Answer:
The correct answer option is 43%.
Step-by-step explanation:
We are given that 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair.
We are to find the probability of a student getting selected will have dark hair with blue eyes.
P(D|B) = P(D∩B) / P(B)
Substituting the given values in it to get:
P(D|B) = 0.3 / 0.7 = 0.428
Rounding it to the nearest whole percent we get:
0.428 × 100 = 42.8% ≈ 43%
Which is the most appropriate to describe a quantity decreasing at a steady rate
Which is the most appropriate to describe a quantity decreasing at a steady rate?
With a linear equation.
A car travels 2 5/8 miles in 3 1/2 minutes at a constant speed. Which equation represents the distance, d, that the car travels in m minutes?
Answer:
[tex]d=0.75m[/tex]
Step-by-step explanation:
Let
d------> the distance in miles
m----> the time in minutes
we know that
The speed is equal to divide the distance by the time
so
[tex]speed=d/m[/tex]
we have
[tex]d=2\frac{5}{8}\ miles=\frac{2*8+5}{8}=\frac{21}{8}\ miles[/tex]
[tex]m=3\frac{1}{2}\ minutes=\frac{3*2+1}{2}=\frac{7}{2}\ minutes[/tex]
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
so
In this problem the speed is the constant of proportionality
[tex]d=km[/tex]
Find the value of k
[tex]k=\frac{(21/8)}{(7/2)} =0.75\frac{miles}{minute}[/tex]
[tex]d=0.75m[/tex] ----> linear equation that represent the distance, d, that the car travels in m minutes
An example of dependent events is drawing a blue marble out of one jar and then drawing a
blue marble out of the another jar.
red marble out of the same jar, after replacing the first marble.
red marble out of the same jar, without replacing the first marble.
red marble out of another jar.
Answer:
red marble out of the same jar, without replacing the first marble.
Step-by-step explanation:
Dependant events means one depends on the other. If you don't replace the first marble then the chance of drawing any other marble is changed. To better see it try giving them numbers, how many blue and red marbles start in the jar and calculate probability before and after removing a blue marble.
Dependent events are those in which the outcome of one affects others. Drawing a marble from a jar and then drawing another without replacing the first one is an example of dependent events. Independent events don't affect each other, as when drawing marbles from different jars or replacing a marble before drawing another from the same jar.
The question you've asked pertains to the concept of dependent and independent events in probability theory. Dependent events are events in which the outcome of one affects the outcome of the others.
If we draw a blue marble from the jar and then, without replacing the first marble, we draw another marble, these are dependent events because the second event is affected by the outcome of the first.
On the other hand, if we draw a blue marble from one jar and then draw a marble from another jar, these are independent events because they do not affect each other.
Similarly, if we draw a marble from a jar, replace it, and then draw another, these are also independent events because putting the first marble back makes the second draw unaffected by the first one.
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Translate the point (1, 3) to the new origin given ( h , k ). Given center ( h , k ) = (5, 4), find point ( x ', y ').
Answer:
(6,7)
Step-by-step explanation:
To translate a point, move each coordinate the specified amount and direction. Since the origin (0,0) moved to (5,4) or 5 right and 4 up, move (1,3) the same amount and direction. 1 moves right to 6. 3 moves up to 7. The new point is (6,7)
Answer:
(-4,-1)
Step-by-step explanation:
(h,k)=(5,4) and (x,y)=(1,3)
x' = x - h = 1 - 5 = - 4
y' = y -k = 3 - 4 = - 1
Find the length of the arc shown in brown. Leave your answer in terms of pi.
Answer:
The length of the arc is [tex]8\pi\ ft[/tex]
Step-by-step explanation:
we know that
The measure of the arc shown in brown is equal to
[tex]180\°-60\°=120\°[/tex] -----> by central angle
Remember that
The length of the arc of the complete circle (360 degrees) is equal to the circumference
[tex]C=\pi D[/tex]
we have
[tex]D=24\ ft[/tex]
substitute
[tex]C=\pi (24)=24 \pi\ ft[/tex]
so
by proportion
Find the length of the arc for a measure of [tex]120\°[/tex]
[tex]\frac{24\pi }{360} \frac{ft}{degrees} =\frac{x }{120} \frac{ft}{degrees}\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft[/tex]
Charles rolled a ball across the floor and noticed that it stopped before reaching the other side of the room. A force applied to the ball in the opposite direction in which it was rolling caused this to happen. What is the name of this force? A. Friction B. Gravity C. Electricity D. Magnetism
Answer:
Friction
Step-by-step explanation:
Because friction between the floor and the ball made the ball stopped from rolling.
Answer:
Friction
Step-by-step explanation:
The force that acts in opposite direction to the motion of the ball thereby causing it to stop is the force of friction.
This frictional force is a force of opposition that causes bodies moving in a particular direction to come to an halt. The force always acts in the opposite direction to the moving force acting on a body.
Which is the definition of a ray?
A.a part of a line that has one endpoint and extends indefinitely in one direction
B.the set of all points in a plane that are a given distance away from a given point
C.lines that lie in the same plane and do not intersect
D.a part of a line that has two endpoints
The correct answer is (A)!
Evaluate arccsc sqrt 2.
Answer:
{π/4 +2πn, 3π/4 +2πn}
Step-by-step explanation:
csc = 1/sin, so when csc(θ) = √2, sin(θ) = 1/√2. Then θ = π/4 or 3π/4.
This means arccsc(√2) will be the set of angles shown above.
___
Once you recognize that π/4 is one of the angles, you can eliminate all but the correct answer choice.
Of course this is much easier if you have memorized the short list of trig function values:
sin(π/6) = cos(π/3) = 1/2
sin(π/4) = cos(π/4) = 1/√2 = (√2)/2
sin(π/3) = cos(π/6) = (√3)/2
tan = sin/cos
sec = 1/cos
csc = 1/sin
Answer:
the above answer is correct
1.
Use technology or a z-score table to answer the question.
The expression P(z<1.45) represents the area under the standard normal curve below the given value of z.
What is P(z<1.45)?
0.0735
0.0749
0.9251
0.9265
2.Use technology or a z-score table to answer the question.
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test.
What percent of students scored below Jake?
Round your answer to the nearest whole number.
33%
57%
63%
72%
3.Use technology or a z-score table to answer the question.
Lengths of newborn girls are normally distributed with a mean of 49.2 cm and a standard deviation of 1.8 cm. Consider a group of 2000 newborn girls.
Approximately how many girls will be 51 cm or shorter?
1683
1856
1928
1964
4.The number 0.9967 represents the area under the standard normal curve below a particular z-score.
What is the z-score?
Enter your answer, as a decimal to the nearest hundredth, in the box.
5.Use technology or a z-distribution table to find the indicated area.
Suppose ages of cars driven by company employees are normally distributed with a mean of 8 years and a standard deviation of 3.2 years.
Approximately 75% of cars driven by company employees are older than what age?
2.1
4.8
5.9
10.2
Answer:
1.) 0.9265
2.) 63%
3.) 1683
4.) 5.9
I hope this helped and give me brainiest please
Answer:
Step-by-step explanation:
1) From standard distribution table we find that
P(Z<1.45) = 0.5+0.4265
=0.9265 Option d
2) Given that X, The scores on a standardized test is N(500,60)
percent of students who scored below Jake
[tex]=100*P(X<520)\\=100*P(Z<\frac{20}{60} )\\=100(0.5+0.1293)\\=62.93%\\=63%[/tex]
3) X, lengths of new born girls is N(49.2, 1.8)
n = 2000
P(X<51) = P(Z<1) =0.84
No of girls =2000(0.84) =1683
4) P(Z<2.72) is the answer
5)X, ages of cars driven is N(8,3.2)
75% correspond to z=0.675
X = 8+0.675(3.2) =10.16=10.2
You are standing 50 meters from a hot air balloon that is preparing to take off. The angle of the elevation to the top of the balloon is 28. Find the height of the balloon
Answer:
27 meters
Step-by-step explanation:
Think of it like a right triangle. One leg is 50m long (the distance you are from the balloon) and the goal is to find the other leg of the triangle. From the place you're standing, the angle is 28°. In relation to that angle, you're given the adjacent side (50m) and need to find the opposite side. Recall SOH-CAH-TOA. You have to use tangent to get the length. Tan = opposite/adjacent. The tan of 28 = x / 50. Use algebra to solve: tan28 (50) = x; aproximately 26.6m = x. So, the height of the hot air balloon is roughly 26.6m or 27m depending on how you round.
WHAT ARE THE ELEMENTS NEEDED TO PROVE SIMILARITY BETWEEN TWO FIGURES? EXPLAIN.
Answer:
AAA (Angle Angle Angle) Proving that the angles are the same (Or of the same ratio if diluted), if this is true, the two figures are similar.
SSS (Side Side Side) Proving all the sides are the same size (Or again of the same ratio) also proves similarity.
SAS (Side Angle Side) If two sides and the angle in between are the same, then the triangles are similar.
Step-by-step explanation:
EX)
Triangle A has sides 10, 5, and 12
Triangle B has sides 20, 10, and 24
The relationship is the same between both triangles, just that the sides are multiplied by 2. This is SSS
If Triangle A has two sides 5 and 10 with an angle of 25 degrees, then Triangle B must have that same angle alongside those two sides, or at least a consistent ratio if diluted. Proof SAS
If Triangle A and B have the same angles, they are similar.
What is the are of a triangle (picture provided)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
* Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
Angle 3 and angle 4 are supplementary angles. Angle 3 is 88°. What is the measure of angle 4?
1. You do 180-88 because supplementary angles add up to 180°.
2. 180-88=92°. Angle 4 is 92°
Answer:
92 degrees
Step-by-step explanation:
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The expression 2x(3x^2+4) can be simplified into which of the following?
a. 6x^3+4
b. 5x^3+6x
c. 6x^2+8x
d. 6x^3+8x
Answer:
[tex]\large\boxed{d.\ 6x^3+8x}[/tex]
Step-by-step explanation:
[tex]2x(3x^2+4)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(2x)(3x^2)+(2x)(4)\\\\=6x^3+8x[/tex]
Which statement about function F and Function G is true?
Answer:
C. Both functions have a y-intercept of -2
Step-by-step explanation:
A. Function F in decreasing then increasing, therefore it's incorrect
B. Function F is symmetrical about the y-axis, but Function G is not
C. Both functions intercept the y-axis at (0,-2) so it's correct
D. Only function G shows a linear relationship.
To look at a picture of what Function G looks like. Press y= on your Ti-84 calculator (top left) put the function in, and then press graph (top right)
This is 100% correct. I took algebra 1 last year.
Our goal is to make add-on sales during 85% of sales. If you make 35 sales, how many add-on sales do.You need to make to meet the goal?
Answer:
30 add-on sales to make the goal
Step-by-step explanation:
multiply 35*85% (or 0.85)
35*0.85 = 29.75
Since you can't make 0.75 of a goal, round up to the next highest number = 30
Express the following rate as a unit rate.
answering 36 questions in 3 minutes
18 questions per minute
12 questions per minute
15 questions per minute
36 questions per minute
The answer is 12 questions per minute as you divide 36 by 3
Answer=12 questions per minute
Answer:
12
Step-by-step explanation:
Match the following items by evaluating the expression for x = -6.
x^-2
x^-1
x^0
x^1
x^2
Choices:
1/36
-6
36
1
-1/6
x^-2 matches 1/36
x^-1 matches -1/6
x^0 matches 1
x^1 matches -6
x^2 matches 36
Explanation:When evaluating expressions with exponents for a specific value, we simply substitute that value for x and follow the order of operations (PEMDAS). Here's the breakdown for each expression:
x^-2: (-6)^-2 = 1/(-6)^2 = 1/36
x^-1: (-6)^-1 = 1/(-6) = -1/6
x^0: (-6)^0 = 1 (any non-zero number raised to the power 0 equals 1)
x^1: (-6)^1 = -6 (any non-zero number raised to the power 1 equals itself)
x^2: (-6)^2 = (-6) * (-6) = 36
Therefore, the matches are as listed above.
Joey runs diagonally across a rectangular field. The field had a width of 15 yards and a length of 36 yards. How far did Joey run
Answer:
Joey ran 39 yards
Step-by-step explanation:
a²+b²=c²
15²+36²=c²
225+1296=c²
1521=c²
√1521=√c²
39=c
The points A, B, C, and D are taken in order on the circumference of a circle. Chords AC and BD intersect at point E. mABarc = 76° and mCDarc = 80°. Draw chord AD. Find m∠AEB.
Answer:
∠AEB = 78°see attached for a drawingStep-by-step explanation:
The angle where the chords cross is the average of the two intercepted arcs:
∠AEB = (∠AOB +∠COD)/2 = (76° +80°)/2 = 78°
___
Chord AD connects points A and D.
Pham's annual salary is $78,000. Pham gets paid each month. Find Pham's monthly gross salary?
Answer:
Pham earns 6,500 per month.
Step-by-step explanation:
To get the monthly salary, divide the yearly salary by 12.
78,000/12 = 6,500
Answer:
78,000 / 12 = 6,500
Step-by-step explanation:
Pham's annual salary is $78,000
To find Pham's month salary
Divide 78,000 by 12
Thus 6,500
A non toxic furniture polish can be made by combining vinegar and oil. The amount of oil should be five times the amount of vinegar. How much of each ingredient is needed in order to make 27 oz of furniture polish?
There should be 4.5 oz of vinegar and 22.5 oz of oil
-5x+y=0
x+y=27
-6x=-27
V^2-8v=0 solving quadratic equation
Answer:
v = 0, or v = 8
Step-by-step explanation:
The quadratic can be factored, then the zero product rule applied.
v^2 -8v = 0
v(v -8) = 0
A product will be zero when any of the factors is zero. So, the solutions are values of v that make the factors be zero.
v = 0
v -8 = 0 . . . ⇒ . . . v = 8
The temperature at 8:00am is 5 degrees Celsius and increases 2 degrees per hour. Does this equal y=2x+5
Answer:
no
got correct on algebra nation
Mental break time. What is 1+1?
A) Not this one
B) Still not this one
C) 2
D) You've gone too far, go back to C
C is the correct answer. Appreciate it if you gave me brainliest!
Answer:
C
Step-by-step explanation:
and thank you for this it was funny and a good break from algebra 1! XD
Laura sold 3/4 of a case of Girl Scout cookies. Anna sold 2/3?Of a case. Witch girl sold more cookies?
we can simply put both fractions with the same denominator, and thus then we can just compare which numerator is larger.
we can do so by multiplying each fraction by the other's denominator, let's proceed.
[tex]\bf \stackrel{Laura}{\cfrac{3}{4}\cdot \cfrac{3}{3}}\implies \cfrac{9}{12}~\hfill \stackrel{Anna}{\cfrac{2}{3}\cdot \cfrac{4}{4}}\implies \cfrac{8}{12} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{Laura}{\cfrac{9}{12}}~>~\cfrac{8}{12}~\hfill[/tex]
Anita earns 60 points every time she shops at a grocery store.She needs a total of 2,580 points to receive a free prize.So far she has earned 480 points.How many more times will Anita have to shop at the grocery store in order to earn the additional points she needs for a prize?
Answer: 43 more times
2580÷60=43.
Step-by-step explanation: 43×60 =2580
This proves that 43 times is correct.
Answer:
c 43
Step-by-step explanation:
How do i solve for X
2x+4-7x+9x= -2
What is X?
Answer:
x = -3/2 or -1.5
Step-by-step explanation:
You have to get X on one side by itself.
2x + 4 - 7x + 9x = -2
Subtract the 4
2x - 7x + 9x = -6
Combine like terms
-5x + 9x = -6
Combine like terms
4x = -6
Divide by 4
x = -6/4
Simplify
x = -3/2 or -1.5
If a fair die is tossed, find the probability that the uppermost face displays a(n):
if a fair dice is tossed the probability is (T, H) (H, T) ( T, T) (H, H)
A fair, six-sided die has six equally likely outcomes. The probability of any one face showing up when the die is tossed is 1/6 or approximately 0.1667. Probability is a long term expectation under ideal theoretical conditions.
Explanation:The question is asking about the probability of each face showing up when a six-sided die is tossed. A fair, six-sided die has six possible outcomes: the faces are numbered 1, 2, 3, 4, 5, or 6. Each face is equally likely to be the uppermost face when the die is tossed. Therefore, the probability of any one face showing up is 1 out of 6, or approximately 0.1667.
Probability is a theoretical concept that tells us how likely an event is to occur. It does not describe the short-term results of an experiment. Rather, it gives information about what can be expected in the long term. Thus, if you were to toss a fair, six-sided die many times, you would expect that each face would come up about one-sixth of the time. This expectation is based on the assumption of ideal theoretical conditions where the die is fair.
Probability is a key concept in statistics and is used in many different areas of life, including in decision making, prediction, risk management, and games of chance.
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What is SIN A?
Question 4 options:
3/4
4/3
3/5
4/5
Final answer:
The value of sin A cannot be determined without knowing the value of angle A.
Explanation:
The question is asking for the value of sin A. In mathematics, sin A represents the sine of angle A. The sine function is a mathematical function that relates the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.
The correct answer to the question is 3/5. To find this value, you need to know the value of angle A. Without that information, we cannot determine the exact value of sin A.
Final answer:
The correct value of SIN A from the given options cannot be determined without additional context. SIN A refers to the ratio of the side opposite to angle 'A' to the hypotenuse in a right triangle or the y-coordinate on the unit circle at angle 'A'. Possible values are within the range of -1 to 1.
Explanation:
The question 'What is SIN A?' is seeking the trigonometric value of the sine function at a particular angle denoted by 'A'. When presented with options like 3/4, 4/3, 3/5, and 4/5, we need additional information regarding angle 'A' or the context of a right triangle or unit circle to determine the correct value. Without this information, we cannot definitively answer which option is correct.
Generally, in a right triangle, SIN A would represent the ratio of the length of the side opposite to angle 'A' to the length of the hypotenuse. Therefore, it is a value between -1 and 1. The options 3/4 and 3/5 could potentially be correct since they are within this range, but 4/3 cannot be because it exceeds this range. In a unit circle context, sin A would represent the y-coordinate of a point on the circle's circumference at an angle 'A' from the x-axis.