Answer:
The sample should be a random sample from the entire set of students and should include enough students to be reliable. Small samples have more variation, which leads to less reliable inferences.
To find out how many sixth through eighth grade students are interested in joining a running club, you can conduct a survey among these students. Choose a sample by randomly selecting a certain number of students from the list, ensuring diversity. Contact the selected students to ask about their interest in joining the club and calculate the percentage of interested students.
Explanation:To find out how many sixth through eighth grade students are interested in joining a running club, you would need to conduct a survey or questionnaire among the students in these grades. Here's how you can choose a sample that will give you a good representation of the whole population:
Start by listing all the sixth through eighth grade students in your school.You can then use a random sampling method, such as drawing names out of a hat or using a random number generator, to select a certain number of students from the list.Ensure that the sample includes a diverse group of students, representing different genders, ethnicities, and interests.Contact the selected students and ask them if they would be interested in joining a running club.Record their responses and calculate the percentage of students who are interested in joining the club.f(x)=x^2. what is g(x)? NEED ASAP WILL MARK BRAINLIEST
Answer:
[tex]g(x)= \frac{1}{9} \times x^2[/tex]
Step-by-step explanation:
Here we can see that the parent function is [tex]f(x)=x^2[/tex] and the translated function is g(x). f(x) is a parabola.
Rule says that any factor if multiplied by f(x) is going to contract the graph towards the y axis and vice versa.
Similarly any factor if f(x) is divided by some factor it is going to be stretch the graph away from the y axis and vice versa.
Here we can see that the translated graph g(x) is stretched away from the y axis with reference to the parent function f(x). Hence as per he rule discussed above, we get a preliminary information that the parent function f(x) is being divided by some factor.
now we are given that
[tex]f(x) = x^2[/tex]
[tex]f(3) = 3^2 = 9[/tex]
Where as
[tex]g(3) = 1[/tex] {as given in the graph}
Hence
at x=3 , f(x) = 9 and g(x) = 1 , and also we have discussed above that f(x) is divided by some factor. Hence [tex]g(x)= \frac{1}{9}f(x)[/tex]
[tex]g(x)= \frac{1}{9} \times x^2[/tex]
Assume that instead of conducting experiments, Latané and Darley had used a correlational method to study the relation between the number of bystanders who witness an emergency and how quickly a victim receives help. Assume that the correlational data were compatible with results from experiments: the more bystanders, the longer it took bystanders to help. What type of correlation is this?A) a nonlinear correlationB) a zero correlationC) a positive correlationD) a spurious correlationE) a negative correlation
Answer:
C) a positive correlation
Step-by-step explanation:
More people ⇒ Longer time is a positive correlation between those variables. However, longer time is not the desired outcome.
Rather, shorter time is the desired outcome. The correlation between more people and shorter time is negative. In order to compute that correlation numerically, one would have to define a function that would give a numerical value for "shorter time" that would model the goodness of outcome as time gets shorter.
Sarah takes a full-time position that pays $32,500 per year. The government takes out 3% for Social Security, 1.2 % for Medicare, and 14% for federal income tax. She does not live in state with state income tax.
MAMDM .A.3.a: What is her gross annual income?
Answer:
$32,500
Step-by-step explanation:
Sarah's gross income is the income amount before taxes and other deductions. It is $32,500.
SEE PHOTO! If 1 measures 135°, what is the measure of 8? (Lines b and c are parallel.)
A) 45°
B) 135°
C) 65°
D) 67.5°
Answer:
Measure 8 is 135°
Step-by-step explanation:
Measure 1 and Measure 8 are alternate exterior angles.
Answer:
B) 135°
Step-by-step explanation:
<1 = <4 vertical angles
<4 = <5 alternate interior angles
<5 = <8 vertical angles
Therefore <1 = <8
Since <1 = 135, we know <8 = 135
y-8/5 = 3 solve for y
a. 23
b. 7
c. -7
d. -23
Answer:
[tex]\large\boxed{a.\ 23}[/tex]
Step-by-step explanation:
[tex]\dfrac{y-8}{5}=3\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{y-8}{5\!\!\!\!\diagup_1}=5\cdot3\\\\y-8=15\qquad\text{add 8 to both sides}\\\\y-8+8=15+8\\\\y=23[/tex]
Use the net to find the lateral area of the prism.
___cm^2
Answer:
[tex]900\ cm^2[/tex]
Step-by-step explanation:
We can notice that the the prism provided is a rectangular prism.
By definition, The lateral area of a rectangular prism can be calculated by multiplying the perimeter of its base by its height.
The height is:
[tex]height=15\ cm[/tex]
Then, the perimeter of the base is:
[tex]Perimeter=17\ cm+17\ cm+13\ cm+13\ cm=60\ cm[/tex]
Then the lateral area is:
[tex]LA=60\ cm*15\ cm\\\\LA=900\ cm^2[/tex]
Most animals give birth during a general time of year. This is because animals naturally breed so that their young will be born at the time of year when there will be adequate food supply. The bar graph shows the number of live births of a jackrabbit native to California over the course of Year X. Based on the data, which of the following would be an appropriate conclusion?
A) In general, rabbits give birth during the spring months
B) In general, rabbits give birth during the summer months
C) In general,m California jackrabbits give birth during the spring months
D) In general, California jackrabbits give birth during the summer months
Answer:
I guess c I just plain out guessed
If Rick wishes to reduce his BMI to 27, he needs to eat fewer kcalories than he expends. For an adolescent who carries excess fat, the recommended maximal weight loss is one pound per week. Since there are 3500 kcalories in a pound of body fat, a deficit of 3500 kcalories for the week or 500 kcalories per day would be required. Calculate the maximum number of kcalories Rick can consume per day to achieve a weight loss of one pound per week. Assume that his weight is 205 pounds and that his physical activity factor is "low active."
This question is not complete because his height and age was not indicated in the above question.
Complete Question:
Rick is a healthy 19-year-old college student who is 70 inches tall and weighs 205 pounds. He has decided to "get a six-pack" over the summer with a diet and exercise program. As part of his new plan, he has stopped drinking soda and is eating more salads in addition to his usual diet. Besides of these changes, he is unclear on how to proceed to reach his fitness goal. Rick's mother wants to make sure his approach will not interfere with his normal growth and development, and has asked him to seek reliable information to help him make a reasonable plan.
If Rick wishes to reduce his BMI to 27, he needs to eat fewer kcalories than he expends. For an adolescent who carries excess fat, the recommended maximal weight loss is one pound per week. Since there are 3500 kcalories in a pound of body fat, a deficit of 3500 kcalories for the week or 500 kcalories per day would be required. Calculate the maximum number of kcalories Rick can consume per day to achieve a weight loss of one pound per week. Assume that his weight is 205 pounds and that his physical activity factor is "low active."
Answer:
2696 kilocalories
Step-by-step explanation:
STEP 1
First we need to calculate Rick's Basal Metabolic Rate( BMR)
Weight in pounds = 205 pounds
Age = 19 years
Height in inches = 70 inches
The formula for calculating Basal Metabolic Rate for men =
BMR = 66.47 + ( 6.24 × weight in pounds ) + ( 12.7 × height in inches ) − ( 6.755 × age in years )
BMR = 66.47 + ( 6.24 × 205 ) + ( 12.7 × 70 ) − ( 6.755 × 19)
= 2247
STEP 2:
The next step is to calculate the maximum amount kilocalories per day Rick should consume
Formula is given as :
For a person with physical activity factor of a ' low Active'
Maximum amount of kilocalories to consume per day = Basal Metabolic rate × 1.2
= 2247 × 1.2
= 2696 Kilocalories (kcalories) per day
4x(3x − 7) − 19x2
the 2 behind the x is an exponent
Answer:
-7x(x + 4)
Step-by-step explanation:
Not sure exactly what you're doing with this, but I know you're not solving it for x because there's no " = " there so I am assuming you're simplifying it as much as possible. I'm going with that.
First thing is to distribute through the parenthesis by multiplying 4x by 3x and then 4x by -7 to get:
[tex]12x^2-28x-19x^2[/tex]
Now combine like terms to get
[tex]-7x^2-28x[/tex]
The last thing you could do now is pull out what's common between each of those terms which is -7x. When you do that, you're left with
-7x(x + 4)
Help calculus module 6 DBQ
please show work
1. Let [tex]a,b,c[/tex] be the three points of intersection, i.e. the solutions to [tex]f(x)=g(x)[/tex]. They are approximately
[tex]a\approx-3.638[/tex]
[tex]b\approx-1.862[/tex]
[tex]c\approx0.889[/tex]
Then the area [tex]R+S[/tex] is
[tex]\displaystyle\int_a^c|f(x)-g(x)|\,\mathrm dx=\int_a^b(g(x)-f(x))\,\mathrm dx+\int_b^c(f(x)-g(x))\,\mathrm dx[/tex]
since over the interval [tex][a,b][/tex] we have [tex]g(x)\ge f(x)[/tex], and over the interval [tex][b,c][/tex] we have [tex]g(x)\le f(x)[/tex].
[tex]\displaystyle\int_a^b\left(\dfrac{x+1}3-\cos x\right)\,\mathrm dx+\int_b^c\left(\cos x-\dfrac{x+1}3\right)\,\mathrm dx\approx\boxed{1.662}[/tex]
2. Using the washer method, we generate washers with inner radius [tex]r_{\rm in}(x)=2-\max\{f(x),g(x)\}[/tex] and outer radius [tex]r_{\rm out}(x)=2-\min\{f(x),g(x)\}[/tex]. Each washer has volume [tex]\pi({r_{\rm out}(x)}^2-{r_{\rm in}(x)}^2)[/tex], so that the volume is given by the integral
[tex]\displaystyle\pi\int_a^b\left((2-\cos x)^2-\left(2-\frac{x+1}3\right)^2\right)\,\mathrm dx+\pi\int_b^c\left(\left(2-\frac{x+1}3\right)^2-(2-\cos x)^2\right)\,\mathrm dx\approx\boxed{18.900}[/tex]
3. Each semicircular cross section has diameter [tex]g(x)-f(x)[/tex]. The area of a semicircle with diameter [tex]d[/tex] is [tex]\dfrac{\pi d^2}8[/tex], so the volume is
[tex]\displaystyle\frac\pi8\int_a^b\left(\frac{x+1}3-\cos x\right)^2\,\mathrm dx\approx\boxed{0.043}[/tex]
4. [tex]f(x)=\cos x[/tex] is continuous and differentiable everywhere, so the the mean value theorem applies. We have
[tex]f'(x)=-\sin x[/tex]
and by the MVT there is at least one [tex]c\in(0,\pi)[/tex] such that
[tex]-\sin c=\dfrac{\cos\pi-\cos0}{\pi-0}[/tex]
[tex]\implies\sin c=\dfrac2\pi[/tex]
[tex]\implies c=\sin^{-1}\dfrac2\pi+2n\pi[/tex]
for integers [tex]n[/tex], but only one solution falls in the interval [tex][0,\pi][/tex] when [tex]n=0[/tex], giving [tex]c=\sin^{-1}\dfrac2\pi\approx\boxed{0.690}[/tex]
5. Take the derivative of the velocity function:
[tex]v'(t)=2t-9[/tex]
We have [tex]v'(t)=0[/tex] when [tex]t=\dfrac92=4.5[/tex]. For [tex]0\le t<4.5[/tex], we see that [tex]v'(t)<0[/tex], while for [tex]4.5<t\le8[/tex], we see that [tex]v'(t)>0[/tex]. So the particle is speeding up on the interval [tex]\boxed{\dfrac92<t\le8}[/tex] and slowing down on the interval [tex]\boxed{0\le t<\dfrac92}[/tex].
A and B are complementary. If B = 26°, what is the measure of A?
1) 26°
2) 64°
3) 154°
4) 74°
Answer:
2) 64°
Step-by-step explanation:
If A and B are complementary, that means that they add up to 90. Therefore, A + 26 = 90 and A = 64.
Answer:
2.) 64 degrees
Step-by-step explanation: 90-26 = 64
Reminder: Complementary are 90 degrees angle
Supplementary are 180 degrees angle
Identify the semiregular tessellation. HELP ASAP. PLEASE I AM DESPERATE!!
Answer:
see below
Step-by-step explanation:
A regular tessellation involves repeated use of a single regular polygon to cover the plane.
A semiregular tessellation involves repeated use of two or more regular polygons (in the same order around each polygon vertex) to cover the plane.
The first and third diagrams do not involve regular polygons. The fourth involves only a single regular polygon. Hence the second diagram is the one of interest.
The required second diagram is a semiregular tessellation.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex.
Regular tessellation uses one regular polygon repeatedly to cover the plane, while semiregular tessellation involves two or more regular polygons used in the same order around each polygon vertex to cover the plane. The second diagram, which involves semiregular tessellation, is of interest. The first and third diagrams do not use regular polygons, and the fourth diagram only uses a single regular polygon.
Thus, the required second diagram is a semiregular tessellation.
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Please help me with this math question
Answer:
[tex]x=140\degree[/tex]
Step-by-step explanation:
The tangents meet the circle at right angles.
The sum of angles in a quadrilateral is 360 degrees
The two given angles will therefore add up to 180 degrees.
This implies that;
[tex]x+40\degree=180\degree[/tex]
We solve for x to obtain:
[tex]x=180\degree-40\degree[/tex]
This simplifies to
[tex]x=140\degree[/tex]
[tex]\therefore x=140\degree[/tex]
What are the vertices of the hyperbola with equation 4y^2 - 25x^2 = 100?
bearing in mind that the variable with the positive sign is the "y", meaning the hyperbola is opening vertically, and thus its vertices/foci will be along the center's y-coordinate.
[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 4y^2-25x^2=100\implies \cfrac{4y^2-25x^2}{100}=1\implies \cfrac{4y^2}{100}-\cfrac{25x^2}{100}=1 \\\\\\ \cfrac{y^2}{25}-\cfrac{x^2}{4}=1\implies \cfrac{(y-0)^2}{5^2}-\cfrac{(x-0)^2}{2^2}=1\qquad \begin{cases} h=0\\ k=0\\ a=5\\ b=2 \end{cases} \\\\\\ \stackrel{\textit{vertices}}{(0, 0\pm 5)}\implies \begin{cases} (0,5)\\ (0,-5) \end{cases}[/tex]
A sports team came to town. The stadium filled all 10,000 seats at two-level pricing. Level 1 tickets are $50 each, and level 2 tickets are $150 each. The stadium made $75,000 in ticket sales. The system of equations that models this scenario is:
x + y = 10,000
50x + 150y = 75,000
What do the x and y represent in the system?
A.x represents the number of level 2 tickets; y represents the number of level 1 tickets
B.x represents the cost of level 1 tickets; y represents the cost of level 2 tickets
C.x represents the cost of level 2 tickets; y represents the cost of level 1 tickets
D.x represents the number of level 1 tickets; y represents the number of level 2 tickets
D. [tex]x[/tex] represents the number of level 1 tickets; [tex]y[/tex] represents the number of level 2 tickets
Explanation:The costs of the tickets are represented as constants ([tex]50[/tex] and [tex]150[/tex]), and so they are not variables.
We know [tex]x[/tex] is level 1 tickets and [tex]y[/tex] is level 2 tickets because the price of a level 1 ticket is $50 and the second equation contains [tex]50x[/tex]. Similarly, the cost of a level 2 ticket is $150 and the equation contains [tex]150y[/tex].
Answer:
(D) X represents the number of level 1 tickets.
HELP ME MATH
Match each quadratic function to its graph.
See the attached picture.
The negative sign in front of the 2 makes the graph an upside down U shape.
We know that the general equation of a parabola in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]
where the vertex of the parabola is at (h,k)
and if a>0 then the parabola is open upward and if a<0 then the parabola is open downward.
a)
[tex]f(x)=-2(x+3)^2-1[/tex]
Since, the leading coefficient is negative.
Hence, the graph of the function is a parabola which is downward open.
The vertex of the function is at (-3,-1)
b)
[tex]f(x)=-2(x+3)^2+1[/tex]
Again the leading coefficient is negative.
Hence, graph is open downward.
The vertex of the function is at (-3,1)
c)
[tex]f(x)=2(x+3)^2+1[/tex]
The leading coefficient is positive.
Hence, graph is open upward.
The vertex of the function is at (-3,1)
d)
[tex]f(x)=2(x-3)^2+1[/tex]
The leading coefficient is positive.
Hence, graph is open upward.
The vertex of the function is at (3,1)
Pulease helpp
Determine the area of the following triangle:
it has two sides (10 and 15)
and one angle whic is 37
A.area=45.1 units
B.59.9 units
its not C
D area=119.8 units
Answer:
A
Step-by-step explanation:
using formula
area of triangle=1/2 × AB×AC×sinA
WHERE AB=10 andAC=15 and sinA=37○
Answer: the answer is A
Step-by-step explanation:
please help will give brainliest
Apply the distributive property to factor out the greatest common factor.
Answer:
9 + 15 = 3(3 + 5)
Step-by-step explanation:
The greatest common factor of 9 and 15 is 3.
Factor 3 out of both 9 and 15.
9 + 15 = 3(3 + 5)
Brian and Jared live in the same apartment complex and they both bike to and from work every day. The figure above shows a typical commute home for each of them. Based on the figure, which of the following statements is true?
A) It takes Brian longer to bike home because his work is farther away
B) It takes Jared longer to bike home because his work is farther away
C) Jared and Brian arrive home at the same time, so they must bike at about the same rate
D) Jared bikes a longer distance than Brian in the same amount of time, so Jared must bike at a faster rate
Answer:
A) It takes Brian longer to bike home because his work is farther away.
Step-by-step explanation:
Out of the four statements, A makes the most sense. B and C are implausible based on the given information. D makes no sense seeing that it isn't given that they work in/at the same place, making it something that can't be proven.
Here is a distribution of six observations, sorted in ascending order:4.7, 9.2, 10.9, 12.3, 16.6, 18.3The mean of this distribution is 12. What is the value of 6 sigma (xi -x with a line over it)
Answer:
0 is the answer
Step-by-step explanation:
What is the value of x? Ik im really dumb whoops
Answer:
B. 75 Degrees
Step-by-step explanation:
A triangle is up to 180 degrees. Since you're given two angles already, you can add both of those together and subtract it from 180.
75 + 35 = 105
180 - 105 = 75
75 + 75 + 35 = 180
If θ is an angle in standard position whose terminal side passes through (3, 4), evaluate tan(1/2)θ.
1/4
3/10
1/2
4/5
The tangent half angle formula, one of several, is
[tex]\tan \dfrac a 2 = \dfrac{1 - \cos a}{\sin a}[/tex]
We have θ is opposite 4 in the 3/4/5 right triangle so
[tex]\cos \theta = \dfrac{3}{5}[/tex]
[tex]\sin \theta = \dfrac{4}{5}[/tex]
[tex]\tan \dfrac{\theta}{2} = \dfrac{1 - 3/5}{4/5} = \dfrac{5-3}{4}=\dfrac{1}{2}[/tex]
Answer: 1/2
This is actually pretty deep. It says half the big acute angle in the 3/4/5 triangle is the small diagonal angle of the 1x2 rectangle. Similarly, the small acute angle in 3/4/5 triangle is twice the small diagonal angle of the 1x3 rectangle.
To find the value of tan(1/2)θ, we calculate θ using the fact that tan(θ) = opposite/adjacent = 4/3, then apply the half-angle formula from trigonometry. We cannot complete the calculation as we don't have the exact cosine value of θ.
Explanation:The question asks to find the value of tan(1/2)θ where θ is an angle in standard position, and its terminal side passes through the point (3, 4). In this case, first, we need to find the value of θ. This can be found using the formula tan(θ)=opposite/adjacent. Given the point (3, 4), let's consider the coordinates as (x,y). Here, 3 is the x-coordinate, which acts as the adjacent side, and 4 is the y-coordinate, which acts as the opposite side. Therefore, θ=tan^-1(4/3).
To find the value of tan(1/2)θ, we can use the half-angle formula from trigonometry: tan(1/2)θ = √((1-cos(θ))/(1+cos(θ)))
However, this question does not provide enough information to determine which option is the solution, as the cosine of θ is needed for completing the calculation.
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i need help so much please help the attachment below is the question i need help on
Answer:
[tex]\dfrac{\sqrt[12]{55296}}{2}[/tex]
Step-by-step explanation:
Rationalize the denominator, then use a common root for the numerator.
[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{(2\cdot 3)^{\frac{1}{4}}}{2^{\frac{1}{3}}}\\\\=\dfrac{(2\cdot 3)^{\frac{1}{4}}}{2^{\frac{1}{3}}}\cdot\dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{2^{\frac{1}{4}+\frac{2}{3}}3^{\frac{1}{4}}}{2}\\\\=\dfrac{2^{\frac{11}{12}}3^{\frac{3}{12}}}{2}=\dfrac{\sqrt[12]{2^{11}3^{3}}}{2}\\\\=\dfrac{\sqrt[12]{55296}}{2}[/tex]
Use the x-intercept method to find all real solutions of the equation.x^3-10x^2+27x-18=0
Answer:
Step-by-step explanation:
Real solutions equal
x=6,3,1
Hope that helps!
ANSWER
[tex]x=1,x=3,x=6[/tex]
EXPLANATION
To solve an equation using the x-intercept method, we must graph the corresponding function and locate x-values of the x-intercepts.
The given polynomial equation is
[tex] {x}^{3} - 10 {x}^{2} + 27x - 18 = 0[/tex]
The graph of the corresponding function
[tex]y = {x}^{3} - 10 {x}^{2} + 27x - 18 [/tex]
Is shown in the attachment.
The x-intercepts are:(1,0), (3,0), (6,0)
Therefore the solutions are,
[tex]x=1,x=3,x=6 [/tex]
The temperature at midnight on a cold winter night was -2?C. Twelve hours later the temperature increased by 9?C. Then after 5 hours it decreased by 8?C. Find the temperature at 5 pm?
Answer: The temperature is -1 degrees
Step-by-step explanation: Trust me!
Bracket answer to each box to complete the paragraph proof triangle ABC Pro ma equals 66 2/3 on the unit test reasoning and proof
Answer:
889
Step-by-step explanation:
The required proof that the measure of the angle A is 60° is below in the solution part.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
By the triangle sum theorem, the sum of angles in a triangle is equal to 180°.
Therefore, m∠A + m∠B + m∠C = 180 using the Substitution property (3x)° + 90° + (x+10)° = 180°
To solve for x, first combine like terms to get 4x + 100 = 180,
using the subtraction property of equality, 4x = 80
using the Division property of equality, x = 20.
To find the measure of the angle A, use the substitution property to get m∠A = 3(20)°.
Finally, simplify the expression gets m∠A = 60°
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The missing figure has been attached below.
A sphere has a radius of 4 in. which equation finds the volume of the sphere?
Answer:
Step-by-step explanation:
By definition, Volume of Sphere = [tex]\frac{4}{3}[/tex]πr³
If r = 4 in,
then Volume = [tex]\frac{4}{3}[/tex]π(4)³ = 268.08 in³
Answer:
267.95
Step-by-step explanation:
4/3 * pi * 4^3
4/3 * pi *64
256/3* pi = 267.95
A bag contains 4 red marbles, 3 green marbles, and 2 yellow marbles. The probability of randomly picking a yellow marble is . What is the probability of not picking a yellow marble?
Probability of randomly picking a yellow marble is [tex]\frac{2}{9}[/tex].
Probability of not picking a yellow marble is [tex]\frac{7}{9}[/tex].
What is probability?Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.
According to the question
A bag contains 4 red marbles, 3 green marbles, and 2 yellow marbles.
Probability of randomly picking a yellow marble is
Number of favorable outcomes = 2
Total number of favorable outcomes = 4 + 3 + 2 = 9
Probability of randomly picking a yellow marble is [tex]\frac{2}{9}[/tex].
Probability of not picking a yellow marble
= 1 - Probability of randomly picking a yellow marble
= 1 - [tex]\frac{2}{9}[/tex]
= [tex]\frac{9-2}{9}[/tex]
= [tex]\frac{7}{9}[/tex]
Probability of not picking a yellow marble is [tex]\frac{7}{9}[/tex].
Hence,
Probability of randomly picking a yellow marble is [tex]\frac{2}{9}[/tex].
Probability of not picking a yellow marble is [tex]\frac{7}{9}[/tex].
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The probability of not picking a yellow marble from a bag with 9 marbles total, where only 2 are yellow, is 7/9 or approximately 77.78%.
The question is related to calculating the probability of an event not occurring—in this case, not picking a yellow marble from a bag that contains different colored marbles. The total number of marbles is 4 red marbles + 3 green marbles + 2 yellow marbles = 9 marbles. To find the probability of not picking a yellow marble, we consider the total marbles that are not yellow, which are 4 red + 3 green = 7 marbles. The probability is then the number of non-yellow marbles divided by the total number of marbles, so it's 7/9. To calculate this, we divide the 7 non-yellow marbles by the total of 9 marbles, resulting in a probability of 7/9, or about 77.78%.
Given: PQRS is a parallelogram
Prove: PR and QS bisect each other at T
Answer:
1) given
3)being alternate angleS
5)ASA condition
6)corresponding sides of congruent triangle are equal
7)Pt=Rt and ST =QT
. A new cell phone comes on the market. Sales (S, in millions) increase at a steady rate for several months then decrease at about the same rate. This can be modeled by the function
S(m)= -0.375|m-12|+15
(a) Graph the function, using correct labels and units.
(b) What is the vertex? What does the vertex mean in terms of the problem?
(c) What is the rate of change of the sales?
Answer:
(a) see below for a graph
(b) the vertex is (months, sales) = (12, 15); sales is $15M at 12 months
(c) .375 million per month increasing and decreasing
Step-by-step explanation:
(a) You can read the vertex from the equation of the function. The equation is of an absolute value function translated so its vertex is at (12, 15), and vertically scaled by a factor of -0.375. The negative scale factor means the graph will open downward.
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(b) Since graph is of sales in millions versus months, the meaning of the vertex at (12, 15) is that sales is $15 millions 12 months after the phone comes on the market.
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(c) If the function were written as a piecewise function, the coefficient of x would be +0.375 for x < 12 and -0.375 for x > 12. The "rate of change" is 0.375 millions per month both going up and coming down.
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Translation of a point on the graph of f(x) by "h" horizontal units and "k" vertical units changes the function to f(x -h) +k. That is, if you can identify the function f(x), you can read the translation from the expression f(x -h) +k. For the absolute value function |x|, the vertex is normally (0, 0). Translating it to (h, k) makes the expression be |x -h|+k, the form you see in this problem. It's not a mystery. It's just pattern matching.