Answer:
∠ 2 = 40°
Step-by-step explanation:
complementary angles sum to 90° , that is
∠ 1 + ∠ 2 = 90°
50° + ∠ 2 = 90° ( subtract 50° from both sides )
∠ 2 = 40°
What score would a student need to have a 30th percentile score on the SAT? Recall that the mean score was 1509, and the standard deviation of the scores is 312.
Group of answer choices
a. 1244
b. 1345
c. 1456
d. 1673
Rounding to the nearest whole number, we get that the score a student would need to have a 30th percentile score on the SAT is 1345. Correct option is B.
To find the score corresponding to the 30th percentile, we need to use the standard normal distribution with a mean of 0 and a standard deviation of 1. We can convert the SAT score to a standard normal score using the formula:
z = (x - μ) / σ
where x is the SAT score, μ is the mean score (1509), and σ is the standard deviation (312).
To find the score corresponding to the 30th percentile, we need to find the z-score that has an area of 0.30 to its left. Using a standard normal table or calculator, we can find that the z-score corresponding to a 30th percentile is approximately -0.52.
Now we can use the formula to find the corresponding SAT score:
-0.52 = (x - 1509) / 312
Solving for x, we get:
x = -0.52 * 312 + 1509 = 1345.36
Therefore, the answer is (b) 1345.
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In the given figure, PQ || RS and PQ=RS. Prove that APUQ = ASUR
APUQ = ASUR, which proves that the two triangles are congruent.
How do we arrive at this assertion?To prove that APUQ = ASUR, we can use the concept of parallel lines and corresponding angles.
Since PQ || RS and PQ = RS, we can conclude that corresponding angles are equal.
In the figure, angle APU and angle ASR are corresponding angles and are therefore equal.
Also, angle UQP and angle USR are corresponding angles and are therefore equal.
Since the angles APU and UQP add up to 180 degrees (because they form a straight line), we can conclude that angle APU = 180 - UQP.
Similarly, angle ASR = 180 - USR.
Therefore, APU + UQP = ASR + USR
So, APUQ = ASUR, which proves that the two triangles are congruent.
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drop-down menu.
An experiment is conducted in which a bead is randomly drawn from a bag, the color is recorded, and then the bead is replaced.
The results of the experiment are given in the table below.
Color
Red
Orange
Yellow
Green
Blue
Purple
Frequency
17
12
10
13
8
5
Which of the following lists would most likely have produced the given experimental results?
Color
List A
List B
Red
33
31
Orange
27
24
Yellow
22
18
Green
30
34
Blue
18
19
Purple
12
5
For the list selected above, what is the theoretical probability of selecting a red bead?
Using the experimental results, if 156 beads are drawn from a bag and returned, which color would have a frequency closest
to 24?
The theoretical probability of selecting a red bead is 0.28.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that,
Color Frequency
Red 17
Orange 12
Yellow 10
Green 9
Blue 8
Purple 5
Color List A List B
Red 33 31
Orange 27 24
Yellow 22 18
Green 30 34
Blue 18 19
Purple 12 5
Probability of selecting a red bead = 17/61
= 0.28
Orange color would have a frequency closest to 24.
Therefore, the theoretical probability of selecting a red bead is 0.28.
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Line segment A B is reflected across a line to form line segment A prime B prime. Points M and N are halfway between points A and A prime and B and B prime.
A reflection line is equidistant from a pre-image point and its image.
Therefore, in segment AA’, point M is the
PLS HELP ME
The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.
What is the distance between two parallel lines?Let the two lines be ax + by + c₁ = 0 and ax + by + c₂ = 0. Then the distance between the lines is given as,
d = |c₂ - c₁| / √(a² + b²)
Let the distance between Line AB and A'B' be d and the equation of the line AB be ax + by + c₁ = 0. Then the value of c₂ is given as,
d = |c₂ - c₁| / √(a² + b²)
d√(a² + b²) = c₂ - c₁
c₂ = d√(a² + b²) + c₁
Then the equation of the line A'B' is given as,
ax + by + c₂ = 0
ax + by + d√(a² + b²) + c₁ = 0
The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.
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Factor the trinomial 2x²
-
2x
3x - 9 using the box method
The factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).
How to factor the trinomial using box methodTo factor the trinomial 2x² - 2x - 3x + 9 using the box method, we first draw a box and divide it into four sections:
| 2x -3 |
|--------|
| -2x 9 |
Then, we fill in the top left section with the coefficient of the leading term, 2x, and the bottom right section with the constant term, 9.
| 2x -3 |
|--------|
| -2x 9 |
Next, we find two numbers that multiply to 2x * 9 = 18 and add to the coefficient of the middle term, -2x - 3x = -5x.
One way to do this is to factor out 2 from the leading two terms, giving 2x² - 2x - 3x + 9 = 2x(x - 1) - 3(x - 3), and then finding the product of (x - 1) and (x - 3) using the AC method:
AC method:
- The product of A and C is -9- The sum of A and C is -4 (since B = -5, which is the sum of A and C)- Find two numbers that multiply to -9 and add to -4: -9 and 1- Rewrite B as the sum of these two numbers, using the distributive property:2x(x - 1) - 3(x - 3) = 2x(x - 1) - 3x + 9 - 3(-1)
We can then place these two numbers in the remaining two sections of the box:
| 2x -3 |
|--------|
| -2x 9 |
| 2x -3 |
|--------|
| -2x 9 |
|--------|
| -3 1 |
We can now factor the trinomial by taking the common factor out of each row and column of the box:
2x(x - 1) - 3x + 9 - 3(-1)
= (2x - 3)(x - 3)
Therefore, the factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).
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Question 29 of 40
Does this graph show a function? Explain how you know.
9
A. Yes; the graph passes the vertical line test.
OB. No; there are y-values that have more than one x-value.
C. No; the graph fails the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
The graph represents a function because the graph passes the vertical line test option (A),
Yes, the graph that passes the vertical line test is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Here, The graph is attached to the picture, please refer to the picture.
Now, We have a graph shown in the picture.
The graph represents the parabola.
As we know, if the graph passes the vertical line test then it can be a function.
Thus, the graph represents a function because the graph passes the vertical line test option (C) Yes, the graph that passes the vertical line test is correct.
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The sides of a triangle measure 32 inches, 22 inches, and 19 inches. What is the area of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place. The area of the triangle is?
The area of the given triangle is approximately 204.2 square inches.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
To calculate the area of a triangle with given side lengths, we can use Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.
In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:
s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5
Now we can plug in these values into the formula and simplify:
Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16
Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.
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Please help. what is an equation of the line best fit. This is urgent
a. The line of the best fit is ŷ = -8.55485X + 118.39451.
b. The value of the correlation coefficient is -0.8619.
What is the line of best fit?A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
Sum of X = 117.4
Sum of Y = 298
Mean X = 10.6727
Mean Y = 27.0909
The sum of squares (SSX) = 0.8618
The sum of products (SP) = -7.3727
Regression Equation = ŷ = bX + a
b = SP/SSX = -7.37/0.86 = -8.55485
a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451
ŷ = -8.55485X + 118.39451
X Values
∑ = 117.4
Mean = 10.673
∑(X - Mx)² = SSx = 0.862
Y Values
∑ = 298
Mean = 27.091
∑(Y - My)² = SSy = 84.909
X and Y Combined
N = 11
∑(X - Mx)(Y - My) = -7.373
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -7.373 / √((0.862)(84.909)) = -0.8619
Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451
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what is 14/20 equivalent to
The expression 14/20 is equivalent to 7/10
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Given the expression:
14/20
The common term between the numerator and denominator is 2. Hence:
= 7/10
The expression 14/20 is equivalent to 7/10
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Marcus has 19 blueberry muffins that he wants to share equally with his two
friends. How many blueberry muffins will Marcus and his two friends receive?
Answer: 6 and 1/3
Step-by-step explanation:
Assuming that sweet generous little Marcus here wants some muffins too, he has to share 19 blueberry muffins between 3 people (Marcus + friend 1 + friend 2.)
Most unfortunately, 19 isn't divisible by 3 to create a whole number (ie. a whole muffin).
Therefore you have 2 options:
Option 1:
19/3 = 6.333....
This means that each person will get 6 and 1/3 of a muffin
Option 2:
19/3 = 6 (and 1 remainder)
This means that each person will get 6 muffins each, but there will be a leftover muffin to feed the birds or something.
(I personally prefer option 2, but I think your teacher is looking for option 1.)
If the tire height is 5.2 in. and the rim diameter is 17 in., what is the tire diameter?
Answer:
Circumference = (3.14)(15) = 47.1 in
Step-by-step explanation:
2x + 3y = 12
2x - y = 4
Answer:
The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)
Step-by-step explanation:
How does the formula for the sample mean differ from the formula for the Population mean?
The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).
The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.
The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :
The mean formula is written thus :
Population mean = Σx / N
Sample mean = Σx / n
Where, x = set of values.
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Need help???!!!! Please
Answer:
+5&-2
Step-by-step explanation:
What is the slope of the line that passes
through the points (5, -6) and (9, -6)?
Write your answer in simplest form.
the slopes would look like this
What does 250 represent in the function y = 250(2.3)"?
250 in the function given represents the exponential constant.
What is function? What is expression?A function is a relationship between a dependent {y} and independent variable {x}.An expression is a combination of terms both constants and variables.Given is the exponential function as -
y = 250(2.3)ˣ
In the exponential function given, 250 represents the exponential constant.
An exponential function is of the form -
y = A(B)ˣ
Therefore, 250 in the function given represents the exponential constant.
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3 out of every 7 workers in a factory are male. How many male workers are there if there are 24 female workers?
Answer: I guess its 10?
Step-by-step explanation:
Answer:28
Step-by-step explanation:
4x/7=24
x=42(total workers)
male workers=42-24=28
Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6,
2√10 ÷ 5 and √14
can anyone help me with this answer please.
The order from least to greatest would be as follows:
√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6
How did we get the value?To order the numbers, we need to first simplify and evaluate each expression.
1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757
2. 2√10 ÷ 5 = 1.265
3. √14 = 3.74166
4. 3√2 = 4.243
5. √19 + 1 = 5.359
6. 6 is simply 6
Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:
0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6
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This graph represents the amount of milk in a bottle in the fridge. Tell a story of the amount of milk in the bottle.
The milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Thus, option (a) is correct.
What is passage?The term “passage” refers to the explanation and description of a sentence in relation to a topic. The passage aimed to describe those details related to the theme of the story. The different passage is to justify to the different things as to clarify. The passage is to define the important terms.
The milk bottle sat on the central shelf, as mentioned in the passage. The artifact is a completely empty milk bottle. The section gives information regarding signs. The passage was Sig's refrigerator, which had been opened. A milk bottle sat on the middle shelf, its cap missing and no milk inside.
As a result, the milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Therefore, option (a) is correct.
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A guy wire runs from the top of a cell tower to a metal stake in the ground. Jacob places a 9-foot tall pole to support the guy wire. After placing the pole, Jacob measures the distance from the stake to the pole to be 1 ft. He then measures the distance from the pole to the tower to be 11 ft. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot, is 109 feet.
What is Pythagoras' theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
From the diagram.
ΔABE is similar to ΔCDE.
CD = 9 ft
DE = 1 ft
BD =11 ft
And we know,
ΔABE ~ ΔCDE.
So, the corresponding sides of similar triangles,
AB/CD = BE/DE
AB/9 = (11 + 1)/1
AB/9 = 12
AB = 12 x 9
AB = 108 feet.
To find AE:
Applying Pythegoras' theorem,
we get,
AE = √(AB² + BE²)
AE = √(108² + 12²)
AE = 108.67
Therefore, AE = 109 feet.
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A car travels at an average speed of 80 km/h for 2 hours. What distance does the car travel? c) A car travels a distance of 330 km at an average speed of
I NEED HELP ON THIS ASAP!!
The solution of both inequalities is (-1, 2).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have the inequalities
x+ y >1.........(1)
-x+ y <3.........(2)
The graph for x+ y >1 is shown by the red shaded region.
and, the graph for -x+ y <3 is shown by the blue shaded region.
Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.
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You want to save up to buy a car. You currently have $500 saved and are going to work this summer cleaning house for your grandma. She will pay you $50 every time you clean her house. Write an equation for this situation. Make sure you define your variables. (How many times will you need to clean her house to have $4,500 for the car you want to buy?
I need answer by 2/25/2023
80 times, the house should be cleaned to buy the car.
Equation for the amount is y = 50t + 500
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Given,
Amount in the savings = $500
Amount to get the car = $4500
Grandma pays $50 for every time after cleaning
then, after t times, the amount will be
y = 50 t + 500
here, y is the total amount after working
t is number of times of cleaning the house
For $4500
4500 = 50t + 500
50t = 4500 - 500
50t = 4000
t = 4000/50
t = 80
Hence, we have to clean the house 80 times to have $4500.
equation for the amount is y = 50t + 500
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I need help on this please
The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).
What is a quadratic function?Generally speaking, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
c represents the constant.
Next, we would solve the above quadratic function by using the factorization method;
x² + x - 72 = 0
x² - 8x + 9x - 72 = 0
x(x - 8) + 9(x - 8) = 0
(x + 9)(x - 8) = 0
(x + 9)(x - 8) = (x + a)(x - b).
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What are the x and y coordinates of the following equations?
y = x - 3
y = 2x + 2
Answer: The coordinates where the two lines intersect are (-5, -8).
Step-by-step explanation:
To find the coordinates where the two lines intersect, we need to solve the system of equations simultaneously. We can do this by substitution or elimination, but we'll use substitution here:
First, we set the two equations equal to each other:
x - 3 = 2x + 2
Next, we solve for x:
x - 2x = 2 + 3
-x = 5
x = -5
Now that we have the value of x, we can substitute it into one of the original equations to find the corresponding value of y. Let's use the first equation:
y = x - 3
y = (-5) - 3
y = -8
Q5. The volume of a cone is 128 cm³. The height of the cone is three time the length of the diameter of its base. Calculate the height of the cone.
The height of the cone in discuss as required to be determined is; 16.38 cm.
What is the height of the cone as described?Since the height of the cone is three times the length of the diameter of its base;
h = 3d;
d = h/3
Therefore, radius,
r = d/2
r = h/3 ÷ 2
multiply by the reciprocal of 2
r = h/3 × 1/2
r = h / 6.
Volume of a cone, V = (1/3) πr²h
128 = (1/3) × (22/7) × (h³/36)
h³ = 4398.55
h = 16.38 cm.
Ultimately, the height of the cone is; 16.38 cm.
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Which graph represents data points that have no correlation?
Answer:
bottom-right
Step-by-step explanation:
the points on the graph are scattered and have no correlation whereas the others all remain in a relatively similar shape
You randomly shuffle a deck of cards and deal two cards from the top. What is the probability that you deal the 7 of Spades followed by a King?
The probability that you deal the 7 of Spades followed by a King is 0.1.
What is a probability? Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is that you randomly shuffle a deck of cards and deal two cards from the top.
We can write the probability as -
P{E} = 1/52 + 4/51
P{E} = 0.02 + 0.08
P{E} = 0.1
Therefore, the probability that you deal the 7 of Spades followed by a King is 0.1.
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Copy each statement. Insert , -, x, + or division symbol to make each statement true.
27 3 5 2 = 19
81 11 8 4 1 = 60
The Complete statement are:
1. 27/3 + 5 x 2
2. 81 + 1 - 8 x 4 x 1 = 60
What are Arithmetic Operations?Combining operands with a single arithmetic operator specifies an arithmetic operation. The ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.
Given:
we have to apply the operation to make
27 3 5 2 = 19
81 11 8 4 1 = 60
so, first 27 3 5 2 = 19
1. 27/ 3 = 9
2. 5 x 2= 10
3. 9+ 10 = 19
For second,
1.81 + 11 = 92
2. 8 x 4 x 1 = 32
3. 92-32 = 60
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Bria and April were comparing text messages during lunch. April sent 20 text messages today. April sent one-fourth of the amount of text messages sent by Bria.
Write an equation to determine how many text messages Bria sent.
t divided by 4 equals 20
4t = 20
t + 4 = 20
t − 4 = 20
The equation that determines how many text messages Bria sent is given as follows:
t/4 = 20.
How to determine the number of messages that Bria sent?The number of messages that Bria sent is obtained applying the proportions in the context of the problem.
The amount sent by April is given as follows:
20 messages.
20 is one fourth of the amount t sent by Bria, hence the equation is given as follows:
t/4 = 20.
The number of messages sent by Bria is then given as follows:
t = 20 x 4
t = 80 messages.
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