The probability that exactly 5 out of the first 10 customers buy a magazine is 0.00126.
Given suspicion of 9.7% that buy a magazine is correct.
We have to find the probability that exactly 5 out of the first 10 customers buy a magazine. Probability is the chance of happening an event among all the events possible.
The binomial distribution is the probability of exactly x successes on n repeated trials and X can only have two outcomes.
[tex]P(X=x)=C_{n,x}p^{x} (1-p)^{n-x}[/tex]
In which [tex]C_{n,x}=n!/x!(n-x)![/tex]
And P is the probability of happening of X.
In the question 9.7% of his customers buy a magazine.
So the value of P=0.097
This can be calculated by :
P(X=5) when n=13
[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]
[tex]P(X=5)=C_{10,5} (0.097)^{5} (1-0.097)^{10-5}[/tex]
=[tex]P(X=5)=C_{10,5} (0.097)^{5} (0.903)^{5}[/tex]
[tex]=10!/5!5!*0.0000085*0.600397[/tex]
=252*0.00000510
=0.001286
Hence the probability that exactly 5 out of the first 10 customers buy a magazine is 0.001286.
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Geometry fence problem. Need help solving
On Sunday, 370 people bought tickets to the county fair. Tickets cost $7 for
adults and $3 for children. The total revenue from ticket sales on Sunday was
$1750. The system of equations below represents the number of people and
total sales for the county fair on Sunday, where x represents the number of
child tickets and y represents the number of adult tickets.
x+y=370
3x+7y=1750
How many child tickets were sold on Sunday?
OA. 180
B. 160
C. 210
D. 220
The number of children ticket sold on Sunday is 210.
How many child tickets were sold?Given this equations:
x+y=370 equation 1
3x+7y=1750 equation 2
Multiply equation 1 by 7
7x + 7y = 2590 equation 3
Subtract equation 2 from equation 3
4y = 840
Divide both sides by 4
y = 840 / 4
y = 210
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Which expression can be modeled using the number line
The answer choice which can be modelled using the number line given in the task content is; (1/10) × 7.
Which answer choice can be modelled by the number line?It follows from the task content that the answer choice which can be modelled using the number line be identified.
Hence, since each successive threshold on the number line is 1/10 from the next. It follows that the number line best models the expression; (1/10) × 7.
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write a formula that will help eric determine how much the potatoes he buys will cost in bulk.
t = total price
p = price for kilograms
k = number of kilograms of food
[tex]t = p*k[/tex] is the formula that will help eric determine how much the potatoes he buys will cost in bulk.
What is Advance algebraic Equations?An equation obtained by equating to zero a sum of a finite number of terms each one of which is a product of positive integral powers (including the zero power) of the variables.
According to the question,
In order to calculate the price of the fruit we need to multiply the amount of food in kilograms by the price per kilogram of that specific food.
Since we are given specific variables for each piece of information needed for the variable.
All we need to do now is to create the formula to calculate the total price of the potatoes that Eric needs to buy.
[tex]t = p*k[/tex]
By using this formula lets Eric calculate the total price of an order of fruit or vegetables.
Therefore,
A formula that will help eric determine how much the potatoes he buys will cost in bulk is [tex]t = p*k[/tex]
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Find the missing term.
(x12)5 x (x-2)⁹ X ____=
(140)5
Answer:
x12×x5x×x-2×9) ____=((140)5
60x × (x-18)x _______=(140)5
60x×x-10x _______=(140)5
60x-18x______=140×5
42x_______=700
42x-42x ____=700-42x
658x
Write an equation for a graph that is the set of all points in the plane that are equidistant from the point F(4, 0) and the line x = –4.
The equation of the graph is y ² = 16x.
What is a Parabola ?A parabola is a U shaped curve ,all the point of which is equidistant from a point called as focus and a line called as Directrix .
In the given question , the graph is a horizontal parabola as the directrix is x = -4 , and as the focus lies on the right side , it is opening towards the right.
The equation for the horizontal parabola is given b y
(y-k)² = 4p(x-h)
h , k is the mid point of focus and the directrix , i.e. the vertex and is given by
h = ([tex]\rm x_f[/tex] +a )/2 , k = [tex]\rm y_f[/tex]
h = (4 -4)/2 , k = 0
h=0 , k = 0
The vertex is 0 , 0
p = (|[tex]\rm x_f[/tex] - a|)/2 = 8/2 = 4
Therefore the equation of the graph is
y ² = 4 * 4 *x
y ² = 16x
The equation of the graph is y ² = 16x.
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can you write 3/5 as a recurring decimal?
can i also have an explanation please :)
Answer:
0.6
Step-by-step explanation:
You can literally put 3/5 into a calculator and you would get the answer 0.6, so I don't know what else to say. Whoever asked you this question, give them the above answer ask them what they were on, because the person was probably way high on LSD.
please help mee, sketch the graph please (50 points will give brainliest!!!)
Values are given below as pairs (x,y) where x coordinate is x values in box and y coordinate is y values on box
(-5,9)(-4,4)(-2,0)(0,4)(1,9)Graph attached
can u help me figure this out lol
Answer:
Cost of a T-shirt is £4
Cost of a Hat is £1
Step-by-step explanation:
Let T be the cost of each T-shirt and H the cost of each hat
We get two equations based on the cost description
3T + 2H = 14 ...... (1)
2T + 7H = 15 ...... (2)
Multiply (1) by 2 and (2) by 3 so that the T terms are the same
(1) x 2 ==> 6T + 4H = 28 ... (3)
(2) x 3 ==> 6T + 21H = 45 ... (4)
Subtract (3) from (4) to eliminate the T terms
21H - 4H = 45 - 28 or 17H = 17 ==> H = 1
Substituting the value of H in either (1) or (2) will give us a value for T
Substitute in (1)
3T + 2*1 = 14 ==> 3T = 12, T = 4
Check
In (1) 3 *4 + 2 *1 = 14
In (2) 2*4 + 7*1 = 15
So satisfies both equations
Eleanor randomly chooses a number from 1 to 10. what is the probability she chooses a number greater than 5?
The probability she chooses a number greater than 5 will be 1/2 or 0.5.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
Probability = (Favorable event) / (Total event)
Eleanor randomly decides a number from 1 to 10.
Then the probability she chooses a number greater than 5 will be
Total event = 10
Favorable event = 5 {6, 7, 8, 9, 10}
Then we have
P = 5/10
P = 1/2
P = 0.5
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A man of height 1.5 m is standing in front of a tower of height 81.5 m. At what angle should he observe the top of the tower from the distance of 80 m?
The angle at which the man should observe is 45 degrees.
To solve the question :Given :
height of man = 1.5m
height of tower = 81.5 m
distance between tower and man = 80 m
Since, ABCD is a rectangle, AD = BC = 80m
Similarly, AB = CD = 1.5m
EC = ED + CD
81.5 = ED + 1.5
ED = 80m
Now, in order to find the angle EAD, we use trigonometric functions,
tan ∅ = perpendicular / base = ED / AD
tan ∅ = 80 /80 = 1
∅ = [tex]tan^{-1} (1)[/tex]
∅ = 45°.
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What is the slope of the line represented by the equation f(x) = -47
2x 4₂
-4
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: slope \:\: of \:\: line = \cfrac{3}{2}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The equation of line is written in slope - intercept form
[tex]\qquad \tt \rightarrow \: f(x) = \dfrac{3}{2} x - 4[/tex]
if we compare it with general slope - intercept equation of line :
[tex]\qquad \tt \rightarrow \: f(x) = mx + c[/tex]
[ m represents slope of line ]
[tex]\qquad \tt \rightarrow \: m = \dfrac{3}{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]\frac32[/tex]
Step-by-step explanation:
Hello!
An equation of a line is usually written in slope-intercept form.
Slope Intercept Form: [tex]y = mx + b[/tex]
m = slopeb = y-interceptIf we compare our given equation with the format:
m = [tex]\frac32[/tex]b = -4This means that [tex]\frac32[/tex] would be our slope for the line.
Can someone help me with question 3? I like to see the working and answer on paper, that would be more helpful, I’m in a hurry
The steps to draw all the three angles have been explained.
What is an Angle ?An angle is made by two rays that have one common end point known as vertex.
To make an angle congruent to the one given , the angle has to be copied
For making both ∠XYZ and∠ UVW , following steps will be followed.
Draw two rays separately and name it YZ and VW .Take a compass and draw a free hand arc from the point B and E and with the same measure draw a free hand arc from the point Y and V respectively.Take the compass to the angle ABC and DEF again , from the point where the arc intersects BC and EF , cut an arc on the ray AB and DE .With the same measure , keep the compass on the point the free hand arc intersected on the ray YZ and VW , cut the arc by the new arc .The point where both the arc intersects will be joined form the end points , Y and V , to form an angle.The angle formed will be copy of ∠ABC and∠ DEFNow to draw RST = ABC + DEF
Draw the angle ABC and repeat the steps to draw DEF taking , AB ray as the base of the angle.The angle obtained will be RST.
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Which of the following describes point D?
O (-4,0)
O (4,0)
O (0,4)
O (0,-4)
Answer:
The answer is C (0,4)
Step-by-step explanation:
Looking at the graph we have to find a point (x,y) of D.
Find point D. It is on the y-axis, but which one? Positive/Negative y-axis.
It appears to be on the positive y-axis.
Now we have to choose either option C or D.
Option C seems like the best choice since the point is (x,y) is (0,4) on the positive y-axis.
Option D is quite the opposite of point D since the point (0, -4) is on the negative y-axis.
The answer is C. (0,4)
Find the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8). ( x - 1) 2 + ( y - 4) 2 = 25 ( x - 4) 2 + ( y - 1) 2 = 25 ( x - 1) 2 + ( y - 4) 2 = 5
Answer:
(x-1)^4 + (y-4)^2 = 25
Step-by-step explanation:
Center at 1,4 means the circle is of the form:
(x-1)^4 + (y-4)^2 = r^2
Find r^2 using distance formula from center to the given point
r ^2 = ( 8-4)^2 + (4-1)^2
r^2 = 16 +9 = 25
so you answer is (x-4)^4 + (y-8)^2 = 25
Cullumber company had $170,000 of net income in 2021 when the selling price per unit was $152, the variable costs per unit were $96, and the fixed costs were $574,800. management expects per unit data and total fixed costs to remain the same in 2022. the president of cullumber company is under pressure from stockholders to increase net income by $106,400 in 2022.
The number of units sold in 2021 = 13,300 units.
The number of units that would have to be sold in 2022 to reach the stockholder's desired profit level = 15,200 units.
Assuming that Cullumber company sells the same number of units in 2022 as it did in 2021, the selling price in order to reach the stockholder's desired profit level = $160.
The net income of a company is its profit function, derived by the formula:
Profit = Sales - Cost.
Sales are the product of the number of units sold and per unit selling price.
Cost is the sum of fixed costs and the product of the number of units produced to the variable cost per unit.
Assuming the number of units sold in 2021 to be x,
we can say sales = $152x, and
cost = ${574800 + 96x}.
Therefore, profit = sales - cost,
or, 170000 = 152x - {574800 + 96x},
or, 170000 = 56x - 574800
or, 56x = 574800 + 170000 = 744800,
or, x = 744800/56 = 13300.
Therefore, the number of units sold in 2021 was 13,300.
In 2022, the desired profit = $170,000 + $106,400 = $276,400.
Assuming the number of units sold in 2022 to be n, at the same unit data and fixed cost, we can say that:
Sales = $152n, and
Cost = ${574800 + 96n}.
Therefore, profit sales - cost,
or, 276400 = 152n - {574800 + 96n},
or, 276400 = 56n - 574800,
or, 56n = 574800 + 276400 = 851200,
or, n = 851200/56 = 15200.
Therefore, the number of units sold in 2022 should be 15,200 to reach the desired profit of the stakeholders.
When the number of units sold in 2022 is the same as in 2021, that is, the number of units = 13,300, we assume the per unit selling price to be $P.
Now we can say that,
Sales = $13300P.
Costs = ${574800 + 96*13300} = ${574800 + 1276800} = $1851600.
Therefore, profit = sales - cost,
or, 276400 = 13300P - 1851600,
or, 13300P = 1851600 + 276400 = 2128000,
or, P = 2128000/13300 = 160.
Therefore, the new selling price per unit to reach stockholders' desired profit, assuming the number of units sold in 2022 to be the same as in 2021 is $160.
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Please help me with my math
Answer:
6.4
Step-by-step explanation:
It's stated that the shapes are similar.
We can use similarity ratio to find the value of x:
LM/CD = KL/BA
x/4 = (11.2)/7 cross multiply expressions
7x = 44.8 divide both sides by 7
x = 6.4
Which expressions are in simplest form? Check all that apply. 0 x²³+y³ 1 - 3 9-9 ·to -12 a² + b ² Which expressions are in simplest form ? Check all that apply . 0 x²³ + y³ 1 - 3 9-9 · to -12 a² + b ²
The expression that's in the simplest term will be -12a² + b².
How to illustrate the expression?It should be noted that an expression means a mathematical statement that has a minimum of two terms containing variables.
In this case, the expression that's in the lowest term will be -12a² + b². This is because it's can't be simplified further.
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5w-8x+20y+6z
Term:
Coefficient:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \sf{5w\rightarrow coefficient = 5} [/tex][tex] \sf{-8x\rightarrow coefficient = -8} [/tex][tex] \sf{20y\rightarrow coefficient = 20} [/tex][tex] \sf{6z\rightarrow coefficient = 6} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Term refers to each variable or constant separated by a mathematical operator.
Coefficient refers to the numberic part of variable or a constant number present in an expression.
[tex]\qquad \tt \rightarrow \: 12a - 10b + 6[/tex]
[tex] \large\textsf{Terms :} [/tex]
[tex] \texttt{5w } [/tex][tex] \texttt{coefficient = 5} [/tex]
[tex] \texttt{-8x} [/tex][tex] \texttt{coefficient = -8 } [/tex]
[tex] \texttt{20y} [/tex][tex] \texttt{coefficient = 20} [/tex]
[tex] \texttt{6z} [/tex][tex] \texttt{coefficient = 6} [/tex]
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Can someone help me please its geometry.
The figure showing the construction is given below.
Steps for the construction of a circle through three points not on a straight line are as follows:
1. To create two lines, connect the points.
2. Create the line's perpendicular bisector.
3. Create the opposite line's perpendicular bisector.
4. The circle's center is where they intersect.
5. Draw your circle by placing the compass on the center point and adjusting its length to reach any point.
What happens if the points are parallel?
The circle traveling through all three points will have an infinite radius if the three points are collinear, or all situated on a straight line. Therefore, a practical circle cannot traverse three collinear locations. The two radii would be parallel and would never come together at a center if you tried the construction. We may claim that they do cross mathematically but at infinity.
Hence, after following the steps we obtain the circle.
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In January, Emma was 62.25 in tall. In December, she was 65.5 inches tall. How much did Emma grow between January and December?
A. 2 inches
B. 3.25 inches
C. 5.5 inches
D. 4 inches
Answer: B. 3.25 inches
Step-by-step explanation:
two months right next to each other
65.5 = final
62.25 = start
65.5 - 62.25 = 3.25 inches
Answer:
3.25
Step-by-step explanation:
65.5 - 62.25
PLEASE HELPPP!!
Solve the system of equations.
Answer:
x= 4
y= -2
Step-by-step explanation:
[tex]-3y+5x=26\\-2y-5x=-16[/tex]
Solve by using the Elimination Method.
[tex]-5y=10\\\\\frac{-5y}{-5} =\frac{10}{-5} \\\\y=-2[/tex]
Now plug y into one of the original equation.
=======================================
[tex]-2y-5x=-16[/tex]
[tex](-2*-2)-5x=-16[/tex]
[tex]4-5x=-16[/tex]
[tex]4-5x+5x=-16+5x[/tex]
[tex]4+16=-16+5x+16[/tex]
[tex]20=5x\\\\\frac{20}{5} =\frac{5x}{5} \\\\x=4[/tex]
=======================================
[tex]\left \{ {{x=4} \atop {y=-2}} \right.[/tex]
Me no like this meth and me is not smart
halp
What decimal is equivalent to ?
7-25
PLEASE HELP ME, I BEG OF YOU TO HAVE MERCY ON MY POOR SOUL
1. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)
2. Using the slope and y-intercept, write the equation of the trend line (y = mx + b).
3. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.
4. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.
The answer for the following question is
1. m= 10
2. y- intercept = 300
3. y = 10x + 300
What is Regression line?A regression line is a graphic representation of the regression equation expressing the hypothesized relationship between an outcome or dependent variable and one or more predictors or independent variables
1.slope= rise/ run
m= 10
2. y- intercept = 300
3. Now, the regression line:
y = 10x + 300
At, x = 1
y = 10(1) + 300
y = 310 calories
and x = 14
y = 10(14) + 300
y = 440
We know the actual value is 330.
Hence, the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.
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(8.6x107)-(9.1x10-8)simplify
Answer:
85,999,999.999 999 909
Step-by-step explanation:
The expression represents the difference of a relatively large number and one that is relatively small. That difference is approximately the value of the large number. The exact value requires 17 digits for its proper expression. Most calculators and spreadsheets cannot display this many digits.
Standard formThe numbers in standard form are ...
86,000,000 = 8.6×10^7
0.000000091 = 9.1×10^-8
DifferenceTheir difference is ...
86,000,000 -0.000000091 = 85,999,999.999 999 909
In scientific notation, this is ...
8.599 999 999 999 990 9×10^7
Help with Pre Calculus
Guys, can you please help me write an expression for shaded circle and please expand and simplify for me, guys, please? :)
Answer:
[tex]\sf Shaded \: Area=14 \pi r+49 \pi[/tex]
Step-by-step explanation:
Area of a circle
[tex]\sf A=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
To find the area of the shaded area, subtract the area of the unshaded circle from the larger circle.
Area of the larger circle
[tex]\implies \sf A=\pi (r+7)^2[/tex]
Area of the smaller (unshaded) circle
[tex]\implies \sf A=\pi r^2[/tex]
Therefore, the area of the shaded area is:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
Expand and simplify the expression:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
[tex]\implies \sf A=\pi (r^2+14r+49)-\pi r^2[/tex]
[tex]\implies \sf A=\pi r^2 +14 \pi r +49 \pi -\pi r^2[/tex]
[tex]\implies \sf A=14 \pi r+49 \pi[/tex]
OUTER CIRCLE AREA
π(r+7)²Inner circle area
πr²Area of shaded one
π(r+7)²-πr²π(r²+14r+49-r²)π(14r+49)14πr+49πA sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.
Which value can be used as the common ratio in an explicit formula that represents the sequence?
One-half
2
6
12
The common ratio of the given Geometric progression is one-half.
Let a be first term and r common ratio of the Geometric progression.
The Geometric sequence is the form a,ar,ar^2, ...
Given that the sequence begins with 12, i.e a = 12
and also given that the sequence are in Geometric Progression.
By dividing the preceeding number by 2, we get the successive number
Then the Geometric sequence is 12, 12×1/2, 12×1/4, 12×1/8, 12×1/16 ...
= 12, 6, 3, 3/2, 3/4, ...
Common ratio = Second term / First term
= 6/12
=1/2
Therefore, the common ratio of the given geometric progression is one-half.
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Answer:
its a
Step-by-step explanation:
when using the rational root theorem, which of the following is a possible root of the polynomial function below? f(x)=2x^2-4x+9
a)4
b)3
c)2
d)5
The only option that meets the root theorem is option b.
which of the following is a possible root of the polynomial function below?
The polynomial function is:
[tex]f(x) = 2x^2 - 4x + 9[/tex]
The rational root theorem says that if a root is a rational number, then the leading coefficient must be divisible by the denominator of the rational number and the constant term must be divisible by the numerator.
In this case, the constant is 9, and the only option such that the constant is divisible by the numerator is option b: 3
Where 3 is a rational number:
3 = 3/1
The numerator is 3 (which divides 9) and the denominator is 1 (which divides the leading coefficient 9. (notice that it meets the theorem, but it is not an actual root).
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