Answer:
From the time Ms. Cruz purchased a stock till closing time that day, the value of the stock changed by -27.2 points. During that time, the stock value
changed at a steady rate of -6.4 points per hour.
An ice cream store determines the cost of its sundaes by using the formula C = 0.50s + 0.35n + 0.25t, where C is the total cost in dollars, s is the number of scoops of ice cream, n is the number of scoops of nuts, and t is the number of liquid toppings. A Nutty Sundae costs $3.55. It has 3 scoops of nuts and 2 different liquid toppings. How many scoops of ice cream are in this sundae?
Answer:
4 scoops of ice cream
Step-by-step explanation:
Plug in the total cost, number of scoops of nuts, and number of liquid toppings into the formula. Then, solve for s:
C = 0.50s + 0.35n + 0.25t
3.55 = 0.50s + 0.35(3) + 0.25(2)
3.55 = 0.50s + 1.05 + 0.5
3.55 = 0.50s + 1.55
2 = 0.50s
4 = s
So, the sundae had 4 scoops of ice cream.
help me solve this trig
Hello there!
Previously, we learnt that to solve the equation, we have to isolate the sin, cos, tan, etc first.
First Question
The first question has sin both sides. Notice that if we move sin(theta) to left. We get:-
[tex] \displaystyle \large{2 {sin}^{2} \theta - sin \theta = 0}[/tex]
We can common factor out the expression.
[tex] \displaystyle \large{sin \theta(2sin \theta - 1) = 0}[/tex]
It is a trigonometric equation in quadraric pattern.
We consider both equations:-
First Equation
[tex] \displaystyle \large{sin \theta = 0}[/tex]
Remind that sin = y. When sin theta = 0. It means that it lies on the positive x-axis.
We know that 0 satisfies the equation, because sin(0) is 0.
Same goes for π as well, but 2π does not count because the interval is from 0 ≤ theta < 2π.
Hence:-
[tex] \displaystyle \large { \theta = 0,\pi}[/tex]
Second Equation
[tex] \displaystyle \large{2sin \theta - 1 = 0}[/tex]
First, as we learnt. We isolate sin.
[tex] \displaystyle \large{sin \theta = \frac{1}{2} }[/tex]
We know that, sin is positive in Quadrant 1 and 2.
As we learnt from previous question, we use π - (ref. angle) to find Q2 angle.
We know that sin(π/6) is 1/2. Hence π/6 is our reference angle. Since π/6 is in Q1, we only have to find Q2.
Find Quadrant 2
[tex] \displaystyle \large{\pi - \frac{\pi}{6} = \frac{6\pi}{6} - \frac{\pi}{6} } \\ \displaystyle \large{ \frac{5\pi}{6} }[/tex]
Hence:-
[tex] \displaystyle \large{ \theta = \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]
Since both first and second equations are apart of same equation. Therefore, mix both theta from first and second.
Therefore, the solutions to the first question:-
[tex] \displaystyle \large \boxed{ \theta = 0,\pi, \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]
Second Question
This one is a reciprocal of tan, also known as cot.
[tex] \displaystyle \large{cot3 \theta = 1}[/tex]
For this, I will turn cot to 1/tan.
[tex] \displaystyle \large{ \frac{1}{tan3 \theta} = 1}[/tex]
Multiply whole equation by tan3 theta, to get rid of the denominator.
[tex] \displaystyle \large{ \frac{1}{tan3 \theta} \times tan3 \theta = 1 \times tan3 \theta } \\ \displaystyle \large{ 1= tan3 \theta }[/tex]
We also learnt about how to deal with number beside theta.
We increase the interval, by multiplying with the number.
Since our interval is:-
[tex] \displaystyle \large{0 \leqslant \theta < 2\pi}[/tex]
Multiply the whole interval by 3.
[tex] \displaystyle \large{0 \times 3 \leqslant \theta \times 3 < 2\pi \times 3} \\ \displaystyle \large{0 \leqslant 3 \theta < 6\pi }[/tex]
We also know that tan is positive in Quadrant 1 and Quadrant 3.
and tan(π/4) is 1. Therefore, π/4 is our reference angle and our first theta value.
When we want to find Quadrant 3, we use π + (ref. angle).
Find Q3
[tex] \displaystyle \large{\pi + \frac{\pi}{4} } = \frac{5\pi}{4} [/tex]
Hence, our theta values are π/4 and 5π/4. But that is for [0,2π) interval. We want to find theta values over [0,6π) interval.
As we learnt previously, that we use theta + 2πk to find values that are in interval greater than 2π.
As for tangent, we use:-
[tex] \displaystyle \large{ \theta + \pi k = \theta}[/tex]
Because tan is basically a slope or line proportional graph. So it gives the same value every π period.
Now imagine a unit circle, and make sure to have some basic geometry knowledge. Know that when values addition by 180° or π would give a straight angle.
We aren't using k = 1 for this because we've already found Q3 angle.
Since we know Q1 and Q3 angle in [0,2π).
We can also use theta + 2πk if you want.
First Value or π/4
[tex] \displaystyle \large{ \frac{\pi}{4} + 2\pi = \frac{9\pi}{4} } \\ \displaystyle \large{ \frac{\pi}{4} + 4\pi = \frac{17\pi}{4} }[/tex]
Second Value or 5π/4
[tex] \displaystyle \large{ \frac{5\pi}{4} + 2\pi = \frac{13\pi}{4} } \\ \displaystyle \large{ \frac{5\pi}{4} + 4\pi = \frac{21\pi}{4} }[/tex]
Yes, I use theta + 2πk for finding other values.
Therefore:-
[tex] \displaystyle \large{3 \theta = \frac{\pi}{4} , \frac{5\pi}{4} , \frac{9\pi}{4}, \frac{17\pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} }[/tex]
Then we divide every values by 3.
[tex] \displaystyle \large \boxed{\theta = \frac{\pi}{12} , \frac{5\pi}{12} , \frac{9\pi}{12}, \frac{17\pi}{12} , \frac{13\pi}{12} , \frac{21\pi}{12} }[/tex]
Let me know if you have any questions!
a fair coin is flipped. if the flip results in a head, then a fruit is selected from a basket containing 8 apples, 2 bananas, and 6 cantaloups. if the flip results in a tail, then a fruit is selected from a basket containing 6 apples and 4 bananas. what is the probability that the flip resulted in tails, given that the fruit selexted is a banana g
Solution :
We have given two baskets :
[tex]$H_1$[/tex] : 8 apples + 2 bananas + 6 cantaloupes = 16 fruits
[tex]$H_2$[/tex] : 6 apples + 4 bananas = 10 fruits
A fair coin is made to flipped. If the [tex]\text{flip}[/tex] results is head, then the fruit is selected from a basket [tex]$H_1$[/tex].
If the flip results in tail, then the fruit is selected from the basket [tex]$H_2$[/tex].
Probability of head P(H) = [tex]1/2[/tex]
Probability of tail P(T) = [tex]1/2[/tex]
if given event is :
B = selected fruit is BANANA
We have to calculate : P(T|B)
Probability of banana if the flip results is head P(B|H) = [tex]$\frac{2}{16}$[/tex]
Probability of banana if the flip results is tail P(B|T) = [tex]$\frac{4}{10}$[/tex]
From the Bayes' theorem :
Probability of flip results is tail when selected fruit is BANANA.
[tex]$P(T|B) = \frac{P(B|T)\ P(T)}{P(B|T) \ P(T) + P(B|H)\ P(H)}$[/tex]
[tex]$=\frac{\frac{4}{10} \times \frac{1}{2}} {\frac{4}{10} \times \frac{1}{2} + \frac{2}{16} \times \frac{1}{2}}$[/tex]
[tex]$=\frac{\frac{1}{5}}{\frac{1}{5}+\frac{1}{16}}$[/tex]
[tex]$=\frac{\frac{1}{5}}{\frac{21}{80}}$[/tex]
[tex]$=\frac{16}{21}$[/tex]
∴ [tex]$P(\ T|B\ )=\frac{16}{21}$[/tex]
Can someone do these please? ❤️
Answer:
-49
8
Step-by-step explanation:
-196/4 =
-49
(3+u)^2
-------------
8
Let u=5
(3+5)^2
-------------
8
(8)^2
-------------
8
64
-----
8
8
If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?
Answer:
The cube root parent function:
f(x) = [tex]\sqrt[3]{x}[/tex]Horizontally stretched by a factor of 4:
g(x) → f(1/4x) = [tex]\sqrt[3]{1/4x}[/tex]Translated 5 units right:
h(x) → g(x - 5) = [tex]\sqrt[3]{1/4x - 5}[/tex]Translated 3 units up:
k(x) → h(x) + 3 = [tex]\sqrt[3]{1/4x - 5} + 3[/tex]What function translates the function f(x)=|x| to the left 3 units and down 4 units?
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
Answer:
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Convert 2546 in base 10 to base 5
Answer:
40141
Step-by-step explanation:
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
HELP
Answer:
8 cm^2
Step-by-step explanation:
If the triangle is isosceles the sides are the same
Let the sides be x
We know that we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse
x^2+x^2 = (4 sqrt(2))^2
2x^2 =16(2)
2x^2 = 32
Divide by 2
2x^2/ 32/2
x^2 = 16
Taking the square root of each side
sqrt(x^2) = sqrt(16)
x = 4
The area of the triangle is
A =1/2 bh
A = 1/2 (4) (4)
A = 1/2(16)
A = 8
Answer:
8
Step-by-step explanation:
a^2 + b^2 = c^2
c = [tex]4\sqrt{2}[/tex]
[tex]c^{2} = 32[/tex]
a^2 + b^2 = 32
a=b (isosceles triangle)
a=b=4
base = 4
height = 4
area = 1/2 bh = 1/2(4)(4) = 8
what is the volume of the solid?
9514 1404 393
Answer:
(9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Step-by-step explanation:
The area of the hexagon is given by the formula ...
A = (3/2)√3·s^2 . . . . for side length s
The area of the hexagonal face of this solid is ...
A = (3/2)√3·(2 ft)^2 = 6√3 ft^2
__
The area of the circular hole in the hexagonal face is ...
A = πr^2
The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.
A = π(1 ft)^2 = π ft^2
Then the area of the "solid" part of the face of the figure is ...
A = (6√3 -π) ft^2
__
The volume is ...
V = Bh . . . . . where B is the area of the base of the prism, and h is its height
V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3
The length of a rectangle is five times its width. If the perimeter of the rectangle is 108 in, find its area.
Answer:
Step-by-step explanation:multiple 5 times 108 and that gives you your answer..
Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 30% of the passengers are on business while on ordinary jets 25% of the passengers are on business. Of Global's air fleet, 60% of its capacity is provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.)
a) What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?
Answer:
a) 0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.
b) 0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
Event A: Jumbo
Event B: Business
60% of its capacity is provided on jumbo jets.
This means that [tex]P(A) = 0.6[/tex]
On jumbo jets, 30% of the passengers are on business
This means that [tex]P(B|A) = 0.3[/tex]
Desired probability:
We want to find [tex]P(A \cap B)[/tex], so:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.6*0.3 = 0.18[/tex]
0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.
b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?
Event A: Ordinary
Event B: Non-business
60% of its capacity is provided on jumbo jets.
So 100 - 60 = 40% are ordinary, which means that [tex]P(A) = 0.4[/tex]
On ordinary jets 25% of the passengers are on business.
So 100 - 25 = 75% are non-business, that is [tex]P(B|A) = 0.75[/tex]
Desired probability:
We want to find [tex]P(A \cap B)[/tex], so:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.75*0.4 = 0.3[/tex]
0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.
What is the classification for this polynomial?
-9m^2n^3
Answer:
(a) Monomial
(b) Cubic
Step-by-step explanation:
Given
[tex]-9m^2n^3[/tex]
Required
Classify
By number of terms
The above polynomial is single term.
Single term polynomials are referred to as monomial
By degrees
To determine the degree, we consider the variable farthest from the constant.
In this case, n is farther from 9 than m.
And the power or degree of n is 3.
Polynomials with degree 3 are referred to as cubic polynomial
in a survey survey of 1200 students who have passed SEE 150 like to admit in science Faculty 600 in humanity first and 240 like to admit either of faculties and the rest were found not to be admitted in both faculties
Step-by-step explanation:
here is your answer it may help you
There are 700 don't like to admit in both faculties.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
In a survey, survey of 1200 students who have passed SEE 150 like to admit in science Faculty 600 in humanity first and 240 like to admit either of faculties and the rest were found not to be admitted in both faculties
Hence, not to be admit in any faculty = N
Science + Humanity - Either + None = 200
=> 150 + 600 - 240 + N = 1200
=> 750 - 240 + N = 1200
=> N = 700
Hence, 700 don't like to admit in both faculties.
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ2
I need help answering this ASAP
can you zoom in on my pic more or no does it say 1/z
Answer:
Option A. Reciprocal
Answered by GAUTHMATH
a. 15
b. 16
c. 9
d. 14
Answer:
15
Step-by-step explanation:
1-0 =1
3-1 =2
6-3=3
10-6=4
We are adding 1 more each time
10+5 = 15
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the first marble is white and the second marble is blue.
Answer:
3/56
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.
The total number of marbles in the box
= 1 + 3 + 2 + 2
= 8 marbles
The probability that the first marble is white and the second marble is blue
= 3/8 * 1/7
= 3/56
Which of the following can be used as "reasons" in a two-column proof?
Answer:
A definition and a theorem can be used as a reason in a two-column proof. A two column proof is assembled into statement and reason columns, where each statement should have verified reason.
Step-by-step explanation:
Answer:
Definitions and algebraic properties
Step-by-step explanation:
A worker in the automobile industry works an average of 43.7 hours per week. Assume the distribution is normal with a standard deviation of 1.6 hours.
(i) What is the probability that a randomly selected automobile worker works less than 40 hours per week?
(ii) If 15 automobile workers are randomly selected, what is the probability that the sample mean of working time is more than 45 hours per week?
Answer:
The solution is:
(1) 0.0104
(2) 0.0008
Step-by-step explanation:
Given:
Mean,
[tex]\mu = 43.7[/tex]
Standard deviation,
[tex]\sigma = 1.6[/tex]
(1)
⇒ [tex]P(X<40) = P(\frac{x-\mu}{\sigma}<\frac{40-43.7}{1.6} )[/tex]
[tex]=P(z< - 2.3125)[/tex]
[tex]=P(z<-2.31)[/tex]
[tex]=0.0104[/tex]
(2)
As we know,
n = 15
⇒ [tex]P(\bar X > 45)= P(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } } >\frac{45-43.7}{\frac{1.6}{\sqrt{15} } } )[/tex]
[tex]=P(z> 3.15)[/tex]
[tex]=1-P(z<3.15)[/tex]
[tex]=1-0.9992[/tex]
[tex]=0.0008[/tex]
A deli sandwich shop is offering either a ham or turkey sandwich, either tomato or vegetable soup, and either coffee or milk for their lunch special. Which tree diagram below shows all of the combinations for a sandwich, soup, and beverage?
Answer:
A.
Step-by-step explanation:
A. is the answer because they list all of the sandwiches, soups, and beverages with every possible combination.
Graph: y – 3 = 1/2 (x + 2)
Answer:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Step-by-step explanation:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Answer: See below
Concept:
There are different forms of linear equations:
Slope-intercept form: y = mx + bPoint-slope form: y - y₁ = m (x - x₁)Standard form: Ax + By = CIntercept form: x / x₁ + y / y₁ = 1Solve:
Given: y - 3 = 1/2 (x + 2)
Here, we can see the linear equation is in the form of point-slope form.
x₁ = -2
y₁ = 3
m = 1/2
Point included in the graph = (-2, 3)
Slope of the graph = 1/2
Hope this helps!! :)
Please let me know if you have any questions
6+7=10
13+8=18
32+21=32
11+34=0
31+03=?
process please
Answer:
6+7=13
13+8=21
32+21=52
11+34=46
31+03=34
Step-by-step explanation:
im not sure in the 31+03
An empty density bottle weighs 24gm. When completely filled with water it weighs 52 gm, when completely filled with a brine solution. Its weighs 56 gm calculate: a) Volume of bottle b) Density of brine solution
Step-by-step explanation:
Density = weight / volumeWater density = 1 gm/cm³a) Weight of the water:
52 - 24 = 28 gmVolume of bottle:
28 gm : 1 gm/cm³ = 28 cm³b) Weight of brine:
56 - 24 = 32 gmDensity of brine:
32 gm : 28 cm³ ≈ 1.14 gm/cm³Để tuyển nhân viên, một công ty tổ chức kiểm tra 3 vòng độc lập. Một người tham gia thi tuyển với xác suất qua các vòng lần lượt là 0,8 và 0,6 và 0,25.
a) Tìm xác suất để người đó không được nhận vào công ty?
b) Tìm xác suất để người đó thi đỗ ít nhất 1 vòng.
c) Tìm xác suất để người đó thi không đỗ ở vòng 2.
PLEASE HELP!! URGENT
Answer:
y=105
Step-by-step explanation:
82+75+x=180
157+x=180
x=23
82+23=y
105=y
Worth a lot of points.
Answer:
It's the last one.
Step-by-step explanation:
For example, if you have 0, the absolute valeu of 0 is 0. A postive number like 2, has an absolute value of 2. 0 is not greater than 0 and 2 is not greater than 2. Hope this helps!
Answer: Kayla is incorrect. The absolute value of 0 or a positive number is equal to the number.
Absolute numbers cannot be negative numbers. Therefore, an absolute number of a positive number will always be the positive number.Can you please me me
Step-by-step explanation:
1 since a tank holds 121/2 gallons of gas 121/2 multiplied by two it gives 25 -30 it gives 5 450 divided by two it gives 225-25 i guess.
Enter the equation of the line in slope-intercept form. Slope is 4, and (6,4) is on the line. The equation of the line is y=
Michael wants to buy an efficient Smart car that according to the latest EPA standards gets 33 mpg in the city and 40 mpg on the highway. The car that Michael picked out costs $18,560. His dad agreed to purchase the car if Michael would pay it off in equal monthly payments for the next 64 months. The equation y= - 290x +18,560 represents the amount, y
(in dollars), that Michael owes his father after x months.
(a) How much does Michael owe his dad after 3 months?
(b) Determine the slope of the line and interpret its meaning in the context of this problem.
(c) Interpret the meaning of the slope in the context of this problem.
The amount Michael owes his father increases or decreases by ___ per month.
Answer:
17690
Step-by-step explanation:
The amount Michael owes is given by :
y = - 290x +18,560
x = number of months ; y = amount owed
Amount owed after 3 months :
Put x = 3 in the equation :
y= - 290(3) +18,560
y = - 870 + 18560
y = 17690
According to the general form of a linear equation :
y = mx + c
Where, m = slope ; c = intercept
The slope = - 290 ; Intercept = 18560
Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month
The intercept shows that the original amount borrowed is 18560
Amount Michael owes his father decreases by 290 per month.
Part C
Based on feedback from an independent research firm, the flashlight manufacturer has decided to change the design of the flashlight. The reflector now needs to extend 4 centimeters past the center of the bulb, as shown in the diagram. In the new design, how wide will the reflector (CD) be at its widest point? Show your work.
Answer:
The answer is "18".
Step-by-step explanation:
In the given graph by concluding we observe that on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit
[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]
