The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
What is mean?A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilizes the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.acc to our question-
Mean price = total amount spent on computers / number of computers= (6*900 +18*800+14*2600+5*1750)/(6+18+14+5) =64,950/43 = 1510.47x f fx900 6 5400800 18 144002600 14 364001750 5 875043 64950xbar = Σxf/Σf = 64,950/43 = 1510.47hence,The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
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Evaluate the expression when a=5 and b=1/2: 13/2 - 7/2 -b( 2/3) + 4/8 - ab
A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?
To maximize the $40,000 allocated to reach the most people, using linear programming, 10 TV ads and 175 radio ads should be used
The number of people reached is 595,000
What is linear programming?Linear programming is a method of maximizing a straight-line or linear function that consists of two or more variables such as the cost and the number of people reached.
Let R represent the number of radio ads and let T represent the number of television ads.
The constraints are;
200·R + 500·T ≤ 40,000
R ≥ 10
T ≥ 10
The maximum value function is 7,000·T + 3,000·R
R ≥ T
R - T ≥ 0
R ≥ T
The equations are therefore;
200·R ≤ 40,000 - 500·T
R ≤ (40,000 - 500·T)/200 = 200 - 2.5·T
R ≤ 200 - 2.5·T
When R = T, we have;
T = 200 - 2.5·T
3.5·T = 200
T = 200 ÷ 3.5 ≈ 57.14
The value of the maximizing function, 7,000·T + 3,000·R, at the vertices of the feasible region are therefore;
(T, R)
At (10, 10); 7,000 × 10 + 3,000 × 10 = 100,000
At (10, 175); 7,000 × 10 + 3,000 × 175 = 595000
At (57.14, 57.14); 7,000 × 57.14 + 3,000 × 57.14 = 571400
The number of adds of each type that will reach the maximum number of people is 10 television ads and 175 radio adsThe number of persons the ads reaches is 595,000Learn more about linear programming or linear optimization here:
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Write an equation of the parabola in vertex form.
Amusement Park Ride
Height (feet)
YA(0, 180)
(1, 164)
160
80
0 2 4
Time (seconds)
Equation:
Equation of parabola in vertex form is :
[tex](x-h)^{2} = 4a(y-k)[/tex]
[tex](x-0)^{2} = 4a(y-180)[/tex]
it passing through (1,164)
∴ [tex](1-0)^2=4a(164-180)[/tex]
[tex]1 = 4a(-16)[/tex]
⇒ [tex]-64a = 1[/tex]
⇒ [tex]a = -\frac{1}{64}[/tex]
∴ [tex](x-0)^2 = 4 \times \frac{1}{-64} (y-180)[/tex]
[tex]x^2 = -\frac{1}{16}(y-180)[/tex]
[tex]-16x^2 = y-180\\y = -16x^2+180\\[/tex]
Here, the equation of parabola in vertex form is:
[tex]y = -16(x^2)+180 ,\ for \ x\geq 0[/tex]
What is Parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface.
What is cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the Centre of base) called the apex or vertex.
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Please help 25 points
The angles that are congruent are as follows:
∠EBF and ∠GBH∠DEA and ∠BEC∠FBG and ∠HBE∠AEB and ∠CEDWhat are vertical angles?Vertical angles are angles that are opposite of each other when two lines cross. In other words, vertical angles are formed when two lines meet each other at a point.
Vertically opposite angles are congruent.
Therefore, let's find the angles that are congruent in the diagram.
When lines intersect angle relationship such as vertically opposite angles are formed.
Therefore, the following angles are congruent because they are vertically opposite angles.
∠EBF and ∠GBH are congruent. ∠DEA and ∠BEC are congruent. ∠FBG and ∠HBE are congruent. ∠AEB and ∠CED are congruent.learn more on vertical angles here: https://brainly.com/question/24460838
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(42x³ + 16x² + 46x +42) ÷ (7x + 5)
응
Two student groups went to an amusement park on the same day. Group 1 bought 9 tickets and received a $120 discount. Group 2 bought 3 tickets and received a $30 discount. Both groups spent the same total amount of money on tickets. The price of each ticket was the same. What was the cost of each ticket?
The cost of each ticket of the amusement park is $15.
What is the system of equation?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Two student groups went to an amusement park on the same day.
Group 1 bought 9 tickets and received a $120 discount.
Group 2 bought 3 tickets and received a $30 discount.
Let x be the amount of one ticket and y be the total amount.
According to the question:
We have system of equation,
y = 9x - 120 equation1
y = 3x - 30 equation 2
Subtract the equation 2 to equation 1.
So, 6x = 90
x = 15
Therefore, $15 is the cost of each ticket.
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Two numbers have these properties.
Both numbers are greater than 6.
Their highest common factor (HCF) is 6.
Their lowest common
multiple (LCM) is 60.
Find the two numbers, writing your
answers on one line in the form,
The two numbers are .
and .. .
12 and 30 are the two numbers are greater than 6 with HCF 6 and LCM 60.
What is Highest common factor and Least Common Multiple?
Least Common Multiple is the entire name of LCM in mathematics, whereas Highest Common Factor is the full name of HCF. When two or more numbers are given, the HCF identifies the largest factor present, while the LCM defines the least number that is exactly divisible by two or more numbers.
Assume that the two numbers with HCF of 6 are 6a and 6b, where a and b are co-prime and a, b > 1.
HCF x LCM = Product of the numbers.
6 x 60 = 6a x 6b
10 = a x b
10 can be written as, 1 x 10 and 2 x 5.
But a and b > 1.
So, 10 = 2 x 5
a = 2, b = 5
Therefore, the two numbers are,
6a = 6(2) = 12 and
6b = 6(5) = 30
Hence, the two numbers with HCF 6 and LCM 60 are 12 and 30.
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8.7% increase of 525 what is answer
Answer:
Step-by-step explanation:
570.675
ASAP Write an equation of a quadratic formula with the given properties: f(3)=f(-5)=0;f(-6)=-36
The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).
How to derive a quadratic equation that contains three points
In this question we find the coordinates of three points set on Cartesian plane and we are asked to find the quadratic equation that contains the these points. The standard form of the quadratic equation is shown below:
y = a · x² + b · x + c
Where:
x - Independent variable.y - Dependent variable.a, b, c - Real coefficients.We can determine the values of the three coefficients because the number of known points is equal to the number of coefficients. Then, we have the following system of linear equations by replacing x and y on each of the three points:
9 · a + 3 · b + c = 0
25 · a - 5 · b + c = 0
36 · a - 6 · b + c = - 36
Then, the solution to the system is found by numerical methods:
(a, b, c) = (- 4, - 8, 60)
The equation that contains the three points is y = - 4 · x² - 8 · x + 60.
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Which of the following is NOT true about the body mass index? A. uses statistical data of weight and height across the population B. measures the percentage of one's body fat directly C. relies on a correlation between weight and body fat D. does not account for one's body frame size or muscle content Please select the best answer from the choices provided. A B C D Mark this and return
The statement that is not true about body mass index is B. measures the percentage of one's body fat directly
What is Body mass index?The Body Mass Index (BMI) calculates a person's weight in relation to their height. It is not a precise assessment of a person's total body fat, more of an indicative.
The majority of the time, total body fat and BMI are correlated.
The Body mass index (BMI) formula
= weight in kilograms / square of height in meters
BMI Categories values are classified below
Underweight ≤ 18.5
Normal weight = 18.5–24.9
Overweight = 25–29.9
Obesity = BMI of 30 or greater
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Answer:B
Step-by-step explanation:
Considering the Matrix: Give the solution in terms of x. Show work.
1 0 -.05 I 2
0 1 2 I 1
0 0 0 I 0
The solution to the system of equations, in terms of x, considering the augmented matrix, is of:
y = -40x + 81.x = 20x - 40.Augmented matrix of system of equationsThe augmented matrix of a system of equations is built as follows:
Each of the columns before the | represents the coefficients of a variable.The column after the | represents the numeric value of the expression.In this problem, there are three columns before the |, the there are three variables given as follows:
x,y and z.
The expression from the first row is:
x -0.05z = 2.
The expression from the second row is:
y + 2z = 1.
The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:
x - 0.05z = 2
0.05z = x - 2.
z = (x - 2)/0.05
z = 20x - 40.
Hence the solution for y is:
y = 1 - 2z
y = 1 - 40x + 80
y = -40x + 81.
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Given mn, find the value of x.
(2x+6) (x+9)"
Answer:
(2x+6) = (x+9) ; x = 3
Step-by-step explanation:
-x both sides ; 2x-x = x and -6 both sides which is x = 3
In a factory, 40% of k liters of acid are added to 60% of w liters of water.
Express the total volume of the solution as an algebraic expression. Pls help
Answer: (0.4k+0.6w)
Step-by-step explanation:
the answer would be (0.4k+0.6w) Since we do not know the values of k nor w, their coefficients cannot be added together.
The total volume of the solution as an algebraic expression is
0.4k + 0.6w.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount of acid added to the solution = 40% of k
Amount of water added to the solution= 60% of w
Now,
The total volume of the solution.
= 40% of k + 60% of w
= 40/100 x k + 60/100 x w
= 0.40k + 0.60w
Thus,
The volume is 0.4k + 0.6w.
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10. Brock bought a bicycle that cost $40.00 when it was new. If he eventually sold it for 10%
of the original cost, how much was it sold for?
Answer:IT WOULD BE 60.00
Step-by-step explanation:
BC 40 = 60
what are her monthly payments
The interest she is pay total is $2340.822 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
Given that,
For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
We have to find will she pay interest at all.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $6490
r is 7.26%
t is 5 years
So,
i= 6490×0.0726×5
i= $2355.87
Therefore, the interest she is pay total is $2355.87 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
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attachment above please
Jolyn's points per basketball game are normally distributed with a standard deviation of 7 points. If Jolyn scores 48 points, and the z-score of this value is 3, then what is her mean points in a game?
If Jolyn scores 48 points, and the z-score of this value is 3, then her mean points in this normally distributed game is equal to 27.
How to calculate the mean points?In a normal distribution, the relative score or z-score can be calculated by using this formula:
[tex]z=\frac{x\;-\;u}{\sigma}[/tex]
Where:
x represents the sample score.u represents the mean point.σ represents the standard deviation.Making mean (μ) the subject of formula, we have:
μ = x - zσ x
Substituting the given parameters into the formula, we have;
Mean point, μ = 48 - (3 × 7)
Mean point, μ = 48 - 21
Mean point, μ = 27.
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The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
B) if it takes the car 36 minutes to drive down the road, what will it's average speed
Answer:
a) 24 minutes
b) 20 mph
Step-by-step explanation:
Speed - distance -time:time= 12 min
[tex]\sf = \dfrac{12}{60} \ hour[/tex]
speed = 60 mph
[tex]\sf \boxed{distance =speed * time}[/tex]
[tex]\sf = 60 * \dfrac{12}{60}\\\\ = 12 \ m[/tex]
a) Speed = 30 mph
[tex]\sf \boxed{time = \dfrac{distance}{speed}}[/tex]
[tex]\sf = \dfrac{12}{30}\\\\ = \dfrac{2}{5} \ hour\\\\ = \dfrac{2}{5}*60\\\\= 2 * 12\\\\= 24 \ minutes[/tex]
It will take 24 minutes.
c) time = 36 minutes
[tex]\sf = \dfrac{36}{60} \hour[/tex]
[tex]\sf \boxed{speed= \dfrac{distance}{time}}[/tex]
[tex]\sf = \dfrac{12}{ \dfrac{36}{60}}\\\\\\ = 12* \dfrac{60}{36}\\\\= 20 \ mph[/tex]
Average speed = 20 mph
The equation y = 11x represents a proportional relationship. What is the
constant of proportionality?
A.11
B.x
C.1/11
D.0
The constant of proportionality in the equation y = 11x is 11 , the correct option is (a) .
in the question ,
it is given that
the equation is y = 11x
also given that the equation is proportional relationship ,
we need to find constant of proportionality .
we know that the proportional equation is written as y = k*x
where k is the constant of proportionality , on comparing it with the equation y = 11x
, we get k = 11 ,
So , the constant of proportionality is = 11 .
Therefore , The constant of proportionality in the equation y = 11x is 11 .
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what is the total cost of cake option 1
Answer:
give me the question dude......
Step-by-step explanation:
There are 121 boys and 116 girls signed up for a trip to an amusement park. The leader first makes groups of 9 students each and then assigns any remaining students to make some of the groups have 10 students. Part A How many groups of 10 students will there be? Explain. Part B How many groups of 9 students will there be? Explain.
The remainder is the amount "leftover" after performing some computation.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
What is a remainder?
The remainder is the amount "leftover" after performing some computation. In arithmetic, the remainder is the integer "leftover" after dividing one integer by another to produce an integer quotient.
Here given that,
The strength of boys is [tex]121[/tex]
The strength of girls is [tex]116[/tex]
So, the total number of students are
[tex]121+116=337[/tex]
The leader first makes groups of [tex]9[/tex] students and then assigns any remaining students to make some of the groups have [tex]10[/tex] students.
So we divide by [tex]9[/tex] to find out the remainder and the total number of groups are:-
[tex]\frac{337}{9}=37[/tex]
and the remainder value is [tex]4[/tex].
Therefore, there are [tex]37[/tex] groups in the total out of which [tex]4[/tex] are out of [tex]10[/tex]students.
So,
[tex]\frac{37}{4}=33[/tex] groups are of [tex]9[/tex] students.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
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Evaluate the expression when m = -3.
2
m² -7m+6
Answer:
36
Step-by-step explanation:
substitute m = - 3 into the expression
m² - 7m + 6
= (- 3)² - 7(- 3) + 6
= 9 + 21 + 6
= 36
The following number is shown in expanded form:
1 1
4x1+8 x 100 + 9 × 1000
What is the decimal form of the number?
The decimal form of the number is :
9804.0
What is the decimal number?
Decimals are a form of a number in algebra that has a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.
If the question is,
4x1+8 x 100 + 9 × 1000, then simplify it first
4x1+8 x 100 + 9 × 1000=4+800+9000=9804
So, the decimal form is :
9804.0
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How would you investigate the complaints from renters who are
unhappy about their monthly rents?
What statistical measurement would be used?
To investigate the complaints from renters who are unhappy about their monthly rents, the mean rents can be collected
The statistical measurement that would be used is the ANOVA.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."
ANOVA is an abbreviation for Analysis of Variance. It is a statistical test invented by Ronald Fisher in 1918 that has been in use ever since. Simply said, ANOVA determines whether or not there are statistical differences between the means of three or more independent groups. The most basic type is one-way ANOVA. To know of the meansare the same, the ANOVA can be used.
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The equation a = 12850 + 530h gives a hiker's altitude a (in feet), h hours after beginning his hike.
A. At what rate, in feet per hour, is the hiker gaining altitude?
The rate of gaining altitude for the hiker is 530 feet per hour.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
The given equation for hiker's altitude is as below,
a = 12850 + 530h
Here a is the altitude in feet and h is time in hours.
In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,
a = 12850 + 530h
Differentiate the above equation w.r.t h as,
da/dh = 0 + 530
= 530
Hence, the rate of gaining altitude is 530 feet per hour.
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Evaluate 4x ÷ y if y = 2 and x = 4
Answer:
18
Step-by-step explanation:
x = 4
4x
= 4 * 4
= 16
y = 2
4x + y
= 16 + 2
= 18
ASAP
10 yellow, 6 green, 9 orange, and 5 red cards facedown. Once a card selected, NOT replaced.
a. P(two cards that are not orange)
b. P(two cards that are neither red nor green)
The probability of selecting two cards that are not orange, is 0.483 and the probability of selecting two cards that are not red and green, is 0.393.
In the given question we have to find the probability.
From the question it is given that,
10 yellow, 6 green, 9 orange, and 5 red cards facedown.
Total number of cards = 10+6+9+5
Total number of cards = 30
Once a card selected, NOT replaced.
a.) Now finding the probability of selecting two cards that are not orange.
There are total orange cards = 9
The number of cards except orange card = 21
Then the probability of selecting one card except orange = 21/30
Then the probability of selecting other card except orange = 20/29
Then the probability of selecting two cards that are not orange is
P(O) = 21/30 * 20/29
P(O) = 420/870
P(O) = 0.483
Then the probability of selecting two cards that are not orange, is 0.483.
(b) Now finding the probability of selecting two cards that are neither red nor green.
The total number of cards except red and green card = 19
Then the probability of selecting one card except red and green card = 19/30
Then the probability of selecting other card except red and green card = 18/29
Then the probability of selecting two cards that are not red and green card is
P(RG) = 19/30 * 18/29
P(RG) = 342/870
P(RG) = 0.393
Then the probability of selecting two cards that are not red and green, is 0.393.
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mr colton needs 4.62 cups of flour to make 3 pound of dough.How many cups does she need to make 2 pounds of dough
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10
Let the number of cups be represented by x.
This will be expressed as:
2/3 = x/4.62
Cross multiply
3x = 2 × 4.62
3x = 9.24
Divide
x = 9.24 / 3
x = 3.08
Therefore, 3.08 cups are needed.
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Answer:
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
Step-by-step explanation:
Find the values of x and y.
Answer:
y=60°, x=60°
Step-by-step explanation:
X=60° Angles in a Equaliteral triangles are all 60°
Alternate angle to get the base angle close to y
Y=60° because of Isoceless angles
Identity the a, b, h and k values from the parent function, y = x^2
The values from the parent function are a = 1, b = -6, h = 3, and k = -4.
What is the vertex form of quadratic equations?
The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
The given parent function is f(x) = (x - 3)² - 4.
comparing with the standard vertex form of the parabola, we get
a = 1, h = 3 and k = -4.
Now to find 'b', we have to simplify the given function in the form of f(x) = ax² + bx + c
f(x) = (x - 3)² - 4
f(x) = (x² - 6x + 9) - 4
f(x) = x² - 6x + 5
Comparing with f(x) = ax² + bx + c we get, c = -6.
Hence, The values from the parent function are a = 1, b = -6, h = 3, and k = -4.
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