I don’t know this..I need help
Answer:
26
Step-by-step explanation:
To find the area of a triangle, you simply need to multiply the base by the height and divide by 2. In this case, 13*4/2=26 square centimeters. Hope this helps!
The volume of a CONE-shaped hole is 75pi ft cubed. If the hole is 9 feet deep, what is the radius of the hole?
(1 Point)
Answer:
The radius of hole is 5 feet
Step-by-step explanation:
Depth of conical hole = 9 feet
Let the radius of hole be r
Volume of conical hole =[tex]\frac{1}{3} \pi r^2 h[/tex]
So, Volume of conical hole =[tex]\frac{1}{3} \pi \times r^2 \times 9[/tex]
We are given that volume of a CONE-shaped hole is 75pi ft cubed.
So,[tex]\frac{1}{3} \pi \times r^2 \times 9=75 \pi[/tex]
[tex]\frac{1}{3} \times r^2 \times 9=75[/tex]
[tex]r^2=\frac{75 \times 3}{9}[/tex]
[tex]r=\sqrt{\frac{75 \times 3}{9}}[/tex]
r=5
Hence The radius of hole is 5 feet
John took all his money from his savings account. He spent $52 on a radio and 1/2 of what was left on presents for his friends, Of the money remaining, John put 4/13 into checking account and the last remaining $180 was left to charity. How much money did John originally have in his savings account?
Answer:
John had $572 in his savings account.
Step-by-step explanation:
Let the total amount John took from his savings account be T.
He spent $52. That means he has $(T - 52) left.
He then spent 1/2 of what was left on presents for his friends. That is:
[tex]\frac{1}{2} * (T - 52) = \frac{T - 52}{2}[/tex]
Which means he is left with another half of what was left, that is, [tex]\frac{T - 52}{2}[/tex]
Of the money remaining, John put 4/13 into checking account.
This means that he is left with 9/13 of [tex]\frac{T - 52}{2}[/tex].
We are told that this is equivalent to the last remaining $180 that John left to charity.
=> [tex]\frac{9}{13} * \frac{T - 52}{2} = 108[/tex]
Hence:
[tex]\frac{9(T - 52)}{13 * 2} = 180\\\\9(T - 52) = 180 * 13 * 2\\\\9(T - 52) = 4680\\\\T - 52 = \frac{4680}{9} = 520\\\\[/tex]
=> T = 520 + 52 = $572
Hence, John took $572 from his savings account. Since this is all he had in his savings account, John had $572 in his savings account.
Working backward, we determined that John originally had $572 in his savings account before spending on the radio, presents, putting money into his checking account, and giving to charity.
Explanation:To solve this mathematics problem, we need to work backward from the information provided. John spent $52 on a radio and then spent half of the remaining amount on presents. After that, he put 4/13 of the remaining money into his checking account and then gave $180 to charity. Let's represent the original amount of money John had as x.
After buying the radio, John had x - $52 left. He then spent half on presents, so he had (x - $52)/2 remaining. After putting 4/13 of what was left into his checking, the equation becomes ((x - $52)/2) * (9/13) since 9/13 is the complement of 4/13, which goes into the checking account. This amount equaled the last remaining $180.
The equation to find the original amount x is:
(((x - $52) / 2) * (9/13)) = $180
Now solve for x:
Multiply both sides by 13/9 to get (x - $52) / 2 = $260.Multiply both sides by 2 to get x - $52 = $520.Finally, add $52 to both sides to get x = $572.So, the original amount of money John had was $572.
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What value of y makes the equation true. y+2.9=11
Answer:
y = 8.1
Step-by-step explanation:
y+2.9=11
Subtract 2.9 from each side
y+2.9-2.9 = 11-2.9
y =8.1
the sum of two numbers is 9 and their difference is 5.
What are the two numbers?
To solve this problem, we can set up a system of equations using the information given and solve it using the substitution method.
Explanation:To solve this problem, we can set up a system of equations using the information given. Let's call the two numbers x and y.
From the given information, we can write:
x + y = 9 (equation 1)
x - y = 5 (equation 2)
To solve this system, we can use the method of substitution or elimination. Let's solve it using the substitution method:
From equation 2, we can isolate x by adding y to both sides:
x = y + 5
Now substitute this expression for x in equation 1:
(y + 5) + y = 9
Combine like terms:
2y + 5 = 9
Subtract 5 from both sides:
2y = 4
Divide both sides by 2:
y = 2
Now substitute this value for y in equation 1:
x + 2 = 9
Subtract 2 from both sides:
x = 7
So, the two numbers are 7 and 2.
10 = - 9 - x
Show me all the steps
Step-by-step explanation:
10= - 9 - X
- x - 9 = 10
-× = 10 + 19
-× =19
× = -19
A sociologist is studying the social media habits of high school students in a school district. The sociologist wants to estimate the average total number of minutes spent on social media per day in the population. A random sample of 50 high school students was selected, and they were asked, “How many minutes per day, on average, do you spend visiting social media sites?"
Which of the following is the most appropriate inference procedure for the sociologist to use?
A one-sample z-interval for a population proportion
A
A one-sample t-interval for a population mean
B
A matched-pairs t -interval for a mean difference
C
A two-sample z-interval for a difference between proportions
D
A two-sample t-interval for a difference between means
Answer:
A one-sample t-interval for a population mean
Step-by-step explanation:
As the question is "How many minutes per day, on average, do you spend visiting social media sites?", the answer will be in a numerical form (number of hours, positive integer or real number).
As this is not a proportion, the option "A one-sample t-interval for a population mean" is discarded.
As the study does not defined another variable to compare in pairs, it is not a matched-pairs test. Option "A matched-pairs t -interval for a mean difference" discarded.
There are not two means in the study, so there is no "difference between means" variable. Options "A two-sample z-interval for a difference between proportions" and "A two-sample t-interval for a difference between means".
This should be a one-sample t-interval for a population mean, as there is only one sample, one population mean and the population standard deviation is not known.
The required correct statement 'A one-sample t-interval for a population mean'.
We have to determine, Which of the following is the most appropriate inference procedure for the sociologist to use?
According to the question,
The sociologist wants to estimate the average total number of minutes spent on social media per day in the population.,
A random sample of 50 high school students was selected,
And they were asked, “How many minutes per day, on average, do you spend visiting social media sites.
The answer will be in a numerical form (number of hours, positive integer or real number).
The time spent on social media keeps increasing. it can deduce as at now that trending social media platforms take much of the time spent on social media.
On average, spend 240 minutes per day on social media sites. As New social media handles keep coming,
As the given condition is not a proportion, the option "A one-sample t-interval for a population mean" is discarded.
The study does not defined another variable n difference" discarded.
There are not two means in the study, so there is no "difference between means" variable.
"A two-sample z-interval for a difference between proportions" and "A two-sample t-interval for a difference between means".
This should be a one-sample t-interval for a population mean, as there is only one sample, one population mean and the population standard deviation is not known.
Hence, The required correct statement 'A one-sample t-interval for a population mean'.
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According to the US Bureau of labor statistics, 7% of US female workers between 16 and 24 years old are paid at the minimum wage or less. A state politician wants to verify this statement for his state. He uses a sample of 500 female workers and finds 42 are paid at the minimum wage or less. Use a 5% significance level to test to test whether that state differs from the nation.
State clearly the null and the alternative hypothesis, the test statistic, the decision rule and the conclusion.
Answer:
The Null Hypothesis is [tex]H_o:k_o = 0.07[/tex]
The alternative hypothesis is [tex]H_a :k_o \ne 0.07[/tex]
Decision rule
If the test staistics is greater than the critical value of significance level then [tex]H_o[/tex] is accepted else [tex]H_o[/tex] is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
[tex]t_{0.05} = 1.645[/tex]
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
Conclusion
The information is not enough to back the claim that state differs from the nation
Step-by-step explanation:
From the question we are told that
The percentage of US female workers paid at the minimum wage or less is [tex]k_o =[/tex] 7% = 0.07
The sample size is [tex]n = 500[/tex]
The number paid minimum wage or less is x = 42
The significance level is [tex]\alpha =[/tex]5% = 0.05
Now the probability of getting a US female workers paid at the minimum wage or less is mathematically represented as
[tex]\= k = \frac{x}{n}[/tex]
substituting value
[tex]\= k = \frac{42}{500}[/tex]
[tex]\= k = 0.084[/tex]
The Null Hypothesis is [tex]H_o:k_o = 0.07[/tex]
The alternative hypothesis is [tex]H_a :k_o \ne 0.07[/tex]
Generally the test statistics is mathematically evaluated as
[tex]z = \frac{\= k - k_o}{\sqrt{\frac{k_o(1-k_o)}{n} } }[/tex]
substituting value
[tex]z = \frac{0.084 - 0.07}{\sqrt{\frac{0.07 (1-0.07)}{500} } }[/tex]
[tex]z = 1.23[/tex]
Now the Decision rule is stated as
If the test staistics is greater than the critical value of significance level then [tex]H_o[/tex] is accepted else [tex]H_o[/tex] is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
[tex]t_{0.05} = 1.645[/tex]
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
So the conclusion will be
The information is not enough to back the claim that state differs from the nation
What is the circumference of a circle with a radius of 56 feet?
feet
(Use 3.14 for Pi.)
Answer:
351.68
Step-by-step explanation:
c = 2πr
c = 2(3.14)(56)
c = 6.28(56)
c = 351.68
Answer:
Step-by-step explanation:
Given: mKP=2mIP, mIVK =120°
Find: m∠KJL.
Answer:
The measure of angle KJL is 40°.Step-by-step explanation:
Givens
[tex]m(KP)=2m(IP)[/tex]
[tex]m(IVK)=120\°[/tex]
Notice that
[tex]m(KP)+m(IP)+m(IVK)=360\°[/tex], by definition sum of arcs.
Replacing given values, we have
[tex]2m(IP)+m(IP)+120\°=360\°\\3m(IP)=360\° - 120\°\\m(IP)=\frac{240\°}{3}\\ m(IP)=80\°[/tex]
Which means [tex]m(KP)=2(80\°)=160\°[/tex]
Notice that arc KP is the subtended arc by angle KJL.
We know that the angle formed by a tangen and a secant is equal to one-half of the difference of the intercepted arcs.
[tex]m\angle KJL = \frac{1}{2} (m(KP)-m(IP))\\m \angle KJL = \frac{1}{2}(160\° - 80\° )=\frac{1}{2}(80\°)=40\°[/tex]
Therefore, the measure of angle KJL is 40°.
How can you break up the figure into familiar shapes to determine the area?
The area of a 2D form is the amount of space within its perimeter. The area of the composite figure is 5 1/3 ft².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The given figure can be breakdown into two parts as shown below. Therefore, the area of the composite figure will be,
Area of the composite figure = Area A + Area B
= (5 × 1/3) + [0.5×2×(5- 4/3)]
= 5/3 + 11/3
= 16/3 = 5 1/3 ft²
Hence, the area of the composite figure is 5 1/3 ft².
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In 2009, a survey of 23 people who had home access to the Internet asked them how much they paid per month for that access, rounded to the nearest dollar. The following data show each person's response, from smallest monthly bill to largest. $14, $18, $18, $18, $19, $19, $23, $23, $23, $25, $25, $25, $25, $25, $26, $26, $26, $27, $33, $37, $42, $58 Make a histogram of the data on the cost of Internet access using the intervals 0-4, 5-9, 10-14, and so on. Describe the distribution of values in words.
Answer:
See attachment for histogram
Step-by-step explanation:
The histogram shows that the majority of customers have monthly bills between 25 to 29. There is a break between $45-$54 monthly bill as there is no customer with this amount of monthly bill. Then there is one customer between $55-$59 monthly bill.
Final answer:
The histogram of Internet costs shows a concentration between $19-28, with the majority of prices ranging from $23 to $27. It is unimodal and right-skewed with costs spread from $14 to $58, indicating that a smaller number of individuals pay much higher prices for internet access.
Explanation:
To create a histogram of the data on the cost of Internet access using intervals of $5, we will first determine the range of values within each interval:
14-18: $1419-23: $18, $18, $18, $19, $19, $23, $23, $2324-28: $25, $25, $25, $25, $25, $26, $26, $26, $2729-33: $3334-38: $3739-43: $4244-48: None49-53: None54-58: $58From the histogram, we can see that the majority of responses fall within the $19-28 range, specifically between $23 and $27. This signifies that most people in the survey pay a moderate price for Internet access. The distribution is unimodal, skewing right, and has a spread from $14 to $58, with a slight concentration of high costs on the right indicating few individuals pay significantly more for internet access.
Write 3.274 x 10^3 as an ordinary number
3.274 x 10^3 written as an ordinary number is 3274. This is achieved by moving the decimal point three places to the right.
Explanation:The student's question is asking for a conversion from scientific notation to an ordinary number. This process is simple once you understand what the scientific notation represents. The value 3.274 x 10^3 implies that the decimal point in 3.274 is moved to the right three places because the power of 10 is positive 3.
Therefore to write 3.274 x 10^3 as an ordinary number, we move the decimal point three places to the right starting from where it currently is after the number 3. So, 3.274 becomes 3274.
In concise, 3.274 x 10^3 written as an ordinary number is 3274.
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Suppose you are taking a 15 question True/False quiz which you are not prepared for. You find yourself simply guessing at every answer. What is the probability that you get less than 3 answers correct?
Answer:
[tex]P(X=0)=(15C0)(0.5)^0 (1-0.5)^{15-0}=0.0000305[/tex]
[tex]P(X=1)=(15C1)(0.5)^1 (1-0.5)^{15-1}=0.000457[/tex]
[tex]P(X=2)=(15C1)(0.5)^2 (1-0.5)^{15-2}=0.00320[/tex]
And adding the results we got:
[tex] P(X<3) =P(X \leq 2) = 0.0036875[/tex]
Step-by-step explanation:
We can define the variable of interest s X representing the number of correct questions for the exam. and we can model this random variable with a binomial distribution. The probability of select the correct answer would be [tex]p =\frac{1}{2}[/tex] since is a true/false question.
[tex] X \sim Binom (n =15, p=0.5[/tex]
And we want to find this probability:
[tex]P(X <3)= P(X\leq 2)=P(X=0) +P(X=1) +P(X=2)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex]P(X \leq 2)=P(X=0)+P(X=1)+P(X=2)[/tex]
We can find the individual probabilities and we got:
[tex]P(X=0)=(15C0)(0.5)^0 (1-0.5)^{15-0}=0.0000305[/tex]
[tex]P(X=1)=(15C1)(0.5)^1 (1-0.5)^{15-1}=0.000457[/tex]
[tex]P(X=2)=(15C1)(0.5)^2 (1-0.5)^{15-2}=0.00320[/tex]
And adding the results we got:
[tex] P(X<3) =P(X \leq 2) = 0.0036875[/tex]
A college official conducted a survey to estimate the proportion of students currently living in dormitories about their preference for single rooms, double rooms, or multiple (more than two people) rooms in the dormitories on campus. Which of the following does not a ect the college official's ability to generalize the survey results to all dormitory students?(a) Five thousand students live in dormitories on campus. A simple randomsample of only 500 were sent the survey.(b) The survey was sent only to first year students.(c) Of the 500 students who were sent the survey, only 160 responded.(d) All of the above present a problem for generalizing the results.
Answer:
b
Step-by-step explanation:
all the options reflect the college's official's ability ot generalize the survey results except b. Option b represents a particular group of the total population.
The ability to generalize survey results is compromised when the survey is biased, the sample size is inadequate relative to the population, or the response rate is low. Each of the listed issues affects the generalizability of the survey outcome, with specific concerns in terms of sample representativeness and potential biases.
Explanation:The question concerns the ability to generalize survey results to a larger population of dormitory students. Options a, b, and c each presents issues related to sample representativeness and survey methodology, which can affect the college official's ability to generalize findings.
Option a suggests that the sample may be too small relative to the total population. However, a random sample of 500 can theoretically represent 5,000 students well if selected appropriately. Option b indicates a selection bias because only first-year students were surveyed, which does not reflect the entirety of dormitory residents.
Option c points to a low response rate, which can result in nonresponse bias if the 160 respondents have different preferences than those who did not respond.
which word describes the four angels formed by the intersection of two perpendicular lines
The word that describes the four angles formed by the intersection of two perpendicular lines is "right angles" because they each measure 90 degrees and create an L-shaped corner.
The four angles formed by the intersection of two perpendicular lines are often described as "right angles." A right angle measures exactly 90 degrees, and it is the angle at which two lines meet and form a perfect L shape.
Right angles are a fundamental concept in geometry and have many practical applications in everyday life. They are essential in fields such as architecture, engineering, and mathematics. Right angles are known for their symmetry and balance, making them a crucial element in various geometric shapes and constructions.
In summary, the word that describes the four angles formed by the intersection of two perpendicular lines is "right angles" due to their characteristic 90-degree measurement and significance in geometry.
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Complete question below :
What word describes the four angles formed by the intersection of two perpendicular lines?
what is the circumference of a circle with a diameter of 5?
Answer:
C≈15.71cm
Step-by-step explanation:
C=2πr
d=2r
C=πd=π·5≈15.70796cm
y= x^3-19x+30
State the number of complex zeros for each function
Answer:
0
Step-by-step explanation:
Using Descartes' rule of signs, we observe that the signs of the coefficients, + - +, have two changes. Thus there will be 0 or 2 positive real roots, hence 0 or 2 complex roots.
We can do further work to determine if it is 0 or 2. A graphing calculator provides an easy answer.
This function of x has no complex zeros. They are all real.
_____
For a cubic, it isn't always easy to find the zeros. The rational root theorem tells you any rational zeros will be factors of 30. Possibilities are ...
±1, ±2, ±3, ±5, ±6 . . . . . we're pretty sure no roots have magnitude > 6
For x=0, y = 30 . . . . the constant
For x=1, y = 12 . . . . . a smaller value, so we're going in the right direction
For x=2, y = 0 . . . . . one of the real roots
Dividing out this factor*, we get ...
y = (x -2)(x^2 +2x -15)
Factoring the quadratic gives ...
y = (x -2)(x -3)(x +5) . . . . . . all real zeros
_____
* For dividing x^3 -19x +30, synthetic division works well. The work for that is shown in the second attachment.
Subtract the following military times 2330 - 0540
The final result is 17 hours and 50 minutes, or in military time format, 1750.
To subtract the military times 2330 and 0540, we can approach it as a regular subtraction problem, but we need to borrow from the hour when the minutes in the subtrahend (0540) are larger than the minutes in the minuend (2330). Since military time is on a 24-hour clock, we treat 2330 as 23 hours and 30 minutes, and 0540 as 5 hours and 40 minutes.
Step 1: Since we cannot subtract 40 minutes from 30 minutes, we need to borrow 1 hour from the 23 hours, converting it to 22 hours and 90 minutes.
Step 2: Now we subtract the minutes: 90 minutes - 40 minutes = 50 minutes.
Step 3: Then we subtract the hours: 22 hours - 5 hours = 17 hours.
So, the final result is 17 hours and 50 minutes, or in military time format, 1750.
Find the area and perimeter of the given rectangle.
Answer:
Area: 48 sq. units
Perim: 28 units
Step-by-step explanation:
The distance between (-4, 3) and (-4,-3) is 6. The distance between (-4,-3) and (4,-3) is 8. So, 6 x 8 is 48, and that is the area.
6, 6, 8, and 8 are the lengths, so add those up to find the perimeter and you get 28.
Recall that the primes fall into three categories: Let Pi be the set of
primes congruent to 1 (mod 4) and P3 be the set of primes congruent to
3 (mod 4). We know that
{primes} = {2} UP, UP3.
We have previously proved that P3 is infinite. This problem completes
the story and proves that P1 is infinite. You can do this by following these
steps:
A) Fix n > 1 and define N = (n!)2 + 1. Let p be the smallest prime divisor
of N. Show p>n.
B) If p is as in part (a), show that p ⌘ 1 (mod 4). (To get started, note
that (n!)2 ⌘ 1(mod p), raise both sides to the power p1 2 and go from
there. You will need Fermat’s Theorem)
C) Produce an infinite increasing sequence of primes in P1, showing P1
is infinite.
Answer:
Check the explanation
Step-by-step explanation:
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
ABC Restaurant has an ice-cream counter where it sells two main products, ice cream and frozen yogurt. The restaurant makes a gallon ice cream and yogurt each day, and store has enough freezer space for 115 gallons total of both products. A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs $0.93, and the restaurant has budget of $90 for these products. The manager estimates that the store sells at least twice as much ice cream as frozen yogurt. Profit per gallon of ice cream is $4.15, and profit per gallon is $3.60. Formulate a linear programming model for this problem.
Answer:
sorry i cant
Step-by-step explanation:
my eyes hurt reading this
good luck to whoever solves this
rebecca has 21 cupcakes to frost. She has frosted 2/7 of them. How many cuppcakes does she have left to frost
Answer:
15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
21 * 2/7= 42/7=6 cupcakes that she's already frosted.
21-6=15 cupcakes left to frost.
Hope this helps!
The following table shows the number of comments on each of Omar's 9 most recent social media posts.
Based on this data, what is a reasonable estimate of the probability that Omar's next post will get no
comments?
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The following table shows the number of comments on each of Omar's 9 most recent social media posts.
0 2 8
7 0 0
0 6 4
Based on this data, what is a reasonable estimate of the probability that Omar's next post will get no comments?
Answer:
P(0) = 44.4%
Step-by-step explanation:
We are given the number of comments on each of Omar's 9 most recent social media posts.
We want to find the probability that Omar's next post will have 0 comments.
We know that probability is given by
P(0) = No. of desired outcomes/No. of total outcomes
From the above data we know that total number of outcomes are 9.
Now count the number of times Omar got 0 comments.
These are the desired outcomes. (4 times)
Therefore, the probability of getting 0 comments is
P(0) = 4/9
P(0) = 0.444
P(0) = 44.4%
Answer:
4/9.
Step-by-step explanation:
I know where you get these questions from ;)
From a point on the ground 47ft from the base of a tree, the angle
of elevation to the top of the tree is 35 degrees. Find the height
of the tree to the nearest foot.
Answer:
33 ft
Step-by-step explanation:
In a diagram of the geometry, you see that the angle of elevation is opposite the triangle leg representing the tree height, and is adjacent to the triangle leg representing distance from the tree.
The tangent ratio relates these lengths to the angle:
Tan = Opposite/Adjacent
Opposite = Adjacent×Tan
tree height = (47 ft)tan(35°) ≈ 33 ft
The height of the tree is about 33 feet.
The archway to the entrance of an art gallery can be
modeled by y = -}(x - 5)(x + 5), where x and y
are measured in feet. The x-axis represents the floor.
Find the width of the arch at floor level.
The width of the arch at floor level is 5 feet.
Explanation:The equation given to model the archway to the entrance of an art gallery is y = -}(x - 5)(x + 5). To find the width of the arch at floor level, we need to find the x-values that correspond to y = 0. Setting y = 0 and solving for x, we get:
0 = -}(x - 5)(x + 5)
0 = (x - 5)(x + 5)
Using the zero product property, we can separate the equation into two parts:
x - 5 = 0 and x + 5 = 0
Solving each equation separately, we get:
x = 5 and x = -5
Therefore, the width of the arch at floor level is 5 feet.
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The width of the arch at floor level is the distance between these points, which is 10 feet (5 - (-5) = 10).
The archway to the entrance of an art gallery is modeled by the equation y = -1(x - 5)(x + 5). To find the width of the arch at floor level (y = 0), we need to determine the x-intercepts of the equation.
1. Set y = 0 in the equation: 0 = -1(x - 5)(x + 5).
2. This simplifies to (x - 5)(x + 5) = 0.
3. Setting each factor to zero, we get x - 5 = 0 or x + 5 = 0.
4. Solve these equations for x: x = 5 or x = -5.
The x-intercepts are -5 and 5.
Therefore, the width of the arch at floor level is the distance between these points, which is 10 feet (5 - (-5) = 10).
Which function's graph has axis of symmetry x = 2?
y = 3x² + 12x+6
y = 3x2 - 6x+12
y=-3x2 - 12x+6
y=-3x2 + 12x+6
Answer:
y=-3x2 - 12x+6 , x = -(-12)/2*3 = 2 this one has axis of symmetry x = 2
Step-by-step explanation:
y = 3x² + 12x+6 : x = -12/6 = -2
y = 3x2 - 6x+12 , x = -(-6)/2*3 = -1
y=-3x2 - 12x+6 , x = -(-12)/2*3 = 2 this one
y=-3x2 + 12x+6 , x = -12/2*3 = -2
What is the distance to the Earth's Horizon from point P? Enter enter the decimal in the Box round only your final answer to the nearest tenth.
Answer:
The distance to the Eath's Horizon from point P is 352.8 mi, approximately.Step-by-step explanation:
You observe the problem from a graphical perspective with the image attached.
Notice that side [tex]x[/tex] is tangent to the circle, which means is perpendicular to the radius which is equal to 3,959 mi.
We have a right triangle, that means we need to use the Pythagorean's Theorem, to find the distance to the Earth's Horizon from point P.
The hypothenuse is 3959 + 15.6 = 3974.6 mi.
[tex](3974.6)^{2}=x^{2} +(3959)^{2} \\x^{2} =15,797,445.16 - 15,673,681\\x=\sqrt{123,764.16} \approx 351.8[/tex]
Therefore, the distance to the Eath's Horizon from point P is 352.8 mi, approximately.
A marine surveyor uses a rangefinder and a compass to locate a ship and an island in the vicinity of the coast on which she stands. The rangefinder indicates that the island is 353 ft from her position and the ship is 474 ft from her position. Using the compass, she finds that the ship's azimuth (the direction measured as an angle from north) is 320 degrees and that of the island is 58 degrees. What is the distance between the ship and the island?
Answer:
distance between the ship and the island is 465.72 ft
Step-by-step explanation:
given data
island = 353 ft
ship = 474 ft
ship's azimuth = 320 degrees
island = 58 degrees
to find out
distance between the ship and the island
solution
as per given figure we can see that
AC = 353
AB = 474
we get here angle ABC that is = 360 - 320 = 40 degree
and angle BAC is = 180 - 58 = 122
and now we apply here law sign
so
[tex]\frac{BC}{sinA} = \frac{AC}{sinB}[/tex] ...........1
put here value and we get
[tex]\frac{BC}{sin122} = \frac{353}{sin40}[/tex]
BC = 465.72 ft
so distance between the ship and the island is 465.72 ft
A certain vehicle loses 3.5% of its value each year. If the vehicle has an initial value of $11,168, construct a model that represents the value of the vehicle after a certain number of years. Use your model to compute the value of the vehicle at the end of 6 years.
i can't make a model, but the answer is 11167.79