelets b and the number of rings r is 6b + 8r > 600 and 2b + 4r < 275, hence, option A is correct.
Let b represent the number of bracelets and r represent the number of rings that Marisol makes. Marisol plans to sell each bracelet for $6 and each ring for $8. So the amount she earns from selling bracelets is 6b and the amount she earns from selling rings is 8r.
The craft fair committee charges a $25 fee to sell at the fair. So Marisol's total earnings after paying the fee is 6b + 8r - 25. It costs Marisol $2 to make a bracelet and $4 to make a ring. So the total cost of making b bracelets and r rings is 2b + 4r. To make a profit, Marisol's earnings must be greater than her costs,
6b + 8r - 25 > 2b + 4r
Simplifying this inequality, we get,
4b + 4r > 25
We also know that Marisol wants to sell at least $600 in jewelry. This can be expressed as,
6b + 8r > 600
Finally, Marisol wants to spend less than $300 for supplies and the fee. This can be expressed as,
2b + 4r + 25 < 300
Simplifying this inequality, we get,
2b + 4r < 275
Therefore, the system of inequalities that represents the situation is,
6b + 8r > 600
4b + 4r > 25
2b + 4r < 275
where b represents the number of bracelets and r represents the number of rings that Marisol makes.
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The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
40 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A. Mean for both coffee shops because the data distribution is symmetric
B. Median for both coffee shops because the data distribution is not symmetric
C. Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
D. Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric
Why is the median better ?It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.
The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.
The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.
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Find f(−3), f(0) and f(1) for the following function.
f(x)=2x
Answer:
-6, 0, 2Step-by-step explanation:
f(x)=2x
note: putting anything in the f(x) parentheses replaces x in the function with that value
so,
f(-3) = 2(-3) = -6
f(0) = 2*0 = 0
f(2) = 2(2) = 4
Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, converse of the same-side interior angles theorem a is parallel to b, , converse of the same-side interior angles theorem a∥b, converse of the alternate interior angles theorem a is parallel to b, , converse of the alternate interior angles theorem a∥b, converse of the corresponding angles theorem a is parallel to b, , converse of the corresponding angles theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
The high school basketball team is selling donuts to raise money for the new uniforms. This team Mexico to sell at least $1000 in donuts. They are selling a half dozen box of donuts for eight dollars and a full dozen box of donuts for $12. They write the inequality 8X +12 Y is greater than or equal to 1000 to determine how many boxes they need to sell where X is the number of half dozen boxes and why is the number of four dozen boxes they sell which of the following solutions available in terms of the given context select all that apply.
The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
Understanding Word Problem in Solving MathsWe can derive an inequality from the problem statement which is:
8X + 12Y >= 1000
This inequality represents the amount of money the basketball team needs to raise by selling donuts.
X is the number of half dozen boxes sold
Y is the number of full dozen boxes sold.
To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:
If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:
8(50) + 12(50) = $400 + $600 = $1000
So this is a valid solution that meets the fundraising goal.
If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:
8(100) + 12(0) = $800
This is not enough to meet the fundraising goal, so it is not a valid solution.
If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:
8(0) + 12(100) = $1200
This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.
Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
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Use words to describe the relationship between the number of miles and each corresponding number of gallons.
10 gallons 300 miles.
The unit rate that relates the two quantities of distance and volume of gas is:
U = 30 miles per gallon.
How to describe this relation?To do so, we can find the unit rate.
This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.
Here we have the values:
10 gallons and 300 miles.
Then the unit rate is the quotient between these:
300miles/10 gallons = 30 miles per gallon
This says that with one gallon of gas you can travel 30 miles.
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(3d). Mary decided to open a uniform cleaning service at GTUC. When she started the business she had to purchase an Ironing Board for $15 and an Iron for $35. Also, she figured it would cost $1.25 in cleaning products for each uniform, so she decided she was going to charge $3.25 for cleaning and pressing one entire uniform i. Write a system of equations that would represent the above scenario. ii. How many uniforms does Mary have to clean in order to break even?
she needs to clean 15 uniforms to break even
Me González designed a ramp for his caras shown in the picture below
what is the volume of the ramp in cubic feet
The ramp has a volume capacity of around 37.5 cubic feet.
How to solveCalculating the volume of a triangular prism shaped ramp follows a specific formula. First, identify the shape and refer to the equation:
Volume = (1/2) * Base Area * Height
To begin, the base is always in a right-angled triangle form, where its area depends on its width denoted as W, and height noted specifically as H.
Based on these computations, knowing that its triangular base measures 5 feet at its length while taking its height equates 3 feet therefore assessing how much it covers can be found using:
Triangle Area = (1/2) * Base * Height
Substituting values into solving areas leads us to have an answer of over 7 square feet.
Next is computing the volume of the said triangular prism. Placing all given data results in the same formula:
Volume = (1/2) * Base Area * Height
With one-half of the product of both areas which resulted in 7.5 square feet and then multiplying the figure by 10 ft, this yields us an approximate volume of 37.5 cubic feet.
In conclusion, we have determined that the ramp has a volume capacity of around 37.5 cubic feet.
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Length (L) = 10 feet
Width (W) = 5 feet
Height (H) = 3 feet
Mr. González designed a ramp for his car with a length of 10 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the ramp in cubic feet?
for the first question the answer choice is 35, 45, 145, 155,
the second question is a true or false answer
for the first question answer is 35 , which we can clearly see its pointing 35 degree in the protractor .second question is incomplete
what is protractor ?
To measure an angle using a protractor instrument, follow these steps:
Place the protractor on the angle: Place the flat side of the protractor on one of the angle's sides, making sure that the vertex (the point where the two sides of the angle meet) is at the center of the protractor.Align the protractor with the angle: Make sure the protractor is aligned with the angle you want to measure. The zero-degree mark on
In the given question,
for the first question answer is 35 , which we can clearly see in the protractor
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Select the correct answer from each drop-down menu.
Consider the expression below.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.
What is like term?In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).
The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.
Simplifying the expression we het 10 x + 5.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.
2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.
3. If the expression is set equal to -10x + 5, there would be only one solution.
10x + 5 = -10x + 5
20x = 0
x = 0
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Drag-and-Drop Technology-Enhanced
An expression is shown.
14a +7+ 5b+ 2a + 10b
Move words into the columns to describe the parts of the expression. Not all words will be used, and each column should
have at least one word to describe it.
14a
sum
term
factor
7
5
product
quotient
coefficient
2a + 10b
The value of expression 14a +7+ 5b+ 2a + 10b will be 16a + 15b + 7
Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given the expression as;
14a +7+ 5b+ 2a + 10b
Combine like terms;
14a + 2a + 10b +7+ 5b
16a + 15b + 7
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A small country emits 80,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 2.5% per year for the next 7 years. In the first year of the agreement, the country will keep its emissions at 80,000 kilotons and the emissions will decrease 2.5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 7 year period, to the nearest whole number?
The total carbon dioxide emission over a period of 7 years will be 5,13,183 kilotons.
Considering the carbon emissions follow an exponential rate then
A(t)=A₀(1-r)^t
where A₀ is the initial value, and r is the decay rate as a decimal.
For the given problem A₀ =80000 kilotons and emissions will decrease at the rate of 2.5% per year therefore, r=0.025
The general equation for emission becomes
[tex]A(t)=80000(1-0.025)^t[/tex]
[tex]A(t)=80000(0.975)^t[/tex]
To calculate total emissions for 7 years it is calculated as follows
[tex]I=\int\limits^{7}_0 {A(t)} .dt=\int\limits^{7}_0 {80000(0.975)^tdt}[/tex]
[tex]I=80000(0.975)^t/ln (0.975)\left \{ {{t=7} \atop {t=0}} \right.[/tex]
I=5,13,183Kilotonnes
Hence, the total emission of 5,13,183 kilotons of carbon dioxide would be emitted over the course of the 7-year period.
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Stan lawn mower had 1/8 of a gallon of gasoline in the tank he added 6/10 to the tank after he only had 1/4 of a gallon what was the total used
Stan used 19/40 of a gallon of gasoline.
Given that;
At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank.
Hence, It means that the number of gallons of gasoline that he has already put in the tank is
1/8 + 6/10 = 29/40 of a gallon.
Now, After he mowed, 1/4 of a gallon was left in the tank.
Therefore, the total amount of gasoline Stan used is
29/40 - 1/4 = 19/40 of a gallon
Thus, the total amount of gasoline Stan used is, 19/40 of a gallon
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What is the slope-intercept form of the equation 3x-5y=2
Answer: y = 3/5x - 2/5
Step-by-step explanation: The slope-intercept form is y = mx+b. Hence, solve for y. 3x - 5y = 2.
Move 5y to the right side and move 2 to the left. 3x - 2 = 5y. Divided 5 for all sides: 3/5x - 2/5 = y. Hence, writing in slope-intercept form is y= mx + b, y = 3/5x - 2/5.
An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 are white, and 30 are pink. If he reaches into the bag randomly and removes one at a time, what is the probability that the first three cases are all pink? Please help I have no clue how to do this at all. I listen in math class but this is hard!
The probability of drawing a pink case on the first draw is 30/80.
What is probability?Probability is a branch of mathematics that deals with the measurement and analysis of random phenomena. It is the study of the likelihood or chance of an event occurring. It involves analyzing and predicting the likelihood of certain outcomes based on the available information and the rules of probability theory. Probability is used extensively in various fields, including statistics, physics, finance, engineering, and computer science, among others.
In the given question,
The probability of drawing a pink case on the first draw is 30/80. Since the cases are not replaced, the probability of drawing a pink case on the second draw is 29/79 (there are now 29 pink cases left out of 79 total cases). Similarly, the probability of drawing a pink case on the third draw is 28/78. Therefore, the probability of drawing three pink cases in a row is:
(30/80) * (29/79) * (28/78) = 0.0412 or about 4.12%.
So, the probability that the first three cases are all pink is 0.0412 or about 4.12%.
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Which sequence below would best model the description? 50 points!
I need help on this I’m not to sure on it
Answer: your answer would be A.
What is the answer to the equation?
-4(3/2x - 1/2)= -15
A. X= -19/6
B. X= - 29/4
C. X= 13/6
D. X= 17/6
Answer:
D
Step-by-step explanation:
- 4( [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ) = - 15 ← distribute parenthesis by - 4
- 6x + 2 = - 15 ( subtract 2 from both sides )
- 6x = - 17 ( divide both sides by - 6 )
x = [tex]\frac{-17}{6}[/tex] , that is
x = [tex]\frac{17}{6}[/tex]
Perimeter=8x-6 find the missing side of triangle
Answer:
Step-by-step explanation:
I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.
Solve for x. Round to the nearest tenth, if necessary.
x=15.4 units
Step-by-step explanation:First, some definitions before working the problem:
The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.
The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.
Working the problem
For the given triangle, the right angle is at the bottom, so the side on top is the hypotenuse. We know the angle in the upper right corner, so the side across from it with length 4.5, is the opposite side.
For this triangle, the "opposite" leg is known. Additionally, the "hypotenuse" is unknown and is our "goal to find" side.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh". So, the desired function to use for this triangle is the Sine function.
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]sin(17^o)=\dfrac{4.5}{x}[/tex]
Multiply both sides by x, and divide both sides by sin(17°)...
[tex]x=\dfrac{4.5}{sin(17^o)}[/tex]
Make sure your calculator is set to degree mode, and calculate:
[tex]x=\dfrac{4.5}{0.2923717047227...}[/tex]
[tex]x=15.391366289249...[/tex] units
Rounded to the nearest tenth...
[tex]x=15.4[/tex] units
natalie has $330mto send at the amusment park of this total amount 5% is soent on games, 5/11 is for food and drinks, and she spends $13 on parking. the rest of her budget is spent on buying a ticket for herself and a friend. what is the price of one ticket
Answer:
Step-by-step explanation:
This is a word problem involving percentages. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.
Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:
games+food and drinks+parking+tickets0.05×330+115×330+13+2x=total amount=330
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
16.5+150+13+2x2x2xxx=330=330−16.5−150−13=150.5=2150.5=75.25
Therefore, the price of one ticket is $75.25.
A $162,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $14,650 annual income from the investments, how much should the bank invest in bonds? (It's okay to use your calculator to solve the system you set up on this problem.
The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
How to solve for the amount(162,000 - 2x) is invested in mortgages.
The annual income earned from the bond investment is:
0.09x
The annual income earned from the CD investment is:
0.07x
The annual income earned from the mortgage investment is:
0.10(162,000 - 2x) = 16,200 - 0.20x
The total annual income earned from the investments is:
0.09x + 0.07x + 16,200 - 0.20x = 14,650
Simplifying and solving for x, we get:
-0.04x + 16,200 = 14,650
-0.04x = -1,550
x = 38,750
Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
Read more on Bonds here:https://brainly.com/question/25965295
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