A ∩ B is the intersection of sets A and B, which is the set of elements that are in both A and B.
A = {2, 3, 5, 7} and B = {1, 2, 5, 10}, so A ∩ B = {2, 5}.
B ∩ D^c is the intersection of set B and the complement of set D, which is the set of elements in B that are not in D.
B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B ∩ D^c = {1, 10}.
A^c is the complement of set A, which is the set of elements in U that are not in A.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 7}, so A^c = {1, 4, 6, 8, 9, 10}.
C ∩ D is the intersection of sets C and D, which is the set of elements that are in both C and D.
C = {1, 2, 3, 6} and D = {3, 5, 7}, so C ∩ D = {3}.
B u D^c is the union of set B and the complement of set D, which is the set of elements that are in B or in the complement of D, or both.
B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B u D^c = {1, 2, 4, 5, 6, 8, 9, 10}.
Thus, this can be the universal set.
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Jeremy has a fish tank that has a 30 cm by 90 cm rectangular base. The water is 25 cm deep. When he drops rocks in
the tank, the water goes up by 2 cm. What is the volume in liters of the rocks?
The volume of the rocks is ____ L
You roll a 6 sided dice. What is P( not greater than 2 )
In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
2 students play both
Step-by-step explanation:n(u)=28
n(b)=7,n(b)=5,n(who play neither sport)=18
HERE,
n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)
28=7+5-n(BnB)+18
28=30-n(BnB)
n(BnB)=30-28
=2 answer
Consider the graph of the function f(x) = e^x
Which statement describes a key feature of function g if g (x) = e^x - 7?
Try It
Answer the questions to help choose the best data display.
1 Five teams are competing in a variety of events. The table shows the number of darts that hit
the bullseye for team results.
Team
Sharks
Tigers
Bananas
Stem-and-Leaf Plot frequency with
Eagles
Rubies
Number of
Bullseyes
12
2
7
1
10
What type of information is given?
What does the organizer want the display to show?
How will the display be analyzed?
Hill Education
gin
The information given in the table is the number of bullseyes hit by each team in a dart competition.
The organizer wants the display to show the performance of each team in hitting the bullseye in the competition.
The team with the highest number of bullseyes will be considered the best performer, while the team with the lowest number of bullseyes will be considered the worst performer
We have,
The information given in the table is the number of bullseyes hit by each team in a dart competition.
The organizer wants the display to show the performance of each team in hitting the bullseye in the competition.
The display will allow the audience to compare the performance of different teams and draw conclusions about which team performed better in hitting the bullseye.
The display will be analyzed by comparing the number of bullseyes hit by each team.
The team with the highest number of bullseyes will be considered the best performer, while the team with the lowest number of bullseyes will be considered the worst performer.
The audience may also analyze the performance of each team in relation to their expectations or previous performance in similar competitions.
Thus,
The information on the data displayed and its analysis is given above.
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The face of a clock has a circumference of 14 in.What is the area?Use 3.14 for
The area of the face of a clock with a circumference of 14 inches is approximately 15.6 square inches. This is calculated using the formula for the area of a circle, which is πr², where r is the radius of the circle.
To find the area of the face of the clock, we need to use the formula for the area of a circle, which is
A = πr²
where A is the area of the circle, π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle.
Since the circumference of the clock is 14 inches, we can use the formula for the circumference of a circle to find the radius
C = 2πr
14 = 2πr
r = 14 / (2π)
r = 2.227 in (approx)
Now that we know the radius, we can use the formula for the area of a circle
A = πr²
A = 3.14 x (2.227)²
A = 15.6 sq in (approx)
Therefore, the area of the face of the clock is approximately 15.6 square inches.
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The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
A.AP ≅ CP
B.BC ≅ AD
C.m∠ABC=90∘
D.∠CAD≅∠ACB
The statements that are true about diagonal of parallelogram;
A. AP is equal to CP
What is diagonal law of parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal and the sum of the adjascent angles is 180°.
The diagonal of a parallelogram is a line that touches the vertex of opposite angles. Here are some of the properties of diagonal of a parallelogram.
1. The diagonal divides the parallelogram into congruent triangles
2. The diagonal of parallelogram bisects each other but they are not equal.
3. The diagonal of parallelogram bisect each other at 90°.
Therefore, the statement that is true is AP is equal to CP since AC is a diagonal.
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Between last year and this year, the CPI in Blueland rose from 100 to 120 and the CPI In Redland rose from 100 to 115. Blueland's currency unit, the blue, was worth 80 cents (U.S.) last year and is worth 60 cents (U.S.) this year. Redland's currency unit, the red, was worth 20 cents (U.S.) last year and is worth 15 cents (U.S.) this year.
Find the percentage change from last year to this year in Blueland's nominal exchange rate with Redland and in Blueland's real exchange rate with Redland. (Treat Blueland as the home country.) Relative to Redland,
Blueland's nominal exchange rate with Redland decreased by 25% from last year to this year.
Blueland's real exchange rate with Redland decreased by 13.3% from last year to this year.
What is the percentage change in Blueland's exchange rate with Redland?The nominal exchange rate is ratio at which one currency can be exchanged for another. The real exchange rate account for changes in the inflation rate between two countries and provides accurate picture of the purchasing power of the currencies.
Here, Blueland's nominal exchange rate with Redland decreased by 25% from last year to this year, as the blue decreased in value relative to the red.
But Blueland's real exchange rate with Redland decreased by only 13.3%, as Blueland's inflation rate was higher than Redland's inflation rate which means Blueland's goods became relatively more expensive compared to Redland's goods.
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Use continuity to evaluate the limit:
[tex]\lim_{x \to 2}\arctan(\frac{x^2-4}{3x^2-6x} )[/tex]
Find the limit...
[tex]\lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )[/tex]
Factor the top and bottom of the expression.
[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{(x+2)(x-2)}{3x(x-2)} )[/tex]
Cancel the common factor "(x-2)."
[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{x+2}{3x} )[/tex]
Now plug in the limit.
[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{2+2}{3(2)} ) \Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{4}{6} )=\boxed{tan^{-1}(\frac{2}{3} )}[/tex]
[tex]\lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )=\boxed{\boxed{tan^{-1}(\frac{2}{3} )}} \therefore Sol.[/tex]
Thus, the limit is solved.
Carlos le dijo a Luisa: “Al sumar 4 al doble de un número el resultado es 30. ¿Cuál es el número?”
Find the value of x. Then find the area of the triangle.
Step-by-step explanation:
law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the corresponding opposite angles.
so,
16/sin(90) = x/sin(30)
16/1 = x/0.5
0.5 × 16 = x
x = 8 units
Pythagoras now gets us half the baseline (and therefore the full baseline) :
16² = x² + (baseline/2)² = 8² + (baseline/2)²
256 = 64 + baseline²/4
192 = baseline²/4
768 = baseline²
baseline = sqrt(768) = sqrt(256×3) = 16×sqrt(3) units
the area of a triangle is
baseline × height / 2
in our case
16×sqrt(3) × 8 / 2 = 16×sqrt(3) × 4 = 64×sqrt(3) units² =
= 110.8512517... units²
what is the fraction equivalent of the ratio of boys to girls in a class if there are 12 boys and 18 girls ?
In a survey of 2000 U.S adults, 70% said that they would support a national policy requiring rooftop solar panels to be installed on all new homes. The margin of error is plus or minus 2.2%. Give an interval that is likely to contain the exact percent of all U.S adults who would support this policy
The interval that is likely to contain the exact percent of all US adults who would support the policy is 0.7 ± 0.022.
Confidence interval calculationSince the sample size is large (n = 2000) and the proportion of respondents who support the policy is 0.7, we can use the normal distribution to approximate the sampling distribution of the sample proportion.
The margin of error is ±2.2%, which means that we need to construct a 95% confidence interval. The critical value for a 95% confidence interval with a two-tailed test is approximately 1.96.
The formula for a confidence interval for a population proportion is:
sample proportion ± z* (standard error)
sqrt((sample proportion * (1 - sample proportion)) / n)
Substituting the values:
0.7 ± 1.96 * sqrt((0.7 * 0.3) / 2000)0.7 ± 0.022Therefore, the 95% confidence interval for the percentage of all U.S adults who would support a national policy requiring rooftop solar panels to be installed on all new homes is 0.678 - 0.722.
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Will give Brainliest and extra points if correct!!!
An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Heads)?
85%
75%
50%
25%
Answer:
To find the probability of getting no heads, we need to add the frequencies for the outcomes where tails appears twice and divide by the total number of trials:
No heads = Tails, Tails = 50
P(No Heads) = 50/200 = 0.25 = 25%
Therefore, the answer is 25%.
Answer:
The probability of getting no heads when flipping a coin twice is 25%.
The probability of getting heads on a single flip of a coin is 50%.
The probability of getting no heads when flipping a coin twice is:
```
(1 - 0.5)^2 = 0.25
```
Therefore, the probability of getting no heads when flipping a coin twice is 25%.
So the answer is 25%
Step-by-step explanation:
Why are inequalities like the last two problems graphed on a number line while the ones in the
Set portion of this assignment are graphed on a coordinate plane? What difference is there
between the inequalities in the last two problems and the ones found in problems 13-16?
It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.
Why some inequalities are graphed on a number line?The type of diagram that we need to use depends on the number of variables that we have.
A single variable ----> number linetwo variahbles ----> a coordinate plane.3 variables ---> a volume.That is the main reason, for example:
x > 2
Is graphed on a number line.
y > 3x + 4
is graphed on a coordinate plane.
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Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
The coordinates of the vertices for the image if the preimage is translated 3 units up is A′(−3, 6), B′(0, 10), C′(−3, 3) (option b).
In this particular question, we are given a triangle ABC with vertices at A(−3, 3), B(0, 7), and C(−3, 0). Our task is to determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
When a figure is translated, it is moved to a new location without changing its shape or size.
Let's start by looking at vertex A(−3, 3). If we translate this vertex 3 units up along the y-axis, its new coordinates will be A′(−3, 6).
Similarly, if we translate vertex B(0, 7) 3 units up, its new coordinates will be B′(0, 10). Finally, if we translate vertex C(−3, 0) 3 units up, its new coordinates will be C′(−3, 3).
Therefore, the vertices of the image triangle are A′(−3, 6), B′(0, 10), and C′(−3, 3). This is option (B) from the given answer choices.
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A strange new lottery requires players to predict the exact date ( month and day) and time (hours, minutes , and seconds) when an animal will emerge from hibernation One ticket allows you one guess and you need to exactly match both the date and time this event. What is the probability of winning the lottery on a single ticket?
The probability of winning the lottery on a single ticket is
P ( A ) = 1 / (12 * 30 * 24 * 60 * 60)
Given data ,
Let the probability of winning the lottery on a single ticket be P ( A )
Now , There are 12 months in a year.
There are 30 days in a month
There are 24 hours in a day.
There are 60 minutes in an hour.
There are 60 seconds in a minute.
And , the total number of possible outcomes for the date and time is:
12 (months) * 30 (days) * 24 (hours) * 60 (minutes) * 60 (seconds)
So, the probability of winning the lottery on a single ticket is:
1 (winning outcome) / (12 * 30 * 24 * 60 * 60) (total possible outcomes)
Simplifying this fraction, we get:
1 / (12 * 30 * 24 * 60 * 60)
Hence , the probability is P ( A ) = 1 / (12 * 30 * 24 * 60 * 60)
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Question 3-(3 marks available) у, Question 4 10 (3 marks available) X y -X Quadratic Graphs a) Complete the table of values for y=x²+1 -2 -1 0 1 2 3 52 1 2 5 10 b) The graph of y = x² + 1 is drawn or the axes on the left. Use the graph to estimate the values of x when y = 4. Give your answers to 1 decimal place. Quadratic Graphs
The y-values are 5, 2, 1, 2, 5, 10 and 17.
Given that an equation of a curve, y = x²+1, we need to find the values of the y-intercept corresponding to the given x-intercept,
So,
y = x²+1
Putting the values of x,
x = -2,
y = (-2)²+1
y = 5
(-2, 5)
x = -1
y = (-1)²+1
y = 2
x = 0,
y = (0)²+1
y = 1
x = 1
y = 2
x = 2,
y = 2²+1
y = 5
x = 3,
y = 3²+1
y = 10
when x = 4,
y = 4²+1
y = 17
Hence, the y-values are 5, 2, 1, 2, 5, 10 and 17.
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Three radii of the circle are?
For the given circle ,
three radii are BC, CD , and CF , diameter is BD , Chord is HD and BD , Secant is AD and Point of tangency is F.
From the figure of the circle,
Radius is line segment whose one end point is on circumference of circle and other is center.
Three radii of the circle are BC, CD , and CF.
Diameter is a line segment whose endpoints are on the circumference of circle and passing through center.
A diameter of the circle is BD.
Tangent of a circle is a line which touches the circle at one point only.
A tangent of the circle is GE.
A chord of the circle is a line segment whose end points are on the circle.
A chord of a circle is HD and BD.
A secant of the circle is a line intersects at two points.
A secant of the circle is AD.
A point of tangency is a point where tangent touches the circle.
A point of tangency is F.
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Four pens and three pencils cost $\$2.24$. Two pens and five pencils cost $\$1.54$. No prices include tax. In cents, what is the cost of a pencil?
Two cars start at the same point and travel in opposite directions. The first car travels 10
miles per hour faster than the second. In 3 hours, they are 342 miles apart. The formula
below determines the rate of the second car. What is the rate of the second car?
3(r+ 10) + 3r = 342
The rate of the second car (r) is 52 miles/ hour.
Solving algebraic equations.There are many ways in which we can solve word problems leading to algebraic equations depending on the form, variables, and constants given in the equation.
Here, we are given two cars in which the first car travels 10 miles faster than the second car.
Let's assume that:
The miles traveled by the second car are r, Then the distance covered by the first car is r + 10.In three miles, they are 342 miles apart, Thus, we can express this mathematically as:
3(r + 10) + 3r = 342
3r + 30 + 3r = 342
6r + 30 = 342
Collect like terms
6r = 342 - 30
6r = 312
r = 312/6
r = 52
Therefore, we can conclude that the rate of the second car (r) is 52 miles/ hour.
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Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
The percent of saline solution in brand B is 10.83%
How to calculate the percent of saline solution in brand B.Let's assume that brand B has x gallons of the 100% saline solution.
The amount of salt in brand A is 18% of 6 gallons = 0.18 * 6 = 1.08 gallons.
When the two brands are mixed, the total volume of the mixture is 6 + x gallons, and the total amount of salt is 1.08 + x gallons.
Since the resulting mixture is 18 gallons of 8% saline solution, we can set up the equation:
(1.08 + x) / (6 + x) = 0.08
Solving for x, we get:
1.08 + x = 0.48 + 0.08x
0.92x = 0.6
x = 0.65
So, brand B has 0.65 gallons of the 100% saline solution.
Therefore, the percent of saline solution in brand B is:
0.65 / 6) * 100% = 10.83%, which rounded to the nearest whole number is 11%.
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can you help me with this?
Answer:
8 cm³
Step-by-step explanation:
You want the volume of Prism B similar to Prism A, where the volume of Prism A is 216 cm³, its height is 9 cm, and the height of Prism B is 3 cm.
Volume ratioThe ratio of volumes is the cube of the ratio of heights:
(Prism B volume)/(Prism A volume) = ((Prism B height)/(Prism A height))³
(Prism B volume)/(216 cm³) = ((3 cm/(9 cm))³ = 1/27
Prism B volume = (216 cm³)·(1/27) = 8 cm³
The volume is 8 cubic centimeters.
Please answer all of them on both pages please I need this today
4.) The statement that is not true about the cube box is that the volume of the box is one square foot. That is option C.
5.) All the possible dimensions of the bottom layers include the following;
when length= 4 units; width = 3units
when length = 3 units; width = 4 units
when length = 2 units; width = 6 units
How to calculate the volume of a cube?To calculate the volume of a cube box the formula that should be used = a³
where a = 1³
volume = (1×1×1) = 1ft³
The area of the cube = 6(a²)
But a = 1
area = 6(1²)
= 6ft²
Therefore the wrong statement is that the volume of the box is one square foot instead of 1ft³.
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Please solve this as quick as possible, I’ll give brainliest for it, thank you so much if u do it
Answer:
Put your calculator in degree mode.
a = 2, b = 1. So y = 2sin(x)
sin(k) = 12/25, so k = 180° - 28.69° = 151.31°
The figure is omitted--please sketch it to confirm my answer.
√(25^2 - 12^2) = √481
So tan(k) = -(12√481)/481
Select the correct answer.
Determine which equation has the same solutions as the given equation.
x2 − 10x − 11 = 0
A.
(x − 10)2 = 21
B.
(x − 5)2 = 21
C.
(x − 5)2 = 36
D.
(x − 10)2 = 36
Answer:
B. (x - 5)^2 = 21
Step-by-step explanation:
The coordinates of the vertex of a parabola are (7, −4).
What is the equation of the axis of symmetry of the parabola?
The equation of the axis of symmetry of the parabola is x = 7.
We have,
The axis of symmetry of a parabola is a vertical line that passes through the vertex.
Now,
The equation of the axis of symmetry is the vertical line passing through the x-coordinate of the vertex.
And,
The x-coordinate of the vertex is 7.
Now,
So the equation of the axis of symmetry is x = 7.
Thus,
The equation of the axis of symmetry of the parabola is x = 7.
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Does anyone know the answer?
well, let's read the Set Builder
the variable "x", where "x" is greater than or equals to 2
Oh by the way "x" is also less than or equals to 2
hmmm what the heck? how can "x" be greater than 2 and at the same time be less than 2? well, that's kinda like a logical collision, so we can conclude that "x" is neither less than or greater than 2, but another condition is that it could be equal to 2, since the other two collided, the only conclusion is that "x" must be equal to 2.
a cashier at the local bank is expected to serve 12 customers every hour.in the past 15 minutes, he served 4 customer's. assuming that the cashier continue to work at the same rate, wil he meet his goal.
how do you find the height of a composite figure made up of 2 different 3-d shapes?
In order to find the height of 2 different 3-D shapes, we must identify which dimension represents the height for each individual shape and then add them together.
How can we determine height of the composite 3-D figure?The first thing is that we must identify which dimension represents the height for each individual shape, for instance, if one shape is a rectangular prism, its height would be the length of one of its sides.
After we identified the height for each shape, you can add them together to get the total height of the composite figure, but, we must understand that this method assumes that the two shapes are stacked vertically on top of each other with their bases aligned.
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