Answer:
The total amount spent during 2003 was $725.78.
Step-by-step explanation:
Given:
During the 2004 season, New York theater goers bought 11.3 million tickets for a total of $749.0 . Theater goers spent a total of 3.2% more than the year before.
Now, to find the total amount that was spent during 2003.
Let the amount spent during 2003 be [tex]x.[/tex]
The amount spent during 2004 = $749.0.
As, given theater goers spent a total of 3.2% more than the year before.
So, we put equation to get the amount spent during 2003:
[tex]x+3.2\%\ of\ x=749[/tex]
[tex]x+\frac{3.2}{100} \times x=749[/tex]
[tex]x+\frac{3.2x}{100}=749[/tex]
[tex]\frac{100x+3.2x}{100} =749[/tex]
[tex]\frac{103.2x}{100} =749[/tex]
Multiplying both sides by 100 we get:
[tex]103.2x=74900[/tex]
Dividing both sides by 103.2 we get:
[tex]x=\$725.78[/tex]
Therefore, the total amount spent during 2003 was $725.78.
Twenty people get into an elevator in a hotel with seven floors, and all of them get off at some point. How many different possibilities exist for how the people could get off the elevator?
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
Altogether there were 72 slices of pizza. Twice as many slices had pepperoni compared to the the slices with just cheese. How many slice had just cheese?
Answer:24
Step-by-step explanation:
By setting up an equation c + 2c = 72, where 'c' represents cheese slices and '2c' represents pepperoni slices, and solving for 'c', we find there were 24 slices of pizza with just cheese.
To solve the problem about the number of pizza slices with different toppings, we can set up an equation based on the information given.
If 'c' represents the number of slices with just cheese, then 2c would represent the number of slices with pepperoni, because there are twice as many pepperoni slices as there are cheese slices. Since the total number of slices is 72, we can form the following equation:
c + 2c = 72
Combining like terms (c + 2c), we get 3c = 72. To find the value of 'c', we divide both sides of the equation by 3:
3c / 3 = 72 / 3
c = 24
Therefore, there were 24 slices of pizza with just cheese.
113, 183, 479, 120, 117 What is the mean, median and mode? Make sure to label each answer. Round any decimals to the tenths place. Would mean, median or mode be the best measure to describe the data?
A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. What is the probability that a customer must open three or more bottles before winning a prize
Answer:
The probability that the customer must open 3 or more bottles before finding a prize is 0.64
Step-by-step explanation:
In order for a customer to have to open at least 3 bottles before winning a prize, then the first two bottles shouldnt have a price. The probability that a bottle doesnt have a price is 1-0.2 = 0.8. Since the bottles are independent from each other, then the probability that 2 bottles dont have a prize is 0.8² = 0.64. Therefore, the probability that the customer must open 3 or more bottles before finding a prize is 0.64
Answer:
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
Step-by-step explanation:
We know that the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next.
Therefore, we get p=0.2 and q=1-p=1-0.2=0.8.
So we will calculate the probability that the buyer will not win the prize in the first and second bottles. We get:
[tex]P=0.8\cdot0.8=0.64[/tex]
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
At which angle will the hexagon rotate onto itself?
O 60°
90°
120°
180°
Answer: 60°
Step-by-step explanation:
When a figure has a rotational symmetry, it maps onto itself under rotation about a point at the centre.
When an hexagon rotate onto itself,
the vertices must cover to vertices and from sides to sides. There are six angles in a hexagon and the sum of the angles is 360°. Therefore, each angle has a measure of 360°/6 is equal to 60°.
Rotating subsequently by 60 degree will rotate a hexagon onto itself. A hexagon has 6 rotations, that is, a hexagon has a rotational symmetry of 6 and at angle 60°, the hexagon will rotate onto itself.
At an IMAX theater, the giant rectangular movie screen has a width 26 feet less than its length. If its perimeter is 332 feet, find the length and the width of the screen.
Answer:
Length=96 feet
Width=70 feet
Step-by-step explanation:
Let the length = l
The width 26 feet less than its length=l-26
Perimeter of the giant rectangular movie screen= 332 feet
Perimeter of a rectangle = 2(L+W)
332=2(l+l-26)
332=2(2l-26)
Expanding the brackets
332=4l-52
4l=332+52
4l=384
l=384/4=96
The Length of the giant rectangular movie screen is 96 feet.
The Width, W=l-26=96-26=70 feet
The dimensions of the screen are: [tex]Length: 96\ feet[/tex] and [tex]Width: 70\ feet[/tex]
To find the dimensions of the IMAX screen, we need to set up a system of equations based on the given information. Let's denote the length of the screen by [tex]\( L \)[/tex] and the width by [tex]\( W \)[/tex].
Given:
1. The width is [tex]26 \ feet[/tex] less than the length: [tex]\( W = L - 26 \)[/tex]
2. The perimeter of the rectangle is [tex]332\ feet: \( 2L + 2W = 332 \)[/tex]
First, we can simplify the perimeter equation:
[tex]\[2L + 2W = 332\][/tex]
Divide both sides by [tex]2[/tex]
[tex]\[L + W = 166\][/tex]
Now, substitute the expression for [tex]\( W \)[/tex] from the first equation into the simplified perimeter equation:
[tex]\[L + (L - 26) = 166\][/tex]
Combine like terms:
[tex]\[2L - 26 = 166\][/tex]
Add 26 to both sides:
[tex]\[2L = 192\][/tex]
Divide both sides by [tex]2[/tex]
[tex]\[L = 96\][/tex]
Now that we have the length, we can find the width using the equation [tex]W = L - 26 \)[/tex]
[tex]\[W = 96 - 26 = 70\][/tex]
A boeing-747 is flying from New York City to Los Angeles. It leaves La Guardia Airport in NYC at 9:20am with an expectred arrival time at LA of 1:38pm. However, when it reaches Springfield (Illinois) which is 920 miles away from NYC, the piolets are informed that there is a storm in their path which they must avoid. In order to do so they turn 38 degrees to the right. Eventually they cleared to turn back left and return to their original flight path. They rejoin the path when they reach the four corners which is still 650 miles from LA at which point the piolets make one last turn 52 degrees to the right in order to head directly to los angeles. They arrive without futer incidents. How many minutes was the flight delayed
Answer:
I do not know sorry
Step-by-step explanation:
#7 HELP ! WILL GIVE BRANLIEST
Answer:
x = 8, y = 4√3, z = 8√3
Step-by-step explanation:
Assuming that y is the altitude of the triangle (perpendicular to the hypotenuse), the triangles are similar. So we can write proportions:
x / 4 = 16 / x
x² = 64
x = 8
4 / y = y / 12
y² = 48
y = 4√3
z / 12 = 16 / z
z² = 192
z = 8√3
Note: after finding one side, you can also use Pythagorean theorem to find the other two sides.
How many solutions does the system have?
x+y=3
5x+5y=15
A. Exactly one solution
B. No solutions
C. Infinity many solutions
The system has infinitely many solutions because both equations represent the same line in the coordinate plane. So C. Infinity many solutions will be the answer.
To determine the number of solutions for this system of equations, let's analyze it:
[tex]\[\left\{\begin{array}{l}x + y = 3 \\5x + 5y = 15\end{array}\right.\][/tex]
We can simplify the second equation by dividing both sides by 5:
[tex]\[x + y = 3\][/tex]
This equation is identical to the first equation in the system. So, the two equations represent the same line in the coordinate plane.
When two equations represent the same line, they have infinitely many solutions, because every point on the line satisfies both equations.
Therefore, the correct answer is:
(C) Infinitely many solutions
Complete Question:
Kim is a medical supplies salesperson. Each month she receives a 5% commission on all her sales of medical supplies up to $20,000 and 8.5% on her total sales over $20,000. Her total commission for May was $3,975. What were her sales for the month of May?
Answer: her sales for the month of May is $55000
Step-by-step explanation:
Let x represent her total sales for the month of May.
Each month she receives a 5% commission on all her sales of medical supplies up to $20,000. This means that for her first sales worth $20000, she earns a commission of
5/100 × 20000 = 1000
She also earns 8.5% on her total sales over $20,000. This means that for sales over $20000, she earns
8.5/100(x - 20000) = 0.085x - 1700
Her total commission for May was $3,975. The expression becomes
1000 + 0.085x - 1700 = 3975
0.085x = 3975 + 1700 - 1000
0.085x = 4675
x = 4675/0.085
x = 55000
Kim's total sales for the month of May were $55,000. The first $1,000 of her commission came from the 5% commission on her first $20,000 in sales. The remaining $2,975 of her commission came from the 8.5% commission on her additional $35,000 in sales.
Explanation:To find out Kim's sales for the month of May, let's first understand her commission structure. She earns a 5% commission on all her sales of medical supplies up to $20,000, and 8.5% on any of her total sales over $20,000. Her total commission for the month of May is given as $3,975.
If her sales were $20,000 or below, her commission would be 5% of that, which would be $1,000 at most. Her commision is definitely more than that, we can infer that her sales were more than $20,000.
To figure out her actual sales, we need to subtract $1,000 from her total commission of $3,975, which gives us $2,975. This amount is the commission she earned at the rate of 8.5% for sales over $20,000. To find out the sales corresponding to this commission, we should divide $2,975 by 8.5% (or 0.085). That gives us the sales amount over $20,000 as $35000.
Therefore, Kim's total sales for the month are the $20,000 she sold to make the first $1,000 of her commission, plus the additional $35,000. So Kim's total sales for the month of May were $55,000.
Learn more about Commission Calculation here:
https://brainly.com/question/6615293
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Rewrite the radical expression as an expression with a rational exponent. the fourth root of seven to the fifth power
Answer:
[tex]\sqrt[4]{7^5}[/tex]
Step-by-step explanation:
I apologize, I do not know how to explain this.
Answer:
7⁵/₄
Step-by-step explanation:
⁴√7⁵
The fourth root is equivalent to the power 1/4.
= 7^(1/4 * 5)
= 7^(5/4).
In research essays, brackets [ ] are used by writers to demonstrate when:__________.a. small changes have been made within exact quotations. b. outside resources have been cited. c. original sources have been paraphrased. d. parts of a quotation were already within quotation marks.
Answer:
A. small changes have been made within exact quotations.
Step-by-step explanation:
Brackets are pair of marks which enclose words or figures in order to separate them from the context. Thus, the use of brackets indicate that the quotation's exact punctuation has been adapted to the punctuation or grammar structure of the essay.
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed with standard deviation 0.25 volt, and the manufacturer wishes to test
H0:μ=5
volts against
H1:μ≠5
, using n = 8 units. a. The acceptance region is 4.85 ≤
x¯¯¯≤5.15
. Find the value of α. b. Find the power of the test for detecting a true mean output voltage of 5.1 volts.
Answer:
a= 0.0897
b= 0.71186
Power of the test for detecting a true mean output voltage of 5.1 volts is 0.28814.
Step-by-step explanation:
See attached pictures.
The value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.
Probability
It is the ratio of favorable events to the total events.
Given
Standard deviation ([tex]\sigma[/tex]) = 0.25
[tex]\mu[/tex] = 5
n = 8
How to calculate ?The acceptance region as
4.85 ≤ [tex]\rm \bar{x}[/tex] ≤5.15
a. Then type I error of probability,
[tex]\alpha = P(4.85> \bar{x}\ when\ \mu =5) + P(\bar{x}\ > 5.15\ when\ \mu =5)\\\alpha = P(\dfrac{4.85-5}{0.25\sqrt{8} } > \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } ) + (\dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } > \dfrac{4.85-5}{0.25\sqrt{8} })\\\alpha = 2P ( z <-1.697)= 0.0897[/tex]
Where, [tex]z = \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} }[/tex]
b. type II error
[tex]\beta = P(4.85 \leq \bar{x} \leq 5.15\ when\ \mu = 5.1)\\\beta = (\dfrac{4.85 - \mu}{0.25/\sqrt{8} }\leq \dfrac{\bar{x} - \mu}{0.25/\sqrt{8} }\leq \dfrac{5.15 - \mu}{0.25/\sqrt{8} }\ when\ \mu=5.1 )\\\beta = P(-2.8284\leq z\leq 0.5657)\\\beta = P(z\leq 0.5657)- P(z\leq -2.8284)\\[/tex]
therefore, the power of the test for detecting a true mean output voltage of 5.1 volt is
[tex]\begin{aligned} 1 - \beta &= 0.28281 \\\beta &= 0.71186\\\end{aligned}[/tex]
Thus, the value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.
More about the probability link is given below.
https://brainly.com/question/795909
A department store has a policy of charging a 15% service change on all returned checks. If a check for $725 is returned, how much will the service charge be?
Answer:
Step-by-step explanation:
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 15 of the 50 boxes on the shelf have the secret decoder ring. The other 35 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/35
Step-by-step explanation:
(15/50)×(14/49)
= 3/35 or 0.0857
Answer:
3/35.
Step-by-step explanation:
Probability (the first one selected has the decoder ring) = 15/50 = 3/10.
Probability (the second one selected has the decoder ring) = 14/49 = 2/7.
Therefore the probability that both have the ring =
3/10 * 2/7
= 6/70
= 3/35.
Note: The probabilities are multiplied because the 2 events are independent.
Evaluate A ^ 2 for A = - 3 . -9 -6 6 9
Answer:
9
Step-by-step explanation:
We want to evaluate
[tex]A^2[/tex]
for A=-3.
This means, we need to substitute A=-2, into the given equation and simplify.
We substitute to get:
[tex] A^2 = {( - 3)}^{2} [/tex]
In this case the base is -3, so it multiplies itself twice.
[tex]A^2 = {( - 3)} \times - 3[/tex]
This gives us:
[tex]A^2 = 9[/tex]
It is known that a certain function is an inverse proportion. Find the formula for this function if it is known that the function is equal to 12 when the independent variable is equal to 2.
Answer:
[tex]y=\frac{24}{x}[/tex]
Step-by-step explanation:
We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of variation.
Upon substituting [tex]y=12[/tex] and [tex]x=2[/tex] in above equation, we will get:
[tex]12=\frac{k}{2}[/tex]
Let us solve for constant of variation.
[tex]12\cdot 2=\frac{k}{2}\cdot 2[/tex]
[tex]24=k[/tex]
Now, we will substitute [tex]k=12[/tex] in inversely proportion equation as:
[tex]y=\frac{24}{x}[/tex]
Therefore, the formula for the given scenario would be [tex]y=\frac{24}{x}[/tex].
Xavier and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. He bought a total of 11 apples and bananas altogether. Determine the number of apples, x,x, and the number of bananas, y,y, that Xavier bought.
Answer: Xavier bought 2 apples and 9 bananas.
Step-by-step explanation:
Let x represent the number of apples that Javier bought.
Let y represent the number of bananas that Javier bought.
At the store, he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. This is expressed as
0.75x + 0.5y = 6 - - - - - - - - - - - - 1
He bought a total of 11 apples and bananas altogether. This means that
x + y = 11
Substituting x = 11 - y into equation 1, it becomes
0.75(11 - y) + 0.5y = 6
8.25 - 0.75y + 0.5y = 6
- 0.75y + 0.5y = 6 - 8.25
- 0.25y = - 2.25
y = - 2.25/ - 0.25
y = 9
x = 11 - y = 11 - 9
x = 2
The average lethal blood concentration of morphine is estimated to be 2.5 µg/mL with a standard deviation of 0.95 µg/mL. The data is normally distributed. Examine the range of values 0.05 to 4.95 µg/mL. Answer the following questions and provide the appropriate calculations (13 points):
a. What is the probability associated with the range lethal morphine blood levels?
Answer:
The probability associated with the range lethal morphine blood levels is 0.9902.
Step-by-step explanation:
Let X = lethal blood concentration of morphine.
The random variable X is normally distributed with parameter μ = 2.5 μg/ mL and σ = 0.95 μg/ mL.
Compute the probability of X within the range 0.05 to 4.95 μg/ mL as follows:
[tex]P(0.05<X<4.95)=P(\frac{0.05-2.5}{0.95}<\frac{X-\mu}{\sigma}<\frac{4.95-2.5}{0.95})\\=P(-2.58<Z<2.58)\\=P(Z<2.58)-P(Z<-2.58)\\=P(Z<2.58)-[1-P(Z<2.58)]\\=2P(Z<2.58)-1\\=(2\times0.9951)-1\\=0.9902[/tex]
*Use a z-table for the probability.
Thus, the probability associated with the range lethal morphine blood levels is 0.9902.
Using the properties of the normal distribution, we calculate the probability associated with the lethal morphine blood levels range of 0.05 to 4.95 µg/mL is essentially 1.0 (100%), meaning a lethal concentration is almost certain to fall within this range.
Explanation:To calculate the probability associated with the range of lethal morphine blood levels, we need to use the properties of the normal distribution. The mean (μ) lethal concentration is 2.5 µg/mL and the standard deviation (σ) is 0.95 µg/mL. We are examining the range 0.05 to 4.95 µg/mL.
First, we calculate the z-scores for both the lower limit (0.05 µg/mL) and the upper limit (4.95 µg/mL) of the range using the formula:
Z = (X - μ) / σ
For the lower limit:
Zlower = (0.05 - 2.5) / 0.95 ≈ -2.58
For the upper limit:
Zupper = (4.95 - 2.5) / 0.95 ≈ 2.58
Using a standard normal distribution table, we find the corresponding probabilities for both z-scores. Since the z-scores are symmetrical about the mean, the probability for both is the same. Thus, the probability up to Zlower is about 0.495 (adjusted from table values), and the probability up to Zupper is also about 0.495.
To find the probability within the range, we subtract the probability of the lower limit from the upper limit:
P(0.05 µg/mL < X < 4.95 µg/mL) = P(Zupper) - P(Zlower)
P(0.05 µg/mL < X < 4.95 µg/mL) ≈ 0.495 - (1 - 0.495) = 0.495 - 0.505 = -0.01
The negligible negative value suggests an error, likely due to rounding issues when looking up z-scores in the standard normal distribution table. Correctly, the total area under the curve, which corresponds to the probability of the range, should be virtually 1.0 (or 100%) since both z-scores are quite extreme (far in the tails of the distribution).
Therefore, practically, the probability associated with the given range of lethal morphine blood levels is essentially 1.0 (or 100%), meaning it is almost certain that a lethal concentration falls within this range.
-2/x^2-4 + x-1/x^2-2x
1. Identify the type of problem
2. Think of how to do this problem
3. Do the Work
4. Answer
Answer:
I need help with this too
Step-by-step explanation:
Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. A researcher wishes to compare academic aptitudes of married lawyers and their spouses. She obtains a random sample of 517 such couples who take an academic aptitude test and determines each spouse's academic aptitude.
Answer:
a) Independent
b) Quantitative
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 517
Sample:
Married lawyers and their spouses.
Response variable:
Comparison of academic aptitudes of married lawyers and their spouses.
a) The given sampling is an example of independent sampling.
This is an independent sample because an individual of sample does not effect any other individual of the sample.
b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.
It is a quantitative measure because the scores can be expressed in numerical.
Answer:
The sampling is independent and the response variable is quantitative.
Explanation:
Given a random sample of [tex]517[/tex] couples
The researcher wishes to compare academic aptitudes of married lawyers and their spouses. Then, she obtains a random sample of [tex]517[/tex] such couples who take an academic aptitude test and determines each spouse's academic aptitudeAn individual of the sample will not affect any other individual of the sample.Therefore, the sampling is independent.Here, the response variable is the aptitude test.The scores of the academic test are represented in numerical form.Thus, the response variable is quantitative.Learn more about Random sample, refer:
https://brainly.com/question/16786843Write 3.45 as a reduced mixed number.
Answer:
3 [tex]\frac{9}{20}[/tex]
Step-by-step explanation:
3.45=3 45/100
reduce and divided by 5
3 45/100= 3 9/20
Answer:
Step-by-step explanation:
add me on fortnite
Genevieve wants to verify that 1/5 * (5x - 20) - 1/2 * (4x - 8) equivalent to -x which procedure can Genevieve to determine if the two expressions are equivalent?
Answer with Step-by-step explanation:
We are given that
LHS
[tex]\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)[/tex]
Using distribution property
[tex]a\cdot (b+c)=a\cdot b+a\cdot c[/tex]
[tex]\frac{1}{5}(5x)-\frac{1}{5}(20)-\frac{1}{2}(4x)+\frac{1}{2}(8)[/tex]
After multiplication we get
[tex]x-4-2x+4[/tex]
Combine like terms
[tex](x-2x)+(4-4)[/tex]
Then, we get
[tex]-x+0=-x[/tex]
Hence,verified.
Answer:D
Step-by-step explanation: I took the unit test
Ken and Leah are trying to solve a science homework question. They need to find out how much a rock that weighs 4 pounds on Earth would weigh on Venus. They know they can multiply the number of pounds the rock weighs on Earth by 0.91 to find its weight on Venus. Select the partial products Ken and Leah would need to add to find the product of 4 and 0.91. Mark all that apply.
Answer:
The answer is b and d.
Step-by-step explanation:
What does the Principle of Superposition tell us about relative ages of the strata in the cross-sections you were looking at? Older rocks might be found on top of younger rocks-what could cause that? Why is an igneous intrusion younger than the rocks it’s found in?
Answer:
1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.
2. The intrusion of the younger rock by the principle of cross-cutting relationship
3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.
Step-by-step explanation:
In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.
The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.
The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.
Find the area of the shaded region. With steps
Answer: the area of the shaded region is 72.96 ft²
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Diameter of circle = 16 feet
Radius = diameter/2 = 16/2 = 8 feet
Area of circle = 3.14 × 8² = 200.96ft²
The sides of the square are equal. To determine the length of each side of the square, L, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
16² = L² + L²
256 = 2L²
L² = 256/2 = 128
L = √128 ft
Area of the square is
L² = (√128)²
Area = 128 ft²
Area of shaded region is
200.96 - 128 = 72.96 ft²
Dave owns 15 shares of ABC Mining stock. On Monday, the value of each share rose $2, but on Tuesday the value fell $5. What is the change in the value of Dave's shares?
Answer:
The change in the value of Dave's shares = $ 105
Step-by-step explanation:
Total number of shares = 15
Let initial value of a share = x
On Monday, the value of each share rose = $ 2
Now the value of each share = x + 2
Total value of 15 shares on Monday = 15 (x + 2) -------- (1)
On Tuesday the value of each share fell = $ 5
Now the value of each share = x - 5
Total value of 15 shares on Tuesday = 15 (x - 5) --------- (2)
The change in the value of Dave's shares = 15 (x + 2) - 15 (x - 5)
⇒ 15 x + 30 - 15 x + 75 = 105
⇒ Thus the change in the value of Dave's shares = $ 105
ixl geometry help pls !
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{small}{large}\qquad \qquad \stackrel{sides}{\cfrac{3}{7}} ~~ = ~~ \stackrel{areas}{\sqrt{\cfrac{A_1}{98}}}\implies \left( \cfrac{3}{7} \right)^2 = \cfrac{A_1}{98}\implies \cfrac{3^2}{7^2}= \cfrac{A_1}{98} \\\\\\ \cfrac{9}{49}= \cfrac{A_1}{98}\implies 882 = 49A_1\implies \cfrac{882}{49}=A_1\implies 18=A_1[/tex]
Answer:
The answer to your question is 18 in²
Step-by-step explanation:
Data
Big rectangle Small rectangle
Area = 98 in² Area = ?
Height = 7 in Height = 3 in
Process
1.- Calculate the base of the big rectangle
Area = base x height
solve for base
base = Area / height
substitution
base = 98 / 7
base = 14 ni
2.- Use proportions to find the base of the small rectangle
x / 3 = 14 / 7
Simplify
x = (14)(3) / 7
result
x = 6 in
3.- Calculate the area of the small rectangle
Area = 6 x 3
= 18 in²
The expression 475 * 1.076 ^ t the average annual per capita health care costs, in dollars, in the US as a function of the number of years since 1970. What does 1.076 represent in this expression?
Answer:
[tex] Y(t)= 475 (1.076)^t [/tex]
Where Y(t) represent the average annual per capita health care costs
475 represent the initial amount for the average annual per capita health care costs
t represent the number of years since 1970
And 1.076 represent the growth factor given by:
[tex] 1+r = 1.076[/tex]
And solving for r we got:
[tex] r = 1.076-1 =0.076[/tex]
So for this case we can say that the value 1.076 represent the growth factor.
Step-by-step explanation:
For this case we have the following model given:
[tex] Y(t)= 475 (1.076)^t [/tex]
Where Y(t) represent the average annual per capita health care costs
475 represent the initial amount for the average annual per capita health care costs
t represent the number of years since 1970
And 1.076 represent the growth factor given by:
[tex] 1+r = 1.076[/tex]
And solving for r we got:
[tex] r = 1.076-1 =0.076[/tex]
So for this case we can say that the value 1.076 represent the growth factor.
Final answer:
In the provided expression, 1.076 represents the annual growth factor of US health care costs, indicating an annual increase of 7.6% since 1970.
Explanation:
The expression 475 * 1.076 ^ t represents the average annual per capita health care costs in the US as a function of the number of years since 1970. Here, 1.076 signifies the annual growth factor of the costs, which means health care costs have been increasing by 7.6% each year since 1970. This exponential function captures the trend of increasing health care expenditure, which plays a significant role in the nation's economy, consuming a larger share of the Gross Domestic Product (GDP) over time.
Which statement describes the system of equations? It has infinitely many solutions. It has no solution. It has one solution . It has one solution (8, 2).
A system of equations can have no solution, one unique solution, or infinitely many solutions. A single solution indicates that the equations intersect at a point, no solution suggests parallel lines, and infinitely many solutions mean the equations are the same line expressed differently.
Explanation:When discussing a system of equations, the possible solutions include having no solution, one unique solution, or infinitely many solutions. If a system has no solution, this typically means the equations represent parallel lines that never intersect. In contrast, if there is one solution, the equations represent two lines that intersect at a single point, such as the given solution (8, 2). The presence of infinitely many solutions indicates that the equations are the same line, represented in different forms, and thus they intersect at every point along the line.
To determine which of these scenarios applies to a particular system of equations, one should begin by determining the number of unknowns and the number of equations given. A single linear equation in two variables, such as those given in Practice Test 4 Solutions 12.1 Linear Equations, represents a line. A system composed of two linear equations can be solved using algebraic methods such as substitution or elimination.
If the system consists of the same equation expressed differently, such as y = 2x + 3 and 2y = 4x + 6, then they are essentially the same line, and the system would have infinitely many solutions.