Answer:
in four (4) ways 4 people can be selected
There is a triangular number that has 55 dots in its shape. Which one is it? Write your answer as a number.
The triangular number that has 55 dots in its shape is the
-th triangular number.
9514 1404 393
Answer:
10
Step-by-step explanation:
The n-th triangular number is given by ...
t(n) = n(n+1)/2
We went to find n when t(n) = 55.
55 = n(n+1)/2
110 = n(n+1)
Adding 1/4 completes the square.
110.25 = (n +0.5)^2
√110.25 = n+0.5 . . . . . we are interested in the positive value of n
n = 10.5 -0.5 = 10
The triangular number that has 55 dots in its shape is the 10-th number.
__
Additional comment
Here, we have gone to the trouble to formally complete the square to find the value of n. You may realize that it isn't really necessary to go to that trouble.
A reasonable estimate of the value of n is possible by considering that the product n(n+1) is a little more than n², so the value of n will be a little less than √110 ≈ 10.49. The nearest integer is 10, which is the answer we're looking for.
find c.round to the nearest tenth
Answer:
we need a picture...
Step-by-step explanation:
. Mildred bought an old
necklace and pair of earrings
while at an antique show. If
the cost of the jewelry is ]
and tax is 7%, which of the
following equations could be
used to find the total cost of
the jewelry?
a. .07 + ]
b. J +.07 x)
C. (.07x)) + ]
d. 7) + ]
Answer:
j * .07 +j
Step-by-step explanation:
The tax on the jewelry is J* .07
Add the tax to the cost of the jewelry to get the total cost
j * .07 +j
The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensions of the rectangle. Use the formula, area=length*width.
Answer:
The dimensions of the rectangle are 8 by 7 centimeters.
Step-by-step explanation:
The length of a rectangle is 13 centimeters less than three times its width. In other words:
[tex]\ell = 3w-13[/tex]
Given that the area of the rectangle is 56 square centimeters, we want to determine its dimensions.
Recall that the area of a rectangle is given by:
[tex]A = w \ell[/tex]
Substitute in known values and equations:
[tex](56)=w(3w-13)[/tex]
Solve for w. Distribute:
[tex]3w^2-13w=56[/tex]
Isolate the equation:
[tex]3w^2-13w-56=0[/tex]
Factor. We want to find two numbers that multiply to 3(-56) = -168 and that add to -13.
-21 and 8 suffice. Hence:
[tex]3w^2 - 21w + 8w - 56 = 0 \\ \\ 3w(w-7) + 8(w-7) = 0 \\ \\ (3w+8)(w-7) = 0[/tex]
Zero Product Property:
[tex]3w+8=0\text{ or } w-7=0[/tex]
Solve for each case:
[tex]\displaystyle w = -\frac{8}{3} \text{ or } w=7[/tex]
Since the width cannot be negative, we can ignore the first solution.
Therefore, the width of the rectangle is seven centimeters.
Thus, the length will be:
[tex]\ell = 3(7) - 13 = 8[/tex]
Thus, the dimensions of the rectangle are 8 by 7 centimeters.
12 m
15 m
8 m
5 m
5 m
Answer:
Here is your Answer
Step-by-step explanation:
27
Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Surveying 26 people to determine which brand of ice cream is their favorite.
A. Yes
B. No
There are more than two possible outcomes on each trial of the experiment. The experiment does not consist of n identical trials. The trials are dependent.
Answer:
The answer is "No, There are more than two possible outcomes on each trial of the experiment ".
Step-by-step explanation:
When various ice cream products are known. This might surpass 2 brands or more. Thus the number of different results varies considerably.
BINOMIAL DISTRIBUTION:
An investigation with a set set of individual tests, each only with two possible results.
Four conditions are met by the binomial experiment
The set of indicators is fixed.Each attempt is autonomous.2 potential results exist only.In each and every test, the probability of each outcome remains unchanged.Which simplified equation is equivale to the equation shown below? 15x – 5 + x = -47
Answer:
[tex]15x - 5 + x = - 47 \\ 15 + x - 5 = - 47 \\ 16x - 5 = - 47 \\ 16x = - 47 \\ x = \frac{ -16x}{16} = \frac{ - 45}{16} \\ x = - \frac{21}{8} [/tex]
What is the answer to this
Answer:
y = -1.5x - 1
Step-by-step explanation:
We can use the general equation of y = mx + c to form our linear equation as seen on this graph.
Choosing two points on the graph (I will choose 0,-1 and 2,-4) we can find the gradient, m, as the distance between these points
[tex]\frac{Rise}{Run} = \frac{(-1)-(-4)}{(0)-(2)} = \frac{3}{-2} =-1.5[/tex]
We can find the c value by seeing where the graph cuts through the y-axis
This point is -1
Therefore our equation is y = -1.5x - 1
Alternatively, you could write it as [tex]y= -\frac{3}{2} x - 1[/tex]
Answer:
y = -1.5x - 1
A bottling machine fills soda bottles with an average of 12.000 ounces of soda. The standard deviation is 0.002 ounces. If the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces, calculate the process capability index of the machine. Group of answer choices Less than or equal to 1 More than 4 More than 2 but less than or equal to 3 More than 1 but less than or equal to 2
Answer:
the process capability index of the machine is 2.5
Option c) [More than 2 but less than or equal to 3] is the correct answer
Step-by-step explanation:
Given the data in the question;
process average ( x') = 12.000 ounces
standard deviation σ = 0.002 ounces
the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.
so
Upper specification Limit USL = 12.000 + 0.015 = 12.015 ounces
Lower specification Limit LSL = 12.000 - 0.015 = 11.985 ounces
the process capability index of the machine will be;
Cp = ( process average - Lower specification Limit ) / 3σ
so we substitute
Cp = ( 12 - 11.985 ) / ( 3 × 0.002 )
Cp = 0.015 / 0.006
Cp = 2.5
Therefore, the process capability index of the machine is 2.5
Option c) [More than 2 but less than or equal to 3] is the correct answer
I almost got the problem but the problem was the rounding. I believe I rounded right but it is still incorrect. Can someone please help me on the rounding portion of the question? Thank you for your help!!!
Answer: The answer that I got for z was 0.111575, which when you round it to the hundredths place would be 0.11
SCALCET8 3.9.019. A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 7 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking
Answer:
The solution is defined in the attached file please find it.
Step-by-step explanation:
g Find an equation of the line with slope m that passes through the given point. Put the answer in slope-intercept form. (-4, 8), undefined slope Hint: Any line parallel to Y axis has undefined slope.
Answer:
The equation is x + 4 = 0.
Step-by-step explanation:
Point (-4 , 8)
A line parallel to the Y axis has slope is infinite.
The equation of line is
[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]
An oil tanker spills oil that spreads in a circular pattern whose radius increases at a rate of 15 ft/min. Let A be the area of the circle and r be the radius of the circle. How fast is the area increasing when the radius is 30 feet
Answer:
[tex]2827.4 \dfrac{ft}{s}[/tex]
Step-by-step explanation:
[tex] A = \pi r^2 [/tex]
[tex] \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt} [/tex]
[tex] \dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s} [/tex]
[tex] \dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s} [/tex]
need assistance with this, thank you
Answer:
B. 1✓3 in.
Search It ok
I see the answer :)
Whats The Correct Answer ?
Solve for x.
7(x+2) = 6(x+5)
O x=-44
O X=-16
O x= 44
O x= 16
Answer:
x = 16
Step-by-step explanation:
7(x + 2) = 6(x + 5)
First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.
7x + 14 = 6x + 30
Next, let's subtract "6x" from both sides of this equation!
x + 14 = 30
Now, we have to subtract "14" from both sides of the equation.
x = 16
Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.
7(16 + 2) = 6(16 + 5)
7(18) = 6(21)
126 = 126
Since our equations equal each other we know that our x-value is correct!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Find two positive integers such that the sum of the first number and four times the second number is 1000, and the product of the two numbers is as large as possible.
Answer:
The two numbers are:
x = 500
y = 125
Step-by-step explanation:
We want to find two numbers x and y, such that:
x + 4*y = 1000
f(x, y) = x*y is maximum.
From the first equation, we can isolate one of the variables to get
x = 1000 - 4y
now we can replace it in f(x, y):
x*y = (1000 - 4*y)*y = 1000*y - 4*y^2
So now we want to maximize the function:
f(y) =- 4*y^2 + 1000*y
where y must be an integer.
Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.
Remember that for a general quadratic equation:
y = a*x^2 + bx + c
the x-value of the vertex is:
x = -b/(2*a)
so, in the case of:
f(y) =- 4*y^2 + 1000*y
the y-value of the vertex will be:
y = -1000/(2*-4) = 1000/8 = 125
So we found the value of y.
now we can use the equation:
x = 1000 - 4*y
x = 1000 - 4*125 = 1000 - 500 = 500
x = 500
Then the two numbers are:
x =500
y = 125
One number is 4 greater than another. The product of the numbers is 21. Find the numbers.
One pair of numbers, both of which are positive, is
Answer:
7 and 3 are two numbers that work
Step-by-step explanation:
7-3=4
7×3=21
Find the slope and then an equation for each line.
Which equations are true for the values x,y,z? Select 3 options
Answer:
Step-by-step explanation:
Bonnie volunteers to bring bags of candy to her child’s class for the Halloween party this year. She buys one bag of candy A containing 150 pieces of candy, one bag of candy B containing 210 pieces of candy, and one bag of candy C containing 330 pieces of candy. She needs to use all the candy to create identical treat bags. How many treat bags can Bonnie make so that each one has the same number and variety of candy? How many of each type of candy will be in each bag?
Answer:
345 bags and would each have 2
hellppp................
Answer:
[tex]B)[/tex]
[tex](-1,1)(-3,3)\\\frac{3-1}{-3+1} =-1\\1=1+b\\b=0\\y=-x[/tex]
OAmayOHopeO
Question 9 Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
All the angles on the bottom line are 60. The angles on the top line from left to right is 130, 60, 60, 130.
Step-by-step explanation:
Which of these shapes have the same area?
Answer:
wheres the picture?
Step-by-step explanation:
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
9514 1404 393
Answer:
3
Step-by-step explanation:
The length of A'B' is 3 units.
The length of AB is 1 unit.
The scale factor is A'B'/AB = 3/1 = 3.
help me with my work pls
Answer:
-75/4
Step-by-step explanation:
75 x 100 = 7500
4 x 100 = 400
Express the solution graphically of -1/3(2x+1) <3
Answer:
The first picture is the solution that I worked out and the second is the graph of the two solutions.
The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.
What is inequality?"It is a mathematical statement of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two numbers or algebraic expressions."
For given question,
We have been given a inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex]
We solve above inequality.
[tex]\Rightarrow -\frac{1}{3} (2x+1) < 3\\\\\Rightarrow \frac{1}{3} (2x+1) > -3\\\\\Rightarrow 2x+1 > -9\\\\\Rightarrow 2x > -10\\\\\Rightarrow x > -5[/tex]
so, the solution of the inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is all points on the X-axis which are greater than x = -5.
The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.
Learn more about the inequality here:
https://brainly.com/question/19003099
#SPJ2
A passenger car will go 455 miles on 17.5 gallons of gasoline in city driving what is the rate in miles per gallon ?
Answer:
26 gallons
Step-by-step explanation:
Take the miles and divide by the gallons
455 miles / 17.5 gallons
26 miles per gallon
Seeds are often treated with fungicides to protect them in poor-draining, wet environments. A small-scale trial, involving six treated and six untreated seeds, was conducted prior to a large-scale experiment to explore how much fungicide to apply. The seeds were planted in wet soil, and the number of emerging plants were counted. If the solution was not effective and five plants actually sprouted.
Required:
What is the probability that all five plants emerged from treated seeds?
Answer:
0.0076 = 0.76% probability that all five plants emerged from treated seeds
Step-by-step explanation:
The plants were chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 + 6 = 12 seeds, which means that [tex]N = 12[/tex]
6 treated, which means that [tex]k = 6[/tex]
Five sprouted, which means that [tex]n = 5[/tex]
What is the probability that all five plants emerged from treated seeds?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,12,5,6) = \frac{C_{6,5}*C_{6,0}}{C_{12,5}} = 0.0076[/tex]
0.0076 = 0.76% probability that all five plants emerged from treated seeds
solve the inequality.. help me out asap plss
Answer:
[tex]x<\frac{6}{5}[/tex]
Refer to picture for number line
Step-by-step explanation:
To solve this inequality, we want to isolate the variable. We can do this my getting like terms onto one side
[tex]6x-7<2-\frac{3x}{2}[/tex] [add both sides by 7]
[tex]6x<9-\frac{3x}{2}[/tex] [add both sides by 3x/2]
[tex]6x+\frac{3x}{2}<9[/tex] [multiply both sides by 2]
[tex]12x+3x<18[/tex] [add]
[tex]15x<18[/tex] [divide both sides by 15]
[tex]x<\frac{18}{15}[/tex] [simplify]
[tex]x<\frac{6}{5}[/tex]
Now that we have out inequality, we want to graph it. Since we know that [tex]x<\frac{6}{5}[/tex], that means we have an open circle. Since x is less than, the arrow would be pointing left.
