Answers
The number of customers surveyed is 499.
UESTION A
ehe age ranges that fall within the required one for this question are 20-29, 30-39, and 40-49.
The number of people in these groups in total will be:
[tex]\Rightarrow65+87+70=222[/tex]Therefore, the probability of this occurring is calculated to be:
[tex]\Rightarrow\frac{222}{499}=0.4449[/tex]he probability is 0.4449.
QUESTION B
he age ranges for this question are >≥60, <20, and 20-29.
The number of people in these groups in total will be:
[tex]\Rightarrow84+93+65=242[/tex][tex]\Rightarrow\frac{242}{499}=0.4850[/tex]he probability is 0.4850.
QUESTION C
is ≥60.
The number of people in this group is 84.
[tex]\Rightarrow\frac{84}{499}=0.1683[/tex]Related Questions
I need help with the following question
Answers
The values of the trigonometry formulas are sin(240) = -sin(60), cos(225) = -cos(45) and tan(225) = tan(45)
How to determine the values of the trigonometry formulas?The trigonometry ratios are given as
sin(180 - ∅) = sin(∅)
cos(180 - ∅) = -cos(∅)
tan(180 - ∅) = -tan(∅)
Also, we have the following trigonometry ratios are given as
sin(180 + ∅) = -sin(∅)
cos(180 + ∅) = -cos(∅)
tan(180 + ∅) = tan(∅)
Using the above trigonometry ratios, we have
sin(240) = sin(180 + 60)
By comparison, we have
sin(240) = sin(180 + 60)
sin(180 + ∅) = -sin(∅)
This gives
∅ = 60
So, we have
sin(180 + 60) = -sin(60)
Evaluate
sin(240) = -sin(60)
Using the above trigonometry ratios, we have
cos(225) = cos(180 + 45)
By comparison, we have
cos(225) = cos(180 + 45)
cos(180 + ∅) = -cos(∅)
This gives
∅ = 45
So, we have
cos(180 + 45) = -cos(45)
Evaluate
cos(225) = -cos(45)
Using the above trigonometry ratios, we have
tan(225) = tan(180 + 45)
By comparison, we have
tan(225) = tan(180 + 45)
tan(180 + ∅) = tan(∅)
This gives
∅ = 45
So, we have
tan(180 + 45) = tan(45)
Evaluate
tan(225) = tan(45)
Hence, the value is tan(225) = tan(45)
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evaluate 4.141414 as a rational number
Answers
we'll start by moving the recurring part to the left of the decimal point hmmm so the recurring part is 0.14 so if we just multiply that by 100, that'll give us 14.141414...., now let's make the recurring part a variable
[tex]x=0.\overline{14}\hspace{5em} \begin{array}{llll} 100x&=&14.\overline{14141414}\\\\ &&14+0.\overline{14141414}\\\\ &&14+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 100x=14+x\implies 99x=14\implies x=\cfrac{14}{99}[/tex]
Answer:
2070707/500000
Step-by-step explanation:
rational no. simply means a fraction.
A store has 18 cell phones in stock. The manufacturer ships cell phones to the store to sell in boxes that contain four cell phones each. If the store is preparing for a big sale and would like to have 30 cell phones in stock for the sale, how many boxes should they order from the manufacturer?
A. 3
B. 4
C. 8
D. 12
Answers
Answer:
The answer is A, 3
Answer:
4 is the answer
8 ÷ 2(2 + 2)
what is the answer
Answers
Answer: 16
Step-by-step explanation: 8 ÷ 2(2 + 2)
Evaluate a³ - b + 7, if a = 3 and b
=4
Answers
⇒Plug in the given values of the variables in order and then simplify the expression
Given that a= 3 and b=4
⇒[tex]=(3)^{3} -(4)+7\\=27-4+7\\=23+7\\=30[/tex]
⇒The expression evaluated at the given known variables gives 30.
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply
Answers
Solution
Step 1:
Write the rational expression:
[tex]\begin{gathered} f(x)\text{ = }\frac{x+4}{x^2+5x-24} \\ \end{gathered}[/tex]Step 2:
Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).
Step 3
[tex]\begin{gathered} x^2+5x-24=0 \\ \\ x^2+8x\text{ - 3x - 24 = 0} \\ \\ x(x\text{ + 8\rparen-3\lparen x + 8\rparen = 0} \\ \\ (x\text{ - 3\rparen\lparen x + 8\rparen = 0} \\ \\ x\text{ - 3 = 0, x + 8 = 0} \\ x\text{ = 3, x = -8} \end{gathered}[/tex]Step 4:
\ertical} Asymptote is =-8,\ =3,
Zoe is making a rectangular box with measurements as shown below 5 inches 3 inches 3 inches what is the surface area of the box
Answers
Surface area of rectangular box is 78 inches².
What is surface area?The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units. The total area of all faces (or surfaces) on a 3D form is the surface area. The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.
Given Data
rectangular box with measurements as shown below 5 inches 3 inches 3 inches
Length = 5 inches
Width = 3 inches
Height = 3 inches
Surface area formula
2lw + 2lh+2hw
Equating values
2(5)(3) + 2(5)(3) +2(3)(3)
30 + 30 + 18
78
Surface area of rectangular box is 78 inches².
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help me answer this.
Answers
Solution:
The cube is numbered from 1 to 6
[tex](S)=6[/tex]The probability that any of the numbers from 1 to 6 will show will be
[tex]Pr(R)=\frac{1}{6}[/tex]The expected value will be calculated below as
[tex]E.V=xP(x)[/tex][tex]undefined[/tex]the total consumption of fruit juice in a particular country in 2006 was about 2.28 times 10 squared 9 gallons. The population of that country that year was 3 times 10 squares 8 what was the average number of gallons consumed per person in the country 2006
Answers
The average consumption of the fruit juice would be 7.6 gallons for the year 2006.
What do you understand by average consumption?Average consumption is derived by dividing the total measured consumption of that municipal service by that consumer during the three months before by three. It refers to the average consumption of a consumer of a municipal service during a certain time.
How is the average consumption determined?Utilizing the total of quantities consumed or dispersed over a period of time, typically 12 months, the average monthly consumption can be computed. The average number of units used each month is known as average monthly consumption, stock-outs corrected (CA).
Total consumption of the fruit juice in 2006=2.28x109 gallons.
Total population of the country in year 2006=3x108
Average Consumption=(2.28x109)/(3x108)
= 7.6 gallons
Hence the average consumption would be 7.6 gallons per person.
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{1}{10}+\frac{11}{20}
10
1
+
20
11
Answers
The addition of the fraction 1/10 + 11/20 based on the computation will be 13/20.
What is a fraction?In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by ¼.
It should be noted that a fraction simply means a part of a whole number. It should be noted that it's usually expressed as a/b where a is the numerator and b is the denominator.
In this case, we want to add 1/10 + 11/20. This will be illustrated thus:
= 1/10 + 11/20
= 2/20 + 11/20
= 13/20
Therefore the addition is 13/20.
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The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the standard deviation is 3.1 years.
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a gorilla living longer than 23.9 years
Answers
The probability of a gorilla living less than 23.9 years is 0.84 (84%) if the lifespans of gorillas in a particular zoo are normally distributed.
How does probability work?A probability is also called as a numerical representation of the likelihood or chance that any kind of specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Probability refers to potential.
Any random event's occurrence is the exact subject of this area of mathematics. The range of the value varies from 0 to 1. Mathematics has been incorporated probability to forecast the likelihood of various types of events.
How is probability determined?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas.
We need to find the z-score herein of 23.9 years in the kind of standard normal distribution of the lifespans of gorillas in this particular zoo.
z score can be further be calculated using the equation
z = (X-M)/s
and it has been given that X is 23.9 years
M is also called the average gorilla life (20.8 years)
s is given as the standard deviation (3.1 years)
Thus, putting up the values, we have
Z = 1
The Empirical rule that is present here states that 68% of the total lifespans lie within 1 standard deviation from the other mean.
Then Half of it, 68/2 = 34 % lies right side of 1 standard span of the mean.
Since this lifespan is less than mean is 50%, 50%+34% =84% lies less than total z-score 1, that is the probability of a gorilla living less than 23.9 years.
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Question
A golden retriever weighing 85 lb was prescribed a medication. If the dosage is 1 mg for every 5 lb, how much medicine was
the dog given?
Answers
Find the slope and the y-intercept of the line with the equation 9y - 6x + 8 = 0.Select the correct choice below and fill in any answer boxes within your choice. A. The slope is(Type an integer or a simplified fraction.)B. The slope is undefined.Select the correct choice below and fill in any answer boxes within your choice.A. The y-intercept is(Type an integer or a simplified fraction. Type an ordered pair.)B. There is no y intercept
Answers
Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.
Rewrite the given equation as follows:
[tex]\begin{gathered} 9y-6x+8=0 \\ \text{Take x term and the constant to the right side and change their sign} \\ 9y=6x-8 \\ \text{Divide each term by 9:} \\ \frac{9y}{9}=\frac{6x}{9}-\frac{8}{9} \end{gathered}[/tex]Simplify the equation:
[tex]y=\frac{6}{9}x-\frac{8}{9}[/tex]Compare to the equation y=mx+c, to get:
[tex]\begin{gathered} m=\frac{6}{9} \\ c=-\frac{8}{9} \end{gathered}[/tex]Hence, the slope is 6/9 and the y-intercept is -8/9.
You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.
Why is it important the order we write the vertices of a triangle in a congruent statement? SELECT ALL THAT APPLY!
A The middle letter is the vertex of the angle.
B The order tells us what sides are congruent.
C The order does not matter
D The order tells us what angles are congruent.
Answers
It is important the order we write the vertices of a triangle in a congruent statement as
B. The order tells us what sides are congruent.
D. The order tells us what angles are congruent.
How to illustrate the information?A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.
Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.
The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.
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Please help me solve question
Answers
In this problem, we are looking for the doubling time of the wage of the Toyota automobile assembly line workers. Initially, their wage is $6.70 and by the end of 15 years, their salary is now $29.59.
What we can find here first is the rate of the increase of the salary of the workers. We can use the equation
[tex]y=y_0e^{rt}[/tex]We are looking for the value of r. We have to derive an equation solving for r. We have
[tex]\begin{gathered} \frac{y}{y_0^{}}=e^{rt} \\ rt=\ln \frac{y}{y_0} \\ r=\frac{1}{t}\ln \frac{y}{y_0} \end{gathered}[/tex]Now, we solve for the value of r given y = 29.59, y0 = 6.70, and t = 15 years. We get
[tex]\begin{gathered} r=\frac{1}{15}\ln (\frac{29.59}{6.70}) \\ r=0.099yr^{-1} \end{gathered}[/tex]The doubling time is computed as
[tex]d=\frac{\ln 2}{r}[/tex]Substitute the value of r on the equation above and solve, we get
[tex]d=\frac{\ln 2}{0.099}=7.00yr[/tex]Hence, the doubling time for this problem is equal to 7 years.
Answer: 7 years
Find the measure of each angle indicated
Answers
Answer:
68°
Step-by-step explanation:
Alternate exterior angles have the same measurement.
A cement walkway is to be poured .it is consists of the two rectangles with dimensions and a circle with radius 1.5 yards use 3.14 as an approximate value.how many square yards will the walkway be?If a painter it for 3.75 per square yard,how much will the painting cost?
Answers
The area of the walkway in square yards is 22.77 yards²
The cost of painting the walkway will be $85.37.
What is the area of the walkway?The square yards of the walkway can be determined by adding the areas of the two rectangles and the area of the quarter of a circle together.
Area of a rectangle = length x width
Area of the first rectangle = 9.5 x 1.5 = 14.25 yards²
Area of the second rectangle = 4.5 x 1.5 = 6.75 yards²
Area of a circle = πr²
Area of quarter of a circle = 1/4 × πr²
Where:
π = pi = 3.14
r = radius
1/4 x (3.14 x 1.5²) = 1.77 yards²
Area of the walkway = 1.77 yards² + 6.75 yards² + 14.25 yards² = 22.77 yards²
The cost of the painting can be determined by multiplying the area of the walkway by the cost per square yard.
Total cost = 22.77 yards² x 3.75 = $85.37
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850' of #2 wire is sent to your job. On Monday, you cut 3 pieces, each 175' long. On Tuesday, you cut 3 pieces, each 88' long, and 3 pieces, each 20' long. How much wire is left on the reel?
Answers
The remaining wire (W) is just the original wire (850') minus the cut wire on Monday, Tuesday...
[tex]W=850^{\prime}-3\cdot175^{\prime}-3\cdot88^{\prime}-3\cdot20^{\prime}=1^{\prime}[/tex]There is merely 1' of wire in the reel.
Find MK.
08
04
O 14
06
L
4x-2
O
x+2
K
Il
Answers
Answer:
14
Step-by-step explanation:
well, the logic is simply that the sum of the parts must be the same as the whole.
so,
8 + (x + 2) = 4x - 2
10 + x = 4x - 2
12 = 3x
x = 4
therefore,
MK = 4x - 2 = 4×4 - 2 = 16 - 2 = 14
f(-3) = -1, f(-2) = 4
Answers
Answer:
1(-3) = -3, 1f(-2) = -2
Step-by-step explanation:
Identify the correct description of the values in both the domain and range of the function
Answers
Domain is number of minutes water has been added .
Range is amount in the pond
What are domain and range ?The domain and range of a relation are, respectively, the sets of all the x-coordinates and all the y-coordinates of ordered pairs. For example, if the relationship is R = (1, 2), (2, 2), (3,), (4, 3), then
Domain is the set of all x-coordinates that is all with values of 1, 2, 3, and 4.
The set of all y-coordinates in the range is equal to 2, 3.
Domain : Let y = f(x) be a function with an independent variable x and a dependent variable y.
Range : a function represents a defined relationship between an independent variable (x) and a dependent variable (y). The formula to find the range of a function is y = f(x).
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Show your work here. Use the pen as needed. North High School is selling game tickets for one of their football games. Adult tickets (x) cost $7 each and student tickets (y) cost $4 each. Write and graph an inequality to represent the combination of tickets sold, assuming they estimate to make at most $280 in ticket sales for this game.graph it
Answers
Adult tickets cost $7 each
Student tickets cost
Choose all the expressions that are equal to 5/9 × 8
Answers
A.
[tex]\frac{9}{5\cdot8}=\frac{9}{40}\ne\frac{40}{9}[/tex]This is not a correct choice
--------------------------
B.
[tex]\frac{8}{9}\times5=\frac{40}{9}[/tex]This is a correct choice
---------------------------
C.
[tex]\frac{5}{8\times9}=\frac{5}{72}\ne\frac{40}{9}[/tex]This is not a correct choice
------------------------------------------------
D.
[tex]5\times\frac{1}{9}\times8=\frac{40}{9}[/tex]This is a correct choice
-------------------------------------------
E.
[tex]\frac{5\times8}{9}=\frac{40}{9}[/tex]This is a correct choice
Expert hel
me Give example of 6 types of factoring polynomials with Solution
Answers
Answer:
1 Greatest Common Factor
We have to find out the greatest common factor, of the given polynomial to factorise it. This process is nothing but a type of reverse procedure of distributive law.
2. Grouping
This method is also said to be factoring by pairs. Here, the given polynomial is distributed in pairs or grouped in pairs to find the zeros.
3. Using Identities
The factorisation can be done also by using algebraic identities. The most common identities used in terms of the factorisation are:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
a2 – b2= (a + b)(a – b)
4. Zero Factor Property :The Zero Factor Property (also called the Zero Product Property) says that if the product of two quantities is zero, then at least one of those quantities is zero. The only way to get a product equal to zero is to multiply by zero itself.
5. Greatest Common Factor (GCF) Method:
This is almost always the first method applied to factoring polynomials. Look at all of the terms and see if they all have something in common that can be removed.
6. Sum or Difference in Two Cubes
A cube is a term that has been multiplied by itself twice.
[tex] {3}^{3} {x}^{3} and \: \: \: {27x}^{3} [/tex]
are all cubed terms. The trick to remembering how to factor cubed terms is S.O.A.P. S = same sign, O = opposite sign A.P. = always positive.
A number, n, is multiplied by 5/8 The product is -0.4. What
is the value of n?
Answers
Answer:
n= -16/25
Step-by-step explanation:
In triangle ABC, angle B is one-quarter of angle A and angle C is two fifth of angle A. If the size of angle A is (x- 10)°. Form an equation in x and hence calculate the angle of triangle ABC to the nearest degree.
Answers
When in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10) degrees, then the ∠A, ∠B and ∠C are 109 degrees, 27 degrees and 44 degrees respectively
The ∠A = (x-10) degrees
Angle B is one-quarter of angle A
∠B = (1/4)×(x-10)
= (1/4)x - (5/2)
= 0.25x-2.5
The angle C is two fifth of angle A
∠C = (2/5)(x-10)
= (2/5)x - 4
= 0.4x-4
We know sum of the angles in a triangle is 180 degrees
Then,
∠A + ∠B + ∠C = 180
Substitute the values in the equation
(x-10) + 0.25x-2.5 +0.4x-4 = 180
1.65x-16.5 = 180
1.65x = 196.5
x ≈ 119
∠A = (x-10)
= 119-10
= 109 degrees
∠B = 0.25x-2.5
= 0.25×119-2.5
≈ 27 degrees
∠C = 0.4x-4
= 0.4×119-4
≈ 44 degrees
Hence, when in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10) degrees, then the ∠A, ∠B and ∠C are 109 degrees, 27 degrees and 44 degrees respectively
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i..i
哈!
Natalie used 2 1/2 tubes of blue paint to
paint the sky in her picture. Each tube
holds 4/5 ounces of paint. How many
ounces of blue paint did Natalie use?
Answers
How to get the equation of a parabola with 3 pointsy- intercept : (0, -1.4)x-intercept : (0.905,0)3rd point: (2,0.6)
Answers
he standard form of a quadratic efunctionis:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{Where } \\ a,b,\text{ and }c\text{ are real constants such that }a\ne0. \end{gathered}[/tex]Since the y-intercept is (0, -1.4), it follows that:
[tex]\begin{gathered} -1.4=a(0)^2+b(0)+c \\ \text{ Therefore,} \\ c=-1.4 \end{gathered}[/tex]Substitute c = -1.4 into the equation:
[tex]y=ax^2+bx-1.4[/tex]Since the x-intercept is (0.905, 0), it follows that:
[tex]\begin{gathered} a(0.905)^2+b(0.905)-1.4=0 \\ \text{Therefore,} \\ 0.819025a+0.905b=1.4-------(1) \end{gathered}[/tex]Since the graph passes through the third point (2, 0.6), it follows that:
[tex]\begin{gathered} 0.6=a(2)^2+b(2)-1.4 \\ \text{Therefore} \\ 4a+2b-1.4=0.6 \\ 4a+2b=0.6+1.4_{} \\ 4a+2b=2 \\ \text{Divide both sides by }2 \\ 2a+b=1 \\ \text{Hence} \\ b=1-2a---------(2) \end{gathered}[/tex]Substitute equation (2) into equation (1):
[tex]\begin{gathered} 0.819025a+0.905(1-2a)=1.4 \\ 0.819025a+0.905-1.81a=1.4 \\ \text{ Collect like terms:} \\ 0.819025a-1.81a=1.4-0.905 \\ -0.990975a=0.495 \\ \text{ Therefore,} \\ a=\frac{0.495}{-0.990975} \\ a\approx-0.5 \end{gathered}[/tex]Substitute a = -0.5 into equation (2), therefore,
[tex]b=1-2(-0.5)=1+1=2[/tex]Therfore the function is given by:
[tex]y=-0.5x^2+2x-1.4[/tex]The equation of the parabola is y = -0.5x² + 2x - 1.4
.
The sum of the forth and thirteen terms of an arithmetic progression is 80. find the sum of the first sixteen terms.
Answers
The most appropriate choice for Arithmetic Progression will be given by-
The sum of the first sixteen terms of the Arithmetic Progression is 640
What is Arithmetic Progression?
A series of numbers are said to be in Arithmetic Progression if the difference between consecutive terms of the series are same.
If [tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the series, a be the first term and d the common difference,
[tex]a_n = a+(n-1)d[/tex]
If [tex]S_n[/tex] is the sum of first n terms of the series,
[tex]S_n = \frac{n}{2}(2a+(n-1)d)[/tex]
Here,
Let the first term be a and the common difference be d
The sum of the fourth and thirteen terms of an arithmetic progression is 80.
[tex]a_4 + a_{13} = 80[/tex]
[tex]a + (4-1)d + a + (13-1)d = 80[/tex]
[tex]a + 3d +a +12d =80\\2a+15d =80[/tex]
[tex]S_{16} = \frac{16}{2}(2 \times a + (16 -1) \times d)\\[/tex]
[tex]= 8(2a+15d)[/tex]
[tex]= 8 \times 80[/tex]
[tex]= 640[/tex]
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What is the distance between the points A(-1,3) and point B(-8,3)?