Let's use the combination formula:
[tex]\begin{gathered} C(n,k)=nCk=\frac{n!}{k!(n-k)!} \\ n=53 \\ k=3 \\ C(53,3)=53C3=\frac{53!}{3!(50)!}=23426 \end{gathered}[/tex]Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 29 L per minute. There are 400 L in the pond to start. Let W represent the total amount of water in the pond (in liters) and let T represent the total number of minutes that water has been added.Write an equation relating W to T. Then use this equation to find the total amount of water after 13 minutes.Equation : Total amount of water after 13 minutes : liters
In this problem, we have a linear equation of the form
W=mT+b ----> equation in slope-intercept form
where
m is the unit rate or slope of the linear equation
m=29 L/min ----> given
b is the initial value
b=400 L ----> given
substitute
W=29T+400 -------> equation relating W to T.For T=13 min
substitute
W=29(13)+400
W=777 L
the total amount of water after 13 minutes is 777 Lthe population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the pop ulation in 30 years? how fast is the population growing at t 30?
Using the differential equation, the population after 30 years is 760.44.
What is meant by differential equation?In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions. Applications frequently involve a function that represents a physical quantity, derivatives that show the rates at a differential equation that forms a relationship between the three, and a function that represents how those values change.A differential equation is one that has one or more functions and their derivatives. The derivatives of a function define how quickly it changes at a given location. It is frequently used in disciplines including physics, engineering, biology, and others.The population P after t years obeys the differential equation:
dP / dt = kPWhere P(0) = 500 is the initial condition and k is a positive constant.
∫ 1/P dP = ∫ kdtln |P| = kt + C|P| = e^ce^ktUsing P(0) = 500 gives 500 = Ae⁰.
A = 500.Thus, P = 500e^ktFurthermore,
P(10) = 500 × 115% = 575sO575 = 500e^10ke^10k = 1.1510 k = ln (1.15)k = In(1.15)/10 ≈ 0.0140Therefore, P = 500e^0.014t.The population after 30 years is:
P = 500e^0.014(30) = 760.44Therefore, using the differential equation, the population after 30 years is 760.44.
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Rierda Elwynn Garvey takes home $1250 each month. In addition to other expenses, she also makepayments to her debt of $230 per month. What is her Debt Payments to Income Ratio?
The debt payments to income ratio is the amount that Rierda spend paying her debt each mount divided by her monthly income:
[tex]\text{Ratio}=\frac{230}{1250}=\frac{23}{125}=0.184[/tex]Lee Ann is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, five appetizers, and three desserts, but she doesn't not have time to cook. She can choose from 9 bottle drinks, 9 Frozen appetizers, and 12 prepared desserts at the supermarket. How many different ways can lie and pick up the food and drinks to serve at the bridal shower?
2328480 ways
ExplanationWe want to find out how many ways there are to select an item. The combination formula is a formula to find the number of ways of picking "r" items from a total of "n" items.
This number is given by:
[tex]undefined[/tex]Steel bars shrink 8% when cooled from furnace temperature to room temperature. If a cooled steel bar is 46 in. long, how long was it when it was formed?The steel bar was __ in. long when it was formed.(Round to the nearest whole number as needed.)
Answer:
50 inches
Explanation:
Let the length of the steel bar when it was formed = y
Steel bars shrink 8% when cooled from furnace temperature to room temperature.
[tex]\begin{gathered} \text{Room Temperature Length}=(100-8)\%\text{ of y} \\ =92\%y \\ =0.92y \end{gathered}[/tex]Given that a cooled steel bar is 46 in. long, then:
[tex]0.92y=46[/tex]Divide both sides by 0.92.
[tex]\begin{gathered} \frac{0.92y}{0.92}=\frac{46}{0.92} \\ y=50\;in. \end{gathered}[/tex]The steel bar was 50 in. long when it was formed.
12. Suppose you roll a pair of six-sided dice.(a) What is the probability that the sum of the numbers on your dice is exactly 4? (b) What is the probability that the sum of the numbers on your dice is at most 2? (c) What is the probability that the sum of the numbers on your dice is at least 12?
Probability is computed as follows:
[tex]\text{probability}=\frac{\text{ number of favorable outcomes}}{\text{ total number of outcomes}}[/tex]When rolling a pair of six-sided dice, the total number of outcomes is 36 (= 6x6)
(a) number of favorable outcomes: 3 (dice: 1 and 3, 2 and 2, 3 and 1)
Then, the probability that the sum of the numbers on your dice is exactly 4 is:
[tex]\text{probability }=\frac{3}{36}[/tex](b) number of favorable outcomes: 1 (dice: 1 and 1)
Then, the probability that the sum of the numbers on your dice is at most 2 is:
[tex]\text{probability }=\frac{1}{36}[/tex](c) number of favorable outcomes: 1 (dice: 6 and 6)
Then, the probability that the sum of the numbers on your dice is at least 12 is:
[tex]\text{probability }=\frac{1}{36}[/tex]Solve x^2 - 3x - 10 = 0 by factoring. *Mark only one oval.O {-5,2}O (-2,-5)O {-2,5}○ {-10,1}
In order to solve this quadratic equation by factoring, we can do the following steps:
[tex]\begin{gathered} x^2-3x-10=0\\ \\ x^2-3x-5\cdot2=0\\ \\ x^2+2x-5x-5\cdot2=0\\ \\ x(x+2)-5(x+2)=0\\ \\ (x-5)(x+2)=0\\ \\ \begin{cases}x-5=0\rightarrow x=5 \\ x+2=0{\rightarrow x=-2}\end{cases} \end{gathered}[/tex]Therefore the solution is {-2, 5}. Correct option: third one.
Find the value of z that makes quadrilateral EFGH a parallelogram.2zz+10FEHGz=Submit
In a parallelogram opposite sides have the same length therefore, for figure EFGH to be a parallelogram we must have that:
[tex]GF=HE[/tex]Substituting we get:
[tex]z+10=2z[/tex]Now, we solve for "z". First, we subtract "z" from both sides:
[tex]\begin{gathered} z-z+10=2z-z \\ 10=z \end{gathered}[/tex]Therefore, the value of "z" is 10.
Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Answer:
x+121=225
Step-by-step explanation:
√x+11=15
to find the equivalent let's square both sides
(√x)²+11²=15²
x+121=225
This answer is the only one that matches the question
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Solve 7x-2y = 17 for y
hello
the question here is an equation and we are asked to solve for y
we'll follow some steps here
[tex]7x-2y=17[/tex]step 1
take y to the left side of the equation and bring 17 to the right hand side of the equation
note: the sign changes once they cross equality sign
[tex]\begin{gathered} 7x-2y=17 \\ 7x-17=2y \end{gathered}[/tex]step 2
divide both sides by the coeffiecient of y which is 2
[tex]\begin{gathered} 2y=7x-17 \\ \frac{2y}{2}=\frac{7x-17}{2} \\ y=\frac{7x-17}{2} \end{gathered}[/tex]from the calculations above, the value of y = (7x - 17)/2
PLEASE HELP
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 25o. From a point 1,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 29o. How tall (in feet) is the mountain? Round to two decimal places.
The height of the mountain is 2936.39 feet.
Given,
In the question:
The angle of elevation to the top of the mountain is 25°.
To find the height of the mountain, we can draw triangles as in the image attached.
Now, According to the question:
Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(29) = h/x
tan(25) = h/(x+1000)
tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:
h/x = 0.5543 -> x = h/0.5543
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.5543 + 1000) = 0.4663
h = 0.4663 * (h/0.5543 + 1000)
h = 0.8412h + 466.3
0.1588h = 466.3
h = 466.3 / 0.1588 = 2936.39 feet
Hence, the height of the mountain is 2936.39 feet.
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Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor I v Figure IJKE congruent to Figure TUVW because rigid motions be used to map Figure IJRL onto Figure TUVW. Figure IJKE dilations similar to Figure TUVW because rigid motions and/or be used to map Figure IJKL onto Figure TUVW.
Figure IJKL is congruent to Figure TUVW because rigid motions can be used to map Figure IJKL onto Figure TUVW
Figure IJKL is similar to Figure TUVW because rigid motions and/or dilations can be used to map Figure IJKL onto Figure TUVW
Since the figures are congruent, the scale factor is 1
calculate the surface area of a hollow cylinder which is closed at one end if the base radius is 3.5 cm and the height is 8 cm
Answer:
A=2πrh+2πr2=2·π·3.5·8+2·π·3.52≈252.89821cm²
The surface area is 214.305cm².
What is surface area?The surface area is the area of the outer covering of the object.
It is given that radius, r=3.5 cm, and height, h=8 cm.
The surface area of the given object will be the sum of curved surface area and the area of the bottom, which is circle.
Surface Area = Curved Surface Area + Area of bottom circle
=2πrh+πr²
=2π(3.5)(8)+π(3.5)²
=56π+12.25π
=68.25π
Substitute π=3.14 to determine the surface area.
Surface Area = 68.25(3.14)
=214.305
So, the surface area will be 214.305cm².
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Which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
In general, a function f(x) means that the input is x and the output is f(x) (or simply f).
Therefore, in our case, the input is the length of the race and the outcome is the time.
The better option is Time(length), option A.assume the rate of inflation is 7% per year for the next 2 years. what will be the cost of goods 2 years from now adjusted for inflation if the goods cost $330.00 today? round to the nearest cent
To find the cost of the goods after two years we are going to use the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the cost now, r is the inglation rate in decimal form, n is the number of times the interest is taken per year and t is the time.
In this case we have P=$300.00, r=0.07, n=1 (once per year) and t=2 (two years). Plugging this values we have:
[tex]A=330(1+\frac{0.07}{1})^{1\cdot2}=377.82[/tex]Therefore after two years the cost will be $377.82
What should you do to finish solving this equation?6y + 4y + 90 = 36010y + 90 = 360Add 90 then divide by 102 subtract 90 then multiply by 10Add 10 then multiply by 904Subtract 90 then divide by 10O 102O 304h
answer is substract 90 then divide by 10
Finding Slope
HELP ME PLS
The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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98) Cost to store: $145Markup: _?Selling price:$319.
Answer: Mark up is 220%
Cost to store : $145
selling price = $319
let x = mark up
Using the below equation
[tex]\begin{gathered} \text{Part = whole x percentage} \\ \text{part = selling price} \\ \cos t\text{ to store = whole} \\ \text{Mark up = percentage} \\ 319\text{ = 145 }\cdot\text{ x\%} \\ \text{ x\% = }\frac{319}{145}\text{ x 100\%} \\ x\text{ = 2.2 x 100\%} \\ x\text{ = 220\%} \\ \text{Therefore, the mark up is 220\%} \end{gathered}[/tex]A study is done on the number of bacteria cells in a petri dish. Suppose that the population size P(1) after t hours is given by the following exponential function.P (1) = 2000(1.09)Find the initial population size.Does the function represent growth or decay?By what percent does the population size change each hour?
Given:
the population size P(1) after t hours is given by the following exponential function:
[tex]P(1)=2000(1.09)[/tex]Find the initial population size?
The initial size = 2000
Does the function represent growth or decay?
Growth, Because the initial value multiplied by a factor > 1
By what percent does the population size change each hour?
The factor of change = 1.09 - 1 = 0.09
So, the bacteria is increasing by a factor of 9% each hour
Choose the correct equation in point slope form for the line through the given points or through the given point with the given slope
Answer:
[tex]y-3=-1(x+2)[/tex]Explanation:
The point-slope form of the equation of a line is generally given as;
[tex]y-y_1=m(x-x_1)[/tex]where m = the slope of the line
y1 = y-coordinate of the one point
x1 = x-coordinate of the one point
Given the slope of the line as m = -1 and the point (-2, 3) where x1 = -2 and y1 = 3, let's go ahead and substitute these given values into the point-slope formula to obtain the required equation as seen below;
[tex]\begin{gathered} y-3=-1\lbrack x-(-2)\rbrack \\ y-3=-1(x+2) \end{gathered}[/tex]At a local market, 3 apples and 2 pears cost $2.70. Three apples cost the same as 4 pears. Type a system of equations to find the cost for one apple and the cost for one pear.
Data:
Apple: A
Pears: P
3A+2P=$2.70
3A=4P
to find the cost for one apple:
Simplify. 3 6 4 2m n 4 6m Write your answer using only positive exponents. . X Х ?
we have the expression
[tex](\frac{2m^6n^4}{6m^4})^3[/tex][tex](\frac{2m^6n^4}{6m^4})^3=\frac{(2^3)(m^{(18)})(n^{(12)})}{(6^3)(m^{(12)})}[/tex]simplify
[tex]\frac{(8)(m^{(18-12)})(n^{(12)})}{216}=\frac{(m^6)(n^{(12)})}{27}[/tex]Lne segment AC and BD are parallel, what are the new endpoints of the line segments AC and BD if the parallel lines are reflected across the y-axis?
Given a point P = (x, y) a reflection P' alongside the y axis of that point follows the rule:
[tex]P=(x,y)\Rightarrow P^{\prime}=(-x,y)[/tex]We need to multiply the x coordinates of the points by (-1)
The cordinates of the points in the problem are:
A = (2, 5)
B = (2, 4)
C = (-5, 1)
D = (-5, 0)
Then the endpoints of the reflection over the y axis are:
A' = (-2, 5)
B' = (-2, 4)
C' = (5, 1)
D' = (5, 0)
Which is the second option.
if cos ∅=sin 46° find ∅
Answer:
∅ = 44°
Step-by-step explanation:
cos∅ = sin46°
∅ = (90 - 46)°
∅ = 44°
Hope this helps
Consider the following functions. Find the domain. Express your answer in interval notation.
Explanation:
[tex]\begin{gathered} f(x)\text{ = - }\sqrt[]{6-x} \\ g(x)\text{ = 4 - x} \\ (g\text{ - f)(x) = g(x) - f(x)} \end{gathered}[/tex][tex]\begin{gathered} (g\text{ -f)(x) = }4-\text{ x - (-}\sqrt[]{6\text{ - x}}) \\ (g\text{ -f)(x) = 4 - x + }\sqrt[]{6-x} \end{gathered}[/tex][tex]undefined[/tex]in a 30 60 90° triangle giving the short leg equals 5 find a hypotenuse of the triangle
To answer this question we need to remember that the longest and shortest side in any triangle are always opposite to the largest and smallest angle, respectively.
With this in mind we can draw the triangle:
Now, we need to find the hypotenuse. To do this we can use the cosine function for the angle 60. Remember that the cosine function is given as:
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]In this case we have that:
[tex]\begin{gathered} \cos 60=\frac{5}{\text{hyp}} \\ \text{hyp}=\frac{5}{\cos 60} \\ \text{hyp}=10 \end{gathered}[/tex]Therefore the hypotenuse is 10.
the table shows the number of miles people in the us traveled by car annually from 1975 to 2015
In the year 2022, the predicted number of miles of travels would be 3.601 trillion miles.
What is a model?
The term model has to do with the way that we can be able to predict the interaction between variables. In this case, we can see that there is a line of best fit as we can see from the complete question which is in the image that have been attached to his answer.
The question is trying to find out the number of miles that people are going to travel in the year 2022 based on the line of best fit that have been given in the question that we have attached here.
We know that; y = 0.048x + 1.345. Recall that x here stands for the number of years that have passed since the year 1975. We now have 47 years passed since 1975 thus;
y = 0.048(47) + 1.345
y = 3.601 trillion miles
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Simplify the expression.9n+ 18(2n-6)
The given expression is,
[tex]\begin{gathered} 9n+18(2n-6) \\ 9n+36n-108 \\ \\ 45n=108 \end{gathered}[/tex]Solve the quadratic equation by completing the square.x^2+18x+75=0First choose the appropriate form and fill in the blanks with the with the correct numbers. Then solve the equation. If there is more than one solution, separate them with commas.
we have the quadratic equation
x^2+18x+75=0
complete the square
x^2+18x=-75
x^2+18x+81=-75+81
x^2+18x+81=6
rewrite as perfect squares
(x+9)^2=6
Find out the solutions
square root both sides
[tex]x+9=\pm\sqrt[\square]{6}[/tex][tex]x=-9\pm\sqrt[\square]{6}[/tex]The first solution is
[tex]x=-9+\sqrt[\square]{6}[/tex]The second solution is
[tex]x=-9-\sqrt[\square]{6}[/tex]hi, can you help me answer this question please, thank you!
The correct option is B
Explanation:The given statement shows that there is a 95% chance that the mean of a sample of 29 gadgets will be between 12.8 and 34.9
