The solution is the median dress size = 12.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
here, we have,
given that,
from the given data we get,
dress sizes are, 10, 12 , 14, 16
no. of dresses, 16, 38, 27, 19
Hence, using the formula we get, the median dress size = 12.
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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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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
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
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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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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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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Juan lives in a state where sales tax is 6%. This means you can find the total cost of an item, including tax, by using the expression c + 0.06c, where c is the pre-tax price of the item.
Use the expression to find the total cost of an item that has a pre-tax price of $72.00.
The total cost is $76.32.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Juan lives in a state where sales tax is 6%.
The modeled Equation is:
c + 0.06c, where c is the pre-tax price of the item.
If we have the pre-tax price of $72.00.
Total cost = 1.06 c
= 1.06 x 72
= $76.32
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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:
I NEED HELP AND FAST PLEASE HELP !!!!
The solution for f the angle ∠DEF will be 122°.
What is geometry?Geometry is the study of two- and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles.
Symmetry is defined as if the object is cut by its centre line the two cut parts should be the mirror image of each other so that we can call them symmetric to each other.
Given that the angles are:-
∠DCE = (3x + 16)°
∠DEF = (6x - 10)°
∠CDE = (2x - 4)°
In the triangle ΔCDE,
∠DEC = 180 - 3x - 16 - 2x + 4
∠DEC = (-5x + 168)°
∠DEC + ∠DEF = 180
5x + 168 + 6x - 10 = 180
x = 180 - 158
x = 22
The value of the ∠DEF is,
∠DEF = 6x - 10
∠DEF = 6 x 22 - 10
∠DEF = 122°
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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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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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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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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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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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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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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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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
Write an equivalent equation to AB = AC using A^-1 such that, when it is simplified, the resulting equation will simplify to B = C. What property should be used to continue simplifying the above equation? A. (AB)^-1 = B^-1A^-1 B. (A^-1)^T = (A^T)^-1 C. A-^1A = 1 D. (A^-1)^-1 = A
The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.
We can start with the equation AB = AC and multiply both sides by A^-1 on the left:
A^-1(AB) = A^-1(AC)
Using the associative property of matrix multiplication, we can simplify the left-hand side:
(A^-1A)B = (A^-1A)C
Using the fact that A^-1A = I (the identity matrix), we get:
IB = IC
Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:
B = C
Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.
The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.
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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:
Six guests invited by Mr. And Mrs. Bernardo to dinner. They are to be all
seated around a
circular table. How many ways can they be seated?
1. If the couple must sit together?
2. If the couple must not be together?
1) If the couple must sit together, there are 240 ways that they can be seated.
2) If the couple must not be together, there are 720 ways that they can be seated.
1) If the couple must sit together, we can think of them as one unit. So, there are 5 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.
The couple can be arranged in two different ways within their unit. So, the total number of ways they can be seated is: 5! × 2 = 240.
2) If the couple must not sit together, we can think of them as separate units. So, there are 6 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.
The couple cannot be seated next to each other, so there are 3 possible units where they cannot be seated next to each other. Once we have chosen one of these units for the starting point, there are 2 ways to arrange the couple within their unit. Therefore, the total number of ways they can be seated is: 5! × 2 × 3 = 720.
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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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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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Small airplanes weigh both passengers and bags to make sure the plane can hold all the weight aboard. Crew members also use this information to make sure the weight is evenly distributed across the plane. One such airline requires that each passenger and his bag weighs no more than 330 lbs. On this airline, each passenger is allowed to bring exactly one bag that weighs at most 30 lbs. Write and graph a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements.
The solution is, a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements are,
x+ y ≥ 330
y≥ 30
What is inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
given that,
One such airline requires that each passenger and his bag weighs no more than 330 lbs.
On this airline, each passenger is allowed to bring exactly one bag that weighs at most 30 lbs.
let, the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements.
so, a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements are,
x+ y ≥ 330
y≥ 30
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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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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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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.)
What is JK flip-flop and its truth table?
In the JK Flip-Flop truth table, when both inputs of the JK Flip-Flop are set to 1 and the clock input is also set to "High," the circuit is toggled from the SET to the RESET state.
Similar in operation to the SR flip flop is the JK flip flop. The JK flip flop is marked with the letters "J" and "K" rather than "S" and "R." When both inputs are set to 1, SR flip flips yield incorrect states as outputs, while JK flip flops do not, even when both "J" and "K" flip flops are set to 1. The only distinction between JK and SR flip flops is this. The JK Flip Flop is an additional clock input circuitry-equipped gated SR flip-flop. The presence of a clock input circuit prevents the invalid or unlawful output situation from occurring when both inputs are set to 1. The JK flip-flop hence has four input combinations that are possible: 1, 0, "no change," "toggle," and With the exception of the clock input, the JK flip flop's symbol is identical to that of the SR bistable latch.
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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
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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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