Step-by-step explanation:
Direct variation means y = k x
when y = 2 x= 3
2 = k *3
2/3 = k
so the variation becomes y = 2/3 x
when x = 2
y = 2/3 (2)= 4/3
f(x)=−7x^2+8x+2what is the value of the discriminant of f? how many x-intercepts does the graph of f have?
The discriminant value is 120 and 2 is the x - intercept will have the graph of f.
What is X Intercept?The intercept of a line is the point on a graph where the line crosses an axis. There can be both x and y intercepts on a graph. The x-axis is the horizontal line on the graph, therefore the x-intercept can also be referred to as the horizontal intercept. This is the point where the line crosses the x-axis. At this point, the value of y is zero. The y-axis is the vertical axis on a graph. The y-intercept is the point where the line crosses the y-axis and x has a value of zero.
The function, we have:
[tex]f(x) = -7x^2 + 8x + 2[/tex]
We have to find the value of the discriminant of f and how many x- intercepts of the graph?
Firstly, We have to find the value of discriminant is
[tex]b^2 -4ac[/tex]
[tex]where ,ax^2 +bx+c[/tex]
a= -7, b = 8, c=2
The discriminant is:
= [tex]8^2 - 4(-7) (2)[/tex]
= 64 +56
= 120
This will have 2 real x intercepts because 120 > 0
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A national pizza chain collected data from 189 stores about pizza orders on a busy Saturday. The number of pizzas ordered from 15 random stores is below. 28, 53, 35, 66, 35, 28, 66, 48, 53, 53, 66, 53, 66, 66, 35 If the sample was representative of the entire chain, what was the mode of the number of pizzas ordered for all 189 stores? A. 50.07 B. 48 C. 53 D. 66
please hurry ;(
The mode of the number of pizzas ordered for all 189 stores is [tex]66[/tex]. The Option D is correct.
How do we get the mode for this datas?Mode refer he most frequent number, that is, the number that occurs the highest number of times. To find mode, we must determine the value that appears most frequently in the sample.
From the given data: [tex]28, 53, 35, 66, 35, 28, 66, 48, 53, 53, 66, 53, 66, 66, 35[/tex]. We see that the value 66 appears 5 times, which is more than any other value.
Therefore, the number 66 is the mode.
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What is the value of S?
Signed numbers are also called directed numbers true or false
The given statement, "Signed numbers are also called directed numbers" is true.
Signed numbers are numbers that can be positive, negative, or zero, and they are sometimes referred to as directed numbers because they have a direction or orientation on the number line. Positive numbers are usually associated with movements to the right on the number line, while negative numbers are associated with movements to the left.
Therefore, the given statement, "Signed numbers are also called directed numbers" is true.
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A fair coin is tossed times in succession. The set of equally likely outcomes is . Find the probability of getting exactly .
The probability of getting exactly zero tails is,
⇒ 1/4
We have to given that;
A fair coin is tossed two times in succession.
And, The set of equally likely outcomes in {HH,HT,TH, TT}.
Hence, a total number of 4 outcomes (denominator) and there in only 1 chance (numerator) that you will not get tails.
Thus, the probability of getting exactly zero tails is,
⇒ 1/4
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Complete question is,
A fair coin is tossed two times in succession. The set of equally likely outcomes in {HH,HT,TH, TT}. Find the probability of getting exactly zero tails.
Solve for θ if −10sinθ−8=5√3−8 and 0≤θ<2π.
The value of variable θ would be,
⇒ θ = 5π/3 and θ = 4π/3
We have to given that;
Expression is,
⇒ - 10sin θ - 8 = 5√3 - 8
Now, We can simplify as;
⇒ - 10sin θ - 8 = 5√3 - 8
⇒ - 10sin θ = 5√3
⇒ sin θ = - 5√3/10
⇒ sin θ = - √3/2
We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).
However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.
Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.
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a) A manufacturer of floor wax has developed two new brands, A and B. To determine which of the
two is superior, both waxes are applied to the floor surfaces in each of a sample of 25 homes. It is
known that the proportion of people that prefer A is 0.4 while the rest prefer brand B. Find the
probability that at least 8 homes would state a preference for brand B.
The probability of at least 8 homes would prefer brand B compare to compare A is given by 0.672.
Sample size 'n'= 25
Proportion of people prefer brand A = 0.4
This implies ,
Proportion of people prefer brand B 'p' = 1 - 0.4
= 0.6
Using the binomial distribution.
Let X be the number of homes that prefer brand B out of the 25 homes surveyed.
Then X follows a binomial distribution with parameters n = 25 and p = 0.6
Probability that at least 8 homes would state a preference for brand B. expressed as,
P(X ≥ 8) = 1 - P(X < 8)
Using the binomial distribution, compute P(X < 8) as follows,
P(X < 8) = Σ [²⁵Cₓ] × 0.6ˣ × 0.4²⁵⁻ˣ, for x = 0, 1, 2, ..., 7
where ²⁵Cₓ is the binomial coefficient which represents the number of ways to choose k homes out of 25.
Use a binomial calculator ,
⇒P(X < 8) = [²⁵C₀] × 0.6⁰× 0.4²⁵⁻⁰ + [²⁵C₁] × 0.6¹× 0.4²⁵⁻¹ + [²⁵C₂] × 0.6²× 0.4²⁵⁻² + .......+ [²⁵C₇] × 0.6⁷× 0.4²⁵⁻⁷
⇒P(X < 8) ≈ 0.328
This implies,
P(X ≥ 8) = 1 - P(X < 8)
≈ 1 - 0.328
= 0.672
Therefore, the probability that at least 8 homes would state a preference for brand B is approximately 0.672.
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The above question is incomplete , the complete question is:
A manufacturer of floor wax has developed two new brands, A and B. which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes are applied to the floor surfaces in each of a sample of 25 homes. It is known that the proportion of people that prefer A is 0.4 while the rest prefer brand B.
Find the probability that at least 8 homes would state a preference for brand B.
two 1−quart bottles
two 1−quart bottles
two 1−quart bottles and two 1−pint bottles
two 1−quart bottles and two 1−pint bottles
one 1−quart bottle and eight 8−ounce fluid glasses
one 1−quart bottle and eight 8−ounce fluid glasses
Select the objects that hold the same amount of liquid as a 96−fluid-ounce jug. Select all that apply.
three 1−quart bottles
three 1−quart bottles
two 8−ounce fluid glasses and two 1−pint bottles
two 8−ounce fluid glasses and two 1−pint bottles
To determine which objects hold the same amount of liquid as a 96-fluid-ounce jug, we need to convert each of the given measurements to fluid ounces and then add them up. Here are the conversions:
Two 1-quart bottles = 64 fluid ounces (2 x 32)
Two 1-pint bottles = 32 fluid ounces (2 x 16)
One 1-quart bottle and eight 8-ounce fluid glasses = 96 fluid ounces (32 + 8 x 8)
So, the objects that hold the same amount of liquid as a 96-fluid-ounce jug are:
One 1-quart bottle and eight 8-ounce fluid glasses
Three 1-quart bottles
Therefore, the correct answer is:
one 1−quart bottle and eight 8−ounce fluid glasses
three 1−quart bottles
7/5+1/4 Why isn't it giving me the answer
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
If the question is asking you to add the two fraction you would need to follow these steps:
Step 1: find a common denominator (both of the number 20 in common
Step 2: add the numerators ( 7/20 + 1/20 would = 8/20 )
Step 3 simply the fraction ( 8/20 will be simplyed to 2/5)
Answer:
33/20
Step-by-step explanation:
First find the Least common denominator
Then you check how many times each denominator goes into de Least common denominator
After multiply the number you got when you checked for the times the denominator will go into the LCM with the numerator then simplify
As a market researcher, you have been hired by a fast-food chain. They want to know what kind of food containers the public prefers (given environmental and recycling concerns). The question is whether the public prefers their hamburgers wrapped in aluminum foil, foam boxes, or paper. Analyze the following data for whether there is a significant difference.
Foam 74
Paper 103
FOIL 123
Calculate the appropriate statistic, identify the critical value, make your decision and conclusion and present the statistical results in correct form.
The conclusion is there is not a significant difference between the preference for the three food containers.
The appropriate statistic to use in this case is a chi-squared test. This test will help us determine if there is a significant difference between the preference of the three food containers.
The critical value for the chi-squared test with 2 degrees of freedom is 5.991.
The chi-squared statistic is calculated as follows:
(74-103)²/103 + (103-123)²/123 + (123-103)²/103
= 3.9/3.9
= 1.0
The chi-squared statistic (1.0) is less than the critical value (5.991). Therefore, there is not a significant difference between the preference for the three food containers.
The statistical results can be presented in the following form:
Chi-squared statistic = 1.0
Critical value = 5.991
Therefore, the conclusion is there is not a significant difference between the preference for the three food containers.
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please help for this question
Using the translation vector of 3 units up and 1 unit right resulted to image coordinate of
(3, 7)
(3, 5)
(2, 5)
The image is attached
How to find the translation vectorThe translation vector is of the rule 3 units up and 1 unit to the right
The coordinate of the preimage are
(2, 4)
(2, 2)
(1, 2)
The translation is done as below
(2 + 1, 4 + 3) = (3, 7)
(2 + 1, 2 + 3) = (3, 5)
(1 + 1, 2 + 3) = (2, 5)
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1. A new bicycle sells for $300 It is on sale for 1/4 off the regular price. Setect
all the expressions that represent the sale price of the bicycle in dollars.
A 300• 1/4
B.)300• 3/4
C.) 300• (1-1/4)
D.) 300- 1/4
E.)300 - 1/4•300
In a case wherby new bicycle sells for $300 It is on sale for 1/4 off the regular price all the expressions that represent the sale price of the bicycle in dollars are
B)300•3/4C)300•(1-1/4)E) 300-1/4•300How can the regular price all the expressions be known?From the option B)300•3/4, we cam see that (300*3)/4 = 225
From the option C)300•(1-1/4), (300*3)/4 = 225
From the E.)300 - 1/4•300, 300 - 75 = 225
Therefore, the correct options are the option BCE as listd below because they are seen as the one that gives the regular price all the expressions hence they are correct.
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A circular table measures 2.5 feet across the diameter of its top. What is the approximate area of the table top. Use 3.14 for TT.
O 9.42 ft²
O 19.63 ft²
O 4.91 ft²
O 7.85 ft²
b) Convert the pressure you calculated into pound per square inch (PSI) using the following relationship:
1 PSI = 6896.6 kg/m-sec2
The pressure of 1000 Pa is equal to 0.145 pound per square inche(PSI)
Let the pressure be 1000 pascal
We have to convert it to pound per square inche
1 psi = 6896.6 Pa
Therefore, to convert 1000 Pa to psi, we can divide by this conversion factor:
1000 Pa ÷ 6896.6 Pa/psi
= 0.145 psi
Hence, the pressure of 1000 Pa is equal to 0.145 psi.
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3 subtracted from quarter of g is 6
Answer: G=36
Step-by-step explanation:
Step 1: Write out the equation
1/4g-3=6
Step 2: Add 3 to both sides
1/4g=9
Step 3: Divide both sides by 1/4, or 0.25
G=36
The amount of pollution entering the atmosphere varies directly as the number of people living in an area. If 35,000 people create 21,350 tons of pollutants, how many tons enter the atmosphere in a city with a population of 500,000?
Please Help
The city with a population of 500,000 would produce 305,000 tons of pollutants.
We have,
Let's call the unknown amount of pollutants in the second city "x".
According to the problem,
The amount of pollution is directly proportional to the number of people. This means that we can set up a proportion:
Pollution/number of people
= pollution/number of people
Using the values we know:
= 21350/35000
= x/500000
Simplifying:
0.61 = x/500000
To solve for x, we can cross-multiply:
0.61 x 500000 = x
x = 305000
Therefore,
The city with a population of 500,000 would produce 305,000 tons of pollutants.
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What is the length of BD
The value of length BD is 3.0 units
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
since AC is a radius that joins a tangent, the angle between them is 90°. Therefore ∆ABC is a right triangle and Pythagoras theorem can be applied.
therefore c² = a²+b²
c² = 4.5²+6²
c²= 20.25+36
c²= 56.25
c = √7.5
AC = CD(radii of a circle)
therefore BD = BC -CD
= 7.5-4.5
= 3.0units
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
The slope of the polar curve at θ = π/4 is 24. Therefore, option D is correct.
To find the slope of the polar curve r = 6cos(2θ) - 5 at θ = π/4, we need to find the derivative of r with respect to θ, and then substitute θ = π/4 into the resulting expression.
Using the chain rule of differentiation, we have:
dr/dθ = dr/d(cos(2θ)) * d(cos(2θ))/dθ
To find the first derivative, we can use the power rule of differentiation:
dr/d(cos(2θ)) = -12sin(2θ)
To find the second derivative, we can use the chain rule again:
d(cos(2θ))/dθ = -2sin(2θ)
Substituting these into the expression for dr/dθ, we get:
dr/dθ = -12sin(2θ) * (-2sin(2θ)) = 24sin^2(2θ)
Now, substituting θ = π/4, we get:
dr/dθ|θ=π/4 = 24sin^2(π/2) = 24
The slope of the polar curve at θ = π/4 is therefore 24.
None of the given options match this result.
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Add and simplify 12ft. 8in. + 16ft. 11in.
Answer:
Step-by-step explanation:
29 ft
7 in
Determine which function is represented by the graph. Do not use a calculator. (a) f ( x ) = 4 cos ( x + π ) (b) f ( x ) = 4 cos 4 x (c) f ( x ) = 4 sin ( x − π ) (d) f ( x ) = − 4 cos ( x + π ) (e) f ( x ) = 1 − sin x 2
Answer:
The graph of the function appears to be a cosine function that has been shifted to the left by π/2 units, and has an amplitude of 4.
Option (a) is a cosine function that has been shifted to the left by π units, but does not have the amplitude of 4.
Option (b) is a cosine function that has a period of π/2, which is much shorter than the period of the graph.
Option (c) is a sine function that has been shifted to the right by π units, but does not have the amplitude of 4.
Option (d) is a cosine function that has been shifted to the left by π units and has the correct amplitude of 4.
Option (e) is not a cosine or sine function, so it cannot be the correct answer.
Therefore, the function represented by the graph is:
f(x) = -4 cos(x + π)
which is Option (d).
Step-by-step explanation:
If m varies directly with n and m=209 when n=22, find n when m=361
Answer:174
Step-by-step explanation:
209-22=187
361-22=174
Length of the Glass = ? if length of 6 glasses is 34 cm and length of 2 glasses 19 cm find length of 1 glass
The length of the glass is L = 5.67 cm
Given data ,
Let the length of one glass be "x" cm
According to the given information, the length of 6 glasses is 34 cm.
So, the combined length of 6 glasses is 6x cm, which is equal to 34 cm.
Similarly, the length of 2 glasses is 19 cm.
So, the combined length of 2 glasses is 2x cm, which is equal to 19 cm.
6x = 34 be equation (1)
2x = 19 be equation (2)
Now we can solve these equations to find the value of "x", which represents the length of one glass.
On dividing equation 1 by 6, we get:
x = 34/6
x ≈ 5.67 cm
Hence , the length of one glass is approximately 5.67 cm
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.....................
Answer:
(2,0)
Step-by-step explanation:
evaluate the function at the indicated value, using the technique indicated.
9. Find w(-3) using synthetic substitution:
w(x)=11x³ -6x² +2
Using synthetic division, the value at w(-3) of the expression w(x)=11x³ -6x² +2 is -349
What is synthetic substitution?Synthetic substitution is a mathematical method that is used for evaluating the algebra polynomial in the simpler process.
To determine the value of the polynomial at w = -3, we need to carry out the synthetic division.
Then, the value of the remainder is taken as the value of the expression at the particular value
We have the expression as;
w(x)=11x³ -6x² +2/x-3
Let's carry out the synthetic division
Then, this is represented as;
-3) 11 -6 0 2
-33 -117 -351
11 -39 -117 -349
The value is -349
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Given this unit circle what is the value of x? HELP PLEASE
Answer:
x = - [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
consider the right triangle formed by the x- axis, the y- coordinate of the given point and the radius of the circle 1 , to the point from the centre.
using Pythagoras' identity
x² + ( [tex]\frac{4}{5}[/tex] )² = 1²
x² + [tex]\frac{16}{25}[/tex] = 1 ( subtract [tex]\frac{16}{25}[/tex] from both sides )
x² = 1 - [tex]\frac{16}{25}[/tex] = [tex]\frac{9}{25}[/tex] ( take square root of both sides )
x² = ± [tex]\sqrt{\frac{9}{25} }[/tex] = ± [tex]\frac{\sqrt{9} }{\sqrt{25} }[/tex] = ± [tex]\frac{3}{5}[/tex]
since the given point is in the second quadrant , then
x = - [tex]\frac{3}{5}[/tex]
You deposit $500 in an account that earns simple interest at an annual rate of 4%. How much money is in the account after 6 years?
Answer:
The formula for simple interest is:
I = P * r * t
Where:
I = Interest earned
P = Principal amount (initial amount deposited)
r = Annual interest rate (as a decimal)
t = Time in years
Using the given values, we have:
P = $500
r = 0.04 (4% expressed as a decimal)
t = 6 years
I = P * r * t
I = $500 * 0.04 * 6
I = $120
So the interest earned after 6 years is $120. To find the total amount of money in the account, we add the interest to the principal:
Total = P + I
Total = $500 + $120
Total = $620
Therefore, there will be $620 in the account after 6 years.
Step-by-step explanation:
PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
V = π(19.1^2)(11.8) = 13,523.8 cubic mm
V = 3.14(1.91^2)(11.8) = 13,516.9 cubic mm
NEED HELP PLS! IT WAS DUE TODAY!!
An axon is a
long, tubelike structure extending from a neuron's cell body
branch-like fiber extending in clusters from a neuron's cell body
neuron's cell body
messenger of the nervous system.
An axon is a long, tubelike structure extending from a neuron's cell body branch-like fiber extending in clusters from a neuron's cell body messenger of the nervous system is true.
We have,
An axon is a long, tubelike structure that extends from a neuron's cell body.
It is a specialized fiber that carries electrical impulses, known as action potentials, away from the cell body and towards the axon terminals.
Axons are covered by a fatty substance called myelin, which insulates and protects the axon and helps to speed up the transmission of signals.
At the end of the axon, there are small branches called axon terminals, which release chemicals called neurotransmitters into the synapse, the small gap between the axon terminals and the dendrites of the next neuron in the circuit.
This allows the electrical signal to be converted into a chemical signal and transmitted to the next neuron, continuing the chain of communication in the nervous system.
Thus,
An axon is a long, tubelike structure extending from a neuron's cell body branch-like fiber extending in clusters from a neuron's cell body messenger of the nervous system is true.
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Find the surface area of the figure. Round the the
nearest hundredth when necessary.
22 in
17 in
19 in
35 in
20.3 in
The surface area of the figure = 2733.3 sq. in.
First we fine the surface area of the top surface of the figure.
The top surface is an rectangle with length = 19 in. and width = 17 in
Using the formula for the area of rectangle, the area of top face would be,
A₁ = 19 × 17
A₁ = 323 sq. in.
The slant face of the figure is a rectangle with length = 22 in. and width = 17 in
Using the formula for the area of rectangle, the area of slant surface of the figure would be,
A₂ = 22 × 17
A₂ = 374 sq. in.
There are two parallel trapezoidal surface of the figure with bases 35 in. and 19 in. respectively.
The height of the trapezoid = 20.3 in.
Using the formula for that area of trapezoid, the area of two trapezoidal surface of the figure would be,
A₃ = 2 × (sum of lengths two bases/2) × height
A₃ = 2 × (35 + 19/2) × 20.3
A₃ = 1096.2 sq. in.
The area of the bottom surface would be,
A₄ = 35 × 17
A₄ = 595 sq. in.
The area of right surface would be,
A₅ = 20.3 × 17
A₅ = 345.1 sq. in.
So, the total surface area would be,
A = A₁ + A₂ + A₃ + A₄ + A₅
A = 323 + 374 + 1096.2 + 595 + 345.1
A = 2733.3 sq. in.
Therefore, the surface area of the figure = 2733.3 sq. in.
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