Answer:
288
Step-by-step explanation:
Answer: 50 children
18 women
22 men
Step-by-step explanation:
There were 90 people at a party. The persons consists of men, women and children. The men and women are adults.
Let m = number of men at the party
Let w = number of women at the party
Let c = number of children at the party
There were four more men than women. It means
w = m - 4
There were 10 more children than adults. It means
m + w + 10 = c
c = m + w + 10
Substituting w = m- 4 into the above equation, it becomes
c = m + m- 4 + 10 = 2m+ 6
Note: adults = sum of men and women
There were 90 people at a party. It means
m + w + c = 90
Substituting c = 2m+6 and w = m-4, it becomes
m + m-4 + 2m+6 = 90
4m = 90 - 18 = 88
m = 88/4= 22
w = m- 4 = 22-4
w = 18
c = 2m + 6 = 44 + 6 = 50
c = 50
Jenny is comparing the cost of two packages of socks.One package has 8 pairs of socks for $12.Another package has 3 pairs of socks for $6.Are the rates equivalent
Answer:
no
Step-by-step explanation:
The second package costs $2 for each pair of socks. If the first package cost that much, it would be 8×$2 = $16 for 8 pairs of socks. That is not the same as $12 for 8 pairs.
__
Another way to look at it is the first package costs twice as much as the second, but has more than twice as many pairs of socks. That means the rates are not equivalent.
Let production be given by P = bLαK1−α where b and α are positive and α < 1. If the cost of a unit of labor is m and the cost of a unit of capital is n, and the company can spend only p dollars as its total budget, then maximizing the production P is subject to the constraint mL + nK = p. Show that the maximum production occurs when L=αp/m and K=(1-α)p/n.
Answer:
The proof is completed below
Step-by-step explanation:
1) Definition of info given
We have the function that we want to maximize given by (1)
[tex]P(L,K)=bL^{\alpha}K^{1-\alpha}[/tex] (1)
And the constraint is given by [tex]mL+nK=p[/tex]
2) Methodology to solve the problem
On this case in order to maximize the function on equation (1) we need to calculate the partial derivates respect to L and K, since we have two variables.
Then we can use the method of Lagrange multipliers and solve a system of equations. Since that is the appropiate method when we want to maximize a function with more than 1 variable.
The final step will be obtain the values K and L that maximizes the function
3) Calculate the partial derivates
Computing the derivates respect to L and K produce this:
[tex]\frac{dP}{dL}=b\alphaL^{\alpha-1}K^{1-\alpha}[/tex]
[tex]\frac{dP}{dK}=b(1-\alpha)L^{\alpha}K^{-\alpha}[/tex]
4) Apply the method of lagrange multipliers
Using this method we have this system of equations:
[tex]\frac{dP}{dL}=\lambda m[/tex]
[tex]\frac{dP}{dK}=\lambda n[/tex]
[tex]mL+nK=p[/tex]
And replacing what we got for the partial derivates we got:
[tex]b\alphaL^{\alpha-1}K^{1-\alpha}=\lambda m[/tex] (2)
[tex]b(1-\alpha)L^{\alpha}K^{-\alpha}=\lambda n[/tex] (3)
[tex]mL+nK=p[/tex] (4)
Now we can cancel the Lagrange multiplier [tex]\lambda[/tex] with equations (2) and (3), dividing these equations:
[tex]\frac{\lambda m}{\lambda n}=\frac{b\alphaL^{\alpha-1}K^{1-\alpha}}{b(1-\alpha)L^{\alpha}K^{-\alpha}}[/tex] (4)
And simplyfing equation (4) we got:
[tex]\frac{m}{n}=\frac{\alpha K}{(1-\alpha)L}[/tex] (5)
4) Solve for L and K
We can cross multiply equation (5) and we got
[tex]\alpha Kn=m(1-\alpha)L[/tex]
And we can set up this last equation equal to 0
[tex]m(1-\alpha)L-\alpha Kn=0[/tex] (6)
Now we can set up the following system of equations:
[tex]mL+nK=p[/tex] (a)
[tex]m(1-\alpha)L-\alpha Kn=0[/tex] (b)
We can mutltiply the equation (a) by [tex]\alpha[/tex] on both sides and add the result to equation (b) and we got:
[tex]Lm=\alpha p[/tex]
And we can solve for L on this case:
[tex]L=\frac{\alpha p}{m}[/tex]
And now in order to obtain K we can replace the result obtained for L into equations (a) or (b), replacing into equation (a)
[tex]m(\frac{\alpha P}{m})+nK=p[/tex]
[tex]\alpha P +nK=P[/tex]
[tex]nK=P(1-\alpha)[/tex]
[tex]K=\frac{P(1-\alpha)}{n}[/tex]
With this we have completed the proof.
determine the intervals on which the function is increasing, decreasing, and constant
Answer:
Step-by-step explanation:
In general, wherever a function is tending from the upper left to the lower right, it is decreasing; wherever a function is tending from the lower left to the upper right it is increasing. Constant functions are horizontal lines.
Our function is tending from upper left to lower right on negative infinity to an x-value of -4. Then it runs as a horizontal line from x values of -4 to +4. Then it tends from lower left to upper right from +4 to infinity.
What is 10x95 Hgghhjkhhhgvfddddddderhfdcfxdgyggggfffffffffffgggfvgvfgvgbbhbbbbbbbnnbnbbbvbvbbb. Hhhhhjhhhbbbbvvvvgvvv chug. Hbvv g vgggyyyhdhggshhrhehergwgegrgwgrgegrttehrhehrhrhehrhrhrhrgrehthehrhehrhhrhrrhrhrhrhrhthehhrhthrhrhrhrhrhrhrhhrrhhdhddhfhfhudhdhdhdhffhhfhfdh
Answer:
Answer is
=950
A book contains 400 pages. If their are 80 typing errors randomly distributed throughout the book, use the Poisson distribution to determine the probability that a page contains exactly 2 errors
Using the Poisson distribution to determine the probability that a page contains exactly 2 errors is 0.0163
Solution:Given that, a book contains 400 pages.
There are 80 typing errors randomly distributed throughout the book,
We have to use the Poisson distribution to determine the probability that a page contains exactly 2 errors.
The Poisson distribution formula is given as:
[tex]\text { Probability distribution }=e^{-\lambda} \frac{\lambda^{k}}{k !}[/tex]
Where, [tex]\lambda[/tex] is event rate of distribution. For observing k events.
[tex]\text { Here rate of distribution } \lambda=\frac{\text { go mistakes }}{400 \text { pages }}=\frac{1}{5}[/tex]
And, k = 2 errors.
[tex]\begin{array}{l}{\text { Then, } \mathrm{p}(2)=e^{-\frac{1}{5}} \times \frac{\frac{1}{5}}{2 !}} \\\\ {=2.7^{-\frac{1}{5}} \times \frac{\frac{1}{5^{2}}}{2 \times 1}} \\\\ {=\frac{1}{2.7^{\frac{1}{5}}} \times \frac{\frac{1}{25}}{2}}\end{array}[/tex]
[tex]\begin{array}{l}{=\frac{1}{\sqrt[5]{2.7}} \times \frac{1}{25} \times \frac{1}{2}} \\\\ {=\frac{1}{50 \sqrt[5]{2.7}}} \\\\ {=0.0163}\end{array}[/tex]
Hence, the probability is 0.0163
A total of $150000 is invested in two funds paying 6.25% and 6% simple interest. If the total interest for the year is $9212.50, how much is invested at each rate?
Answer:
$85,000 at 6.25%$65,000 at 6.00%Step-by-step explanation:
Let x represent the amount invested at 6.25%. Then the total interest earned is ...
0.0625x + 0.0600(150,000 -x) = 9212.50
0.0025x = 212.50 . . . . . . subtract 9000, collect terms
x = 212.50/0.0025 = 85,000
150,000 - 85,000 = 65,000 . . . . amount invested at the lower rate
$85,000 is invested at 6.25%; $65,000 is invested at 6%.
25 gallons of milk for $56 Target sells 15 gallons of milk for 32.05 dollars give the unit rate for both groceries stores and determine which store has the better deal
Answer:
Step-by-step explanation:
25 gallons of milk for $56
We would need to determine the unit rate for a gallon of milk in this particular store.
If 25 gallons of milk for $56
Then 1 gallon of milk would cost
56/25 = 2.24
Target sells 15 gallons of milk for 32.05 dollars
We would also to determine the unit rate for a gallon of milk in this particular store.
If 15 gallons of milk for $32.05
Then 1 gallon of milk would cost
32.05/15 = 2.137
The unit cost of a gallon of milk at target provides a better deal because it has a lower unit cost than the other
Find the x-intercepts of the function graphed below, and the average rate of change over the interval (-1,4).
x-intercepts:____
Average rate of change:____
Answer:
x-intercepts: -2; 1; 5
Average rate of change: 1.8
Step-by-step explanation:
x- intercepts as per graph are:
-2; 1; 5Average rate of change over the interval (-1, 4) is:
Δy/Δx = (y(4) - y(-1))/(4 - (-1)) = (3 - (-6))/5 = 9/5 = 1.8If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35 ?A) 33B) 28C) 27D) 24E) 23
Answer:
First quartile list of number median is 23
Step-by-step explanation:
List of numbers = 42,24, 30 , 22 , 26, 19, 33, 35
Arrange them in a sequence:
List of numbers = 19, 22, 24, 26, 30, 33, 35, 42
The median of {19, 22, 24, 26, 30, 33, 35, 42} is= 26+30/2 = 28
Numbers that are less than the median are { 19 , 22 , 24 , 26}
then
median of the list = 22+24/2 = 23
So the first quartile list of number median is 23.
The median of the first quartile list is 23.
The given set of numbers {42, 24, 30, 22, 26, 19, 33, 35} can be arranged in ascending order as follows:
{19, 22, 24, 26, 30, 33, 35, 42}.
The median of this sequence is calculated as (26 + 30) / 2, resulting in 28.
The numbers less than the median are {19, 22, 24, 26}.
Next, the median of this subset is found by taking (22 + 24) / 2, yielding 23. Therefore, the median of the first quartile list is 23.
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Leilani rides her bike for exercise and drinks 70 ounces of water each day in order to stay hydrated before her morning ride she drinks 14 ounces of water leilani wants to know what percent of her daily amount of water she has before her ride
Answer: 20%
Step-by-step explanation:
The total amount of water that Leilani drinks throughout is 70 ounces each day. This means that before and after the ride, she drinks a total of 70 ounces daily
in order to stay hydrated before her morning ride she drinks 14 ounces of water.
To determine what percent of her daily amount of water she has before her ride, we would divide the amount she takes before ride by the total daily amount of water and multiply by 100. It becomes
14/70 × 100 = 20%
Answer:
20
Step-by-step explanation:
A researcher predicts that a special training course will be highly effective for females but will have little or no effect for males. This researcher is predicting an interaction between training and gender.True / False.
The researcher's prediction of an interaction between training and gender is true. An interaction occurs when the effect of one variable on an outcome depends on the level of another variable.
Explanation:The researcher's prediction of an interaction between training and gender is True.
An interaction occurs when the effect of one variable on an outcome depends on the level of another variable. In this case, the researcher predicts that the training course will have a different effect on females compared to males.
For example, if the researcher conducts a study where both males and females participate in the training course, and finds that females benefit significantly from the course while males do not, this would support the researcher's prediction of an interaction between training and gender.
Matt has a 5lb bag of apples to make a pie he needs to use 3/5 of the bad how many pounds of apples we use for the pie explain what a model for this problem might look like
Answer:
Pounds of apple to be used for a pie = 3 lb
Step-by-step explanation:
Given the bag contains apples weighting = 5 lb
To make a pie [tex]\frac{3}{5}[/tex] of the apples in the bag is used.
To find the pounds of apples to be used to make a pie we will have to find the [tex]\frac{3}{5}[/tex]th part of 5 lb of apples.
In order to do that we multiply the fraction to the total weight of apples.
Pounds of apple to be used to make a pie
⇒ [tex]\frac{3}{5}\ of\ total\ pounds\ of\ apple[/tex]
⇒ [tex]\frac{3}{5}\times 5[/tex]
⇒ [tex]3[/tex]
∴ Pounds of apple to be used for a pie = 3 lb
What is the measurement of RT?
Answer:
65
Step-by-step explanation:
What would be an appropriate measure to describe the diameter of a music record?
A) millimeters
B) yards
C) Inches
D) kilometers
The Answer is C) Inches
Answer the correctly fast please I need it right now please show work
Answer:
d) 4(s + 4.5) and (s + 4.5) + (s + 4.5) + (s + 4.5) + (s + 4.5)
Step-by-step explanation:
since you know that one side is (s+4.5) and a square has 4 congruent sides the answer would be 4(s + 4.5) and (s + 4.5) + (s + 4.5) + (s + 4.5) + (s + 4.5)
Answer:
The correct answer is D
Step-by-step explanation:
Step one :
The perimeter of a square is the sum of all four sides given a side as
(s+4.5)+(s+4.5)+(s+4.5)+(s+4.5)
Or
Step 2:
(s+4.5)+(s+4.5)+(s+4.5)+(s+4.5)
Opening bracket we have
s+4.5+s+4.5+s+4.5+s+4.5
Summing all "s'" terms
(4s+18)
4(s+4.5)
The distance that a spring will stretch varies directly as the force applied to the spring. A force of 8080 pounds is needed to stretch a spring 88 inches. What force is required to stretch the spring 1919 inches? A nothing-pound force is required to stretch the spring 1919 inches.
Answer:
176 199 pounds
Step-by-step explanation:
To answer this it is first useful to find the proportionality constant.
F= kx
8080 pounds = k.88 in
k = 91.81 pound/inch
So what force is required to stretch the spring to 1919 inches?
F = kx
= 91.81 pound/inch * 1919 inches
= 176 199 pounds
It is worth noting that this force seems rather large and the spring might have long reached its elastic limit
The designer also programs a bird with a path that can be modeled by a quadratic function. The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8). What is the slope of the line that represents the turtle's path?
Answer:
-1.2
Step-by-step explanation:
Given that the designer also programs a bird with a path that can be modeled by a quadratic function.
The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8).
If we treat this curve as line joining these two points then we can find the slope by the formula
Slope = change in y coordinate/change in x coordinate
Here the points given are
(0,20) and (10,8)
[tex]Change in y coordinate = 8-20 = -12\\Change in x coordinate = 10-0 = 10\\Slope = -1.2[/tex]
Slope of the line that represents the turtle's path
=-1.2
Answer: 0.8
Step-by-step explanation: i got it right on edg
second part to the question is
h= 0
k= 20
a= -0.12
third part is letter B
99 POINTS!
Find the standard deviation for the binomial distribution.
n=21; p=0.2
A) 1.83
B) 5.95
C) -0.58
D) 5.10
Standard deviation = √(n * p * q)
You are given n and p
q = 1 - p
q = 1 -0.2 = 0.8
Standard deviation = √(21 * 0.2 * 0.8)
=√3.36 = 1.83
The answer is A.
The standard deviation for a given binomial distribution [tex]n[/tex] and [tex]p[/tex] would be the following:
[tex]\sigma=\sqrt{n \times p \times q}[/tex]
The variable [tex]q[/tex] is equivalent to [tex](p-1)[/tex]
[tex]=\sqrt{n\times p\times(p-1)}[/tex]
Substitute the values of [tex]p[/tex] and [tex]n[/tex] into the equation
[tex]=\sqrt{21\times0.2\times(1-0.2)}[/tex]
[tex]=\sqrt{21\times0.2\times0.8}[/tex]
Use a calculator to solve for this square root since it would be too hard and complicated to do by hand
[tex]=1.83303027798...[/tex]
Round this to the nearest hundredths place since all answer choices are rounded like that
[tex]=1.83[/tex]
Thus, the answer is choice A. Let me know if you need any clarifications, thanks!
~ Padoru
A bowl in the shape of a hemispere is filled with water to a depth h=3 inches. The radius of the bowl is R inches. Express the radius of the bowl R as a function of the angle theta.
The radius of the bowl R as a function of the angle theta is [tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]
Solution:
The figure is attached below
If we consider the centre of hemisphere be A
The radius be AC and AD
According to question,
A bowl in the shape of a hemispere is filled with water to a depth h=3 inches .i.e. BC = h = 3 inches
And radius of the bowl is R inches .i.e. R = AD =AC
Now , using trigonometric identities in triangle ABD we get
[tex]\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{A B}{A D}[/tex]
[tex]\begin{array}{l}{\sin \theta=\frac{A B}{R}} \\\\ {A B=R \sin \theta}\end{array}[/tex]
Since , AC = AB + BC
R = R Sinθ + 3
R - R Sinθ = 3
R (1 – Sinθ ) = 3
[tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]
Which is the required expression for the radius of the bowl R as a function of the angle theta
Which of the following lists is not in order from smallest to largest?
The Answer choices are ; The correct answer choice is ; 2.33, 1.87, 3.6, 7.1
10.1, 10.5, 11.2, 12.9 - False
------------------------------
2.33, 1.87, 3.6, 7.1 - Correct
---------------------------
0.5, 1.3, 2.6, 3.8 - False
-------------------------------------
4.75, 4.8, 4.92, 5 - False
Answer: 2.33, 1.87, 3.6, 7.1
Step-by-step explanation:
2.33, 1.87, 3.6, 7.1 is not arranged from smallest to the largest. Arranging the number will be 1.87, 2.33, 3.6, 7.1.
Answer:
B. 2.33, 1.87, 3.6, 7.1
Step-by-step explanation:
This option is not in order from smallest to largest.
Hope it helped!
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? requals=negative 0.387
Answer:
Coefficient of determination = 0.149769
Step-by-step explanation:
We are given the following in the question:
Coefficient of correlation, r = -0.387
We have to find the coefficient of determination.
Coefficient of determination =
[tex]r^2 = (-0.387)^2 = 0.149769 = 14.98\%[/tex]
Coefficient of determination:
It tells us about the variation explained in the model.This correlation of determination tells that 14.98% of the variation is explained in the model that is we can say that the independent variable explains 14.98% changes or prediction in the dependent variable.It ranges from 0 to 1 and a correlation of determination of 1 means that the dependent variable is 100% predicted by the independent variable.Correlation of determination of 0 means that the dependent variable cannot be predicted by the independent variable.Consider a credit card with a balance of $8500 and an APR of 15.99%. In order to pay off the balance in 3 years, what monthly payment would you need to make?
To pay off a $8500 credit card balance with a 15.99% APR in 3 years, you would need to make monthly payments of approximately $293.12.
To determine the monthly payment needed to pay off a credit card balance of $8500 with an APR of 15.99% in 3 years, you can use the formula for calculating monthly payments on a fixed-rate loan. The formula is:
[tex]\[ M = P \times \frac{r(1+r)^n}{(1+r)^n-1} \][/tex]
where:
- [tex]\( M \)[/tex] is the monthly payment,
- [tex]\( P \)[/tex] is the principal balance (credit card balance),
- [tex]\( r \)[/tex] is the monthly interest rate (annual interest rate divided by 12 and converted to decimal),
- [tex]\( n \)[/tex] is the total number of payments (number of months).
First, convert the annual interest rate to a decimal: [tex]\( 15.99\% = 0.1599 \).[/tex]
Next, calculate the monthly interest rate: [tex]\( r = 0.1599 / 12 = 0.013325 \).[/tex]
Now, plug in the values into the formula:
[tex]\[ M = 8500 \times \frac{0.013325(1+0.013325)^{3 \times 12}}{(1+0.013325)^{3 \times 12}-1} \][/tex]
After performing the calculations, the monthly payment [tex](\( M \))[/tex] is approximately $293.12.
The money multiplier _______. A. decreases if banks increase their desired reserve ratio B. is 1 if the desired reserve ratio equals the currency drain ratio C. increases if the currency drain ratio increases D. increases if banks increase their desired reserve ratio
Answer:
A. decreases if banks increase their desired reserve ratio
Step-by-step explanation:
Since, the money multiplier is the amount of money produced by banks with each dollar of reserves,
In other words,
It estimates, how an initial deposit can lead to a bigger final increase in the total money supply.
For example :
If a commercial bank gains deposits of 1 crore and this leads to a final money supply of 10 crore, the money multiplier would be 10.
That is,
[tex]\text{Money multipliers}=\frac{1}{\text{Reserve ratio}}[/tex]
[tex]\implies \text{Money multipliers}\propto \frac{1}{\text{Reserve ratio}}[/tex]
Therefore, the money multiplier decreases if banks increase their desired reserve ratio
The money multiplier decreases when banks increase their desired reserve ratio, as they lend out less money, reducing the multiplier effect.
The money multiplier is a key concept in understanding how the banking system can increase the money supply within an economy. It is defined as the quantity of money that the banking system is able to generate from each dollar of bank reserves. The question relates the behavior of the money multiplier in response to changes in the reserve ratio and the currency drain ratio.
Answering the student's query, the money multiplier decreases if banks increase their desired reserve ratio because as they keep more reserves relative to deposits, they can lend out less money, effectively reducing the multiplier effect. Conversely, when banks decrease their reserve ratio, they can lend out a larger proportion of their deposits, which leads to an increase in the money multiplier. Therefore, the correct option is A: decreases if banks increase their desired reserve ratio.
If a and b are positive numbers, find the maximum value of f(x)=xa(1−x)b, 0≤x≤1 Your answer may depend on a and b.maximum value =________.
To find the maximum value of f(x) = xa(1−x)b, use calculus to find the derivative of f(x), set it equal to 0, and solve for x to find the critical points. Evaluate f(x) at the critical points and the endpoints of the interval to find the maximum value.
Explanation:To find the maximum value of f(x) = xa(1−x)b, we can use calculus. First, find the derivative of f(x) with respect to x: f'(x) = a(1 - x)b - bx(1 - x)b-1. Set the derivative to 0 and solve for x to find the critical points. The maximum value of f(x) occurs at one of these critical points or at the endpoints of the interval [0, 1]. Plug the values of x into f(x) to find the corresponding maximum values.
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To find the maximum value of f(x)=xa(1−x)b, where a and b are positive numbers and 0≤x≤1, we need to find the critical points by finding when the derivative of the function is equal to zero or does not exist. Then, we evaluate the function at the critical points and the endpoints to determine the maximum value.
Explanation:To find the maximum value of the function f(x)=xa(1−x)b, where a and b are positive numbers and 0≤x≤1, we need to determine when the function reaches its maximum. This can be done by finding the critical points, which occur when the derivative of the function is equal to zero or does not exist.
First, let's find the derivative of f(x):
f'(x) = a(1-x)^{b-1}(bx - (b-1)x -1).
To find the critical points, we set f'(x) = 0 and solve for x.
Solving the equation, we find that the critical point occurs when x = \frac{b}{2b-1}.
Next, we evaluate f(x) at the critical point x = \frac{b}{2b-1} and also at the endpoints x = 0 and x = 1. The maximum value of f(x) will be the largest value among these.
Finally, we compare the values to find the maximum value.
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A circular track is 1/4 mile long. Elena runs on this track, completing each lap in 1/20 of an hour. What is Elena's speed? Include the unit of measure
Answer:
5 mph
Step-by-step explanation:
The relation between speed, distance, and time is ...
speed = distance/time
Filling in the given values, we find the speed to be ...
speed = (1/4 mi)/(1/20 h) = (1/4)(20/1) mi/h = 5 mi/h
Elena's speed is 5 miles per hour.
Esteban has 236 trading cards that he wants to put in storage boxes.Each box holds 18 trading cards. If he puts 18 trading cards in every box, how many trading cards will be left over
Divide the total cards by 18:
236 / 18 = 13.111
Use the whole number and multiply by 18:
13 x 18 = 234
This means 234 cards would be in storage boxes.
236 - 234 = 2 cards would be left over.
What is the value of x to the nearest foot?
Answer:2097
Step-by-step explanation: it is that it the answer plz trust me
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The value of x in the given triangle is equal to 2097 ft by calculating through trigonometric ratios.
What are trigonometric ratios?These are ratios which are expressed as the ratio of sides of a right angled triangle.
How to find a side of right angled triangle?In the given triangle the hypotenuse is 3750 and x is the perpendicular of the triangle.
We have to use sin to calculate because it expresses the ratio of perpendicular and hypotenuse.
sin34°=x/3750
0.5591=x/3750
x= 2096.625
x=2097 approx.
Hence the value of x in the given right angled triangle is 2097 ft.
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Consider the function represented by the equation 6c = 2p – 10. Write the equation in function notation, where c is the independent variable. F(c) = one-thirdp + five-thirds f(c) = 3c + 5 f(p) = one-thirdp + five-thirds f(p) = 3c + 5
Answer:
f(c) = 3c + 5
Step-by-step explanation:
c is independent variable, p is dependent variable, so p = f(c)
6c = 2p -10
3c = p - 5
p = 3c + 5
f(c) = 3c + 5
Answer:
F(c) = 3c +5
Step-by-step explanation:
6c=2p-10
If c is considered to be as the independent variable, then p is the dependent variable
So we will clear and solve for variable p
6c = 2p-10
Dividing both sides by 2. We will have
6c/2 = 2(p-5)/2
3c= p-5
Adding 5 on both sides
3c+5= p
So p =3c+5
By writing the above equation in the functional notation form
F(c) = 3c +5
Which choice could be the equation of a line perpendicular to the line represented by this equation?y = 5x− 2A.B.y = 5x +2C.D.y = −5x + 5
Answer:
5y = -× + c
Step-by-step explanation:
If two lines are perpendicular, the product of their gradient equals -1.
We should note that the general equation of a line is y = mx + c, where m is the gradient.
For the line y = 5x - 2 , the slope is 5. The line that will be perpendicular to this line will have a slope of -1/5.
A line like 5y = -x + c fits the description
simplify the rational expression. state any excluded values.
x^2-3x-10/x+2
Answer:
The answer to your question is x - 5 or x = 5
Step-by-step explanation:
[tex]\frac{x^{2} -3x - 10}{x + 2}[/tex]
1.- Factor the numerator
x² - 3x - 10
find 2 numbers that added equal -3 and multiply equal -10.
These numbers are -5 and + 2
(x - 5)(x + 2)
2.- Simplify
[tex]\frac{(x - 5)(x + 2)}{x + 2)}[/tex]
Delete (x +2) in both numerator and denominator
3.- Result x - 5
x = 5