There are 210 ways that Janelle can choose 4 colors from 10 available colors for her art project.
Janelle needs to choose 4 colors out of 10 available colors for her art project. The order in which she chooses the colors does not matter. We can use the combination formula to determine the number of ways she can choose 4 colors from 10 available colors:
nCr = n! / r!(n - r)!
where n is the total number of colors available, r is the number of colors Janelle needs to choose, and ! denotes the factorial operation.
In this case, we have:
n = 10 (total number of colors available)
r = 4 (number of colors Janelle needs to choose)
Substituting these values into the formula, we get:
10C4 = 10! / 4!(10 - 4)!
= 10! / 4!6!
= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)
= 210
Therefore, for her art assignment, Janelle can select 4 colors from a palette of 10 in 210 different ways.
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what is the length of tr?
Answer:
12
Step-by-step explanation:
Two stores have a laptop computer for sale.
Part A: Store A is selling the laptop for
and has a discount coupon for
off. Calculate the amount of the discount at Store A.
Part B: Store B is selling the laptop for
and has a discount coupon for
off. Calculate the amount of the discount at Store B.
Part C: Which store should you purchase the laptop from? Use details to support your answer.
Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.
What is discount?
Discount means the amount which is deducted by sellers from the amount to be payable by buyers.
Part A:
Store A is selling the laptop for $900 and has a discount coupon for 15% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:
Discount amount = $900 x 15% = $135
Therefore, the amount of the discount at Store A is $135.
Part B:
Store B is selling the laptop for $950 and has a discount coupon for 10% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:
Discount amount = $950 x 10% = $95
Therefore, the amount of the discount at Store B is $95.
Part C:
At Store A, the final price would be:
Final price at Store A = $900 - $135 = $765
At Store B, the final price would be:
Final price at Store B = $950 - $95 = $855
Therefore, Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.
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describe the key features que f the graph of the quadratic function f(x)=x^2-8-20
The graph is a parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).
Define quadratic functionA quadratic function is a type of polynomial function of degree 2. It can be defined as a function in which the highest power of the independent variable x is 2.
The quadratic function f(x) = x² - 8x - 20 has a graph that is a parabola with a vertical axis of symmetry.
Vertex: The vertex of the parabola can be found using the formula x = -b/2a, where a and b are the coefficients of x² and x respectively.
In this case, a = 1 and b = -8, so the x-coordinate of the vertex is x = -(-8)/(2×1) = 4.
To find the y-coordinate of the vertex, substitute x = 4 into the equation: f(4) = 4² - 8(4) - 20 = -4. Therefore, the vertex is located at (4,-4).
Axis of symmetry: The axis of symmetry of the parabola is a vertical line passing through the vertex.
In this case, the axis of symmetry is the line x = 4.
Intercepts: To find the x-intercepts set y = 0 and solve for x: x² - 8x - 20 =0.
this quadratic equation can be factored as (x - 10)(x + 2) = 0
so the x-intercepts are x = 10 and x = -2.
To find the y-intercept, set x = 0 and evaluate f(0) = 0² - 8(0) - 20 = -20. Therefore, the y-intercept is (0,-20).
Image is attached below.
The graph is a upward-facing parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).
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Triangle WXY with W(0, 1), X(-4, 4), Y(0, 2)
in y-axis
(x, y) ⇒ (x − 1, y — 4)
a) Reflection
b) Translation
(a)The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
(b)The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
What is reflection ?a) Reflection: To reflect the triangle across the y-axis, we simply need to negate the x-coordinates of each vertex.
The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
The reflected triangle would be W'X'Y'.
b) Translation: To translate the triangle by the vector (1, -4), we add (1, -4) to the coordinates of each vertex.
The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
The translated triangle would be W'X'Y'.
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your mom got 20 cupcakes in you got 1 plate how the 1 and 20
Answer:
Step-by-step explanation:
explain you question more i cant understand if i could i would help
Pat listed all the numbers that have 15 as a multiple. What’s the numbers in Pats list
Answer:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735...
Step-by-step explanation:
Drag each expression to show whether it is equivalent to 36x+9 or 9(4x-1)
1. 36x+8- 3rd column;
2. (9·4x)+(9·1)=36x+9 - 1st column;
3. (3·12x)-(3·3)=36x+9 - 2nd column;
4. 9(4x+1)=36x+9 - 1st column;
5. 36x-9- 2nd column;
6. 4(9x+2)=36x+8 - 3rd column
Define equationIn mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equals sign (=). Equations can contain one or more variables, which are quantities that can take on different values.
Start with expressions in blue boxes:
1st column) 36x+9;
2nd column) 9(4x-1)=36x-9;
3rd column) (4·9x)+(4·2)=36x+8.
You have 6 expressions. Consider all them:
1. 36x+8- 3rd column;
2. (9·4x)+(9·1)=36x+9 - 1st column;
3. (3·12x)-(3·3)=36x+9 - 2nd column;
4. 9(4x+1)=36x+9 - 1st column;
5. 36x-9- 2nd column;
6. 4(9x+2)=36x+8 - 3rd column
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The complete question is;
Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).
i need the answers please
Answer:
(7) AB is a tangent , (8) AB is not a tangent
Step-by-step explanation:
the angle between a tangent and the radius is 90°
if AB is a tangent then Δ ABC is right with hypotenuse AC
using Pythagoras' identity
the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.
if AC² = AB² + BC² , then AB is a tangent to the circle
(7)
AC² = 34² = 1156
AB² + BC² = 30² + 16² = 900 + 256 = 1156
since AC² = AB² + BC² , then AB is a tangent to the circle
(8)
AC² = 28² = 784
AB² + BC² = 21² + 20² = 441 + 400 = 841
since AC² ≠ AB² + BC² , then AB is not a tangent to the circle
Find the absolute extrema of the function on the closed interval.
y = 3 cos x, [0, 2π]
The absolute extrema for the given function occurred at the critical points for Interval [0, 2π] is 3.
Explain about the absolute extrema of function?The point wherein the minimum or maximum value of the function is reached is known as the absolute extremum (also global extremum) of the function in the given interval.
The absolute extremum, or point equivalent to the highest or least value in the entire function, is frequently the interval specified, which is the domain of the function.
The given function :
y = 3 cos x,
Differentiate the function with respect to 'x'.
y' = -3 sin x
Find the critical point , by y = 0
-3 sin x = 0
x = sin ⁻¹ (0)
Interval [0, 2π]
So, critical points are: x = 0,π, 2π
Now, evaluate function by putting the critical points;
y(0) = 3 cos 0 = 3
y(π) = 3 cos π = 0
y(2π) = 3 cos 2π = 3
Thus, absolute extrema for the given function occurred at the critical points 0 and 2π that is 3.
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Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
__ __
Answer:
[tex]13 < \sqrt{181} < 14[/tex].
Step-by-step explanation:
We have been given an inequality ___[tex]< \sqrt{181} <[/tex]___. We are asked to fill in the blank with two consecutive integers to complete the given inequality.
We know that square root of 181 is not an integer. We can see that 181 is greater than square root 169 and and square root of 196.
[tex]\sqrt{169} < \sqrt{181} < \sqrt{196}[/tex]
We know that [tex]\sqrt{169}=13[/tex] and [tex]\sqrt{196}=14[/tex].
Therefore, our required inequality would be [tex]13 < \sqrt{181} < 14[/tex]
What are the coordinates of the point on the directed line segment from ( − 7 , 3 ) (−7,3) to ( 3 , − 9 ) (3,−9) that partitions the segment into a ratio of 3 to 1?
The coordinates of the point on the directed line segment are (-6, 0)
Define the term coordinates of the point?Coordinates of a point refer to a set of numbers that represent the location of the point in a particular coordinate system.
To find the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1, we can use the following formula:
P = [tex]( (3/4)*x_1 + (1/4)*x_2 , (3/4)*y_1 + (1/4)*y_2 )[/tex]
where P is the point that partitions the line segment, (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the segment, and the coefficients 3/4 and 1/4 correspond to the ratio in which the segment is divided.
Plugging in the values, we get:
P = ( (3/4)*(-7) + (1/4)*3 , (3/4)3 + (1/4)(-9) )
= (-21/4 - 3/4 , 9/4 - 9/4)
= (-6, 0)
Therefore, the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1 are (-6, 0).
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A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red.
Match the events on the left with probabilities on the right.
The probabilities of the events and their values are shown below
Matching the probabilities of the eventsThe total number of marbles in the bag is 13, with 6 blue, 2 green, and 5 red.
P(Blue or Green) represents the probability of selecting a blue or green marble on the first pick.
This is calculated as follows:
P(Blue or Green) = P(Blue) + P(Green)
= 6/13 + 2/13
= 61.5%
P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, with replacement.
Therefore:
P(Blue and Green) = P(Blue) * P(Green)
= (6/13) * (2/13)
= 7.1%
P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, without replacement.
Therefore:
P(Blue and Green) = P(Blue) * P(Green)
= (6/13) * (2/12)
= 7.7%
P(Blue) represents the probability of selecting a blue marble on the first pick.
This is simply the proportion of blue marbles in the bag:
P(Blue) = 46.2%
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In a survey by the Pew Research Center, adult members of the Church of Jesus Christ of Latter-day Saints in the U.S. were asked how important religion is in their life. 558 adults said religion is “very important” in their lives, 79 adults said religion is “somewhat important” in their lives, 20 adults said religion is “not too important” in their lives, and 7 adults said religion is “not at all important” in their lives. Which of the following columns (A, B, C, D, or E) correctly shows the responses to this question as a probability model? (A) (B) (C) (D) (E) Very important 63.5% 84% 84% 12% 77% Somewhat important 22.5% 12% 14% 84% 21% Not too important 2% 3% 5% 1% 5% Not at all important 1% 1% 3% 3% 3%
The correct column is (A), which correctly represents the responses as probability.
Define probabilityProbability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The sum of all the responses is 558 + 79 + 20 + 7 = 664.
To represent the responses as a probability model, we need to divide each response by the total number of respondents, 664.
The correct column is (A), which correctly represents the responses as probabilities:
(A)Very important 558/664 = 0.841
Somewhat important 79/664 = 0.119
Not too important 20/664 = 0.030
Not at all important 7/664 = 0.011
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The polynomials (-3y²-y-8) + (-y² + 2y - 4) when added is:
Answers options
O -4y² + y - 12.
O -4y²-y-12.
O 4y² + y - 12.
O-4y2-3y - 12.
O 4y2-3y - 12.
Answer:
-4y2 +y - 12
Step-by-step explanation:
-3y2 - y2= -4y2
-y+2y= y
-8 - 4= -12
-4y2 + y - 12
The measure of each interior angle of a
regular polygon is 135°. How many sides does the polygon have?
A. 5
B. 6
C. 7
D. 8
E. Cannot be determined from the
information given.
Answer:
8 sides
Step-by-step explanation:
Let n be the number of sides
Then sum of internal angles [tex]=(n-2)180[/tex]
——-(1)
It is given that one internal angle [tex]=135[/tex]
So sum of n equal internal angles [tex]=135n[/tex] ————(2)
From(1) and(2)
[tex](n-2)180=135n[/tex]
[tex]180n-360=135n[/tex]
[tex]180n-135n=360[/tex]
[tex]45n=360[/tex]
[tex]n=360\div45=8[/tex]
[tex]\bold{So \ the \ number \ of \ sides=8}[/tex]
13. A bag contains 40 balls, each of which is black or gold. Anele reaches into the bag and randomly removes two balls. Each ball in the bag is equally likely to If the be removed. probability that two gold balls are removed is how 12 many of the 40 balls are gold?
The number of gold balls in the given bag is determined as 25 gold balls.
How many of the 40 balls are gold?Let's use the formula for calculating probability:
Probability of an event = Number of favorable outcomes / Total number of outcomes
The total number of possible ways to choose 2 balls from a bag of 40 is:
40C2 = (40 x 39) / (2 x 1) = 780
Now we need to find the number of ways to choose 2 gold balls from the bag.
Let's say there are "g" gold balls in the bag. Then the number of ways to choose 2 gold balls is:
gC2 = (g x (g-1)) / (2 x 1)
We want to find the probability that 2 gold balls are removed, so we use the formula above to get:
Probability of choosing 2 gold balls = Number of ways to choose 2 gold balls / Total number of ways to choose 2 balls
Therefore, we have:
Probability of choosing 2 gold balls = gC2 / 40C2
We are given that this probability is 12/95, so we can set up an equation:
(g x (g-1)) / (2 x 1) / (40 x 39) / (2 x 1) = 12/95
Simplifying, we get:
g x (g-1) = (12/95) x (40 x 39)
g x (g-1) = 624
Expanding and rearranging, we get a quadratic equation:
g² - g - 624 = 0
Solving this quadratic equation, we get:
g = 25 or g = -24
We discard the negative solution, as the number of gold balls must be a positive integer. Therefore, there are 25 gold balls in the bag.
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Which expression is equivalent to 5(2 + 1)?
Step-by-step explanation:
5(2 + 1) can be simplified using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Using this property, we get:
5(2 + 1) = 5(2) + 5(1)
Simplifying the expression further, we get:
5(2) + 5(1) = 10 + 5 = 15
Therefore, 5(2 + 1) is equivalent to 15.
Find the measures of angles a and b and of arc c Please
The measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
In the given diagram, we can see that angle ACD is a right angle, since it is formed by the radius AC and tangent CD at point C.
Therefore, angle BCD is equal to angle ACD, which is 90 degrees.
Since angle BCD is an exterior angle of triangle BCF, it is equal to the sum of the two remote interior angles, which are angles BFC and FCB.
Angle BFC is equal to angle ABC (since they are opposite angles), which is 60 degrees.
Similarly, angle FCB is equal to angle ACF, which is also 60 degrees.
Therefore, angle BCD is equal to angle BFC + angle FCB, which is 60 + 60 = 120 degrees.
Now, since arc CD is subtended by angle BCD, its measure is also equal to 120 degrees.
Hence, the measure of arc CD is 120 degrees.
Similarly, angles ACF and FCB are opposite angles in the cyclic quadrilateral AFCB, so they are supplementary. Therefore, angle FCB is equal to 180 - angle ACF,
Which is also 180 - 60 = 120 degrees.
Now we can apply the exterior angle theorem to find the measure of angle BCD. We have:
angle BCD = angle BFC + angle FCB
= 120 + 120
= 240 degrees
Finally, we can conclude that the measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
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Malinda wants to rent a compact car for eight days. Ace Rental rents these cars for $48 per day or $312 per week. Compute the cost of each plan for her. Which plan is more economical?
a) The total cost for renting a compact car for eight days is as follows for each plan:
Daily rental = $384Weekly rental = $360.b) It is more economical to take the weekly rental plan than the daily rental plan.
How is the total cost determined?Each plan's total rental cost is determined using multiplication or addition.
For instance, the total cost for the daily plan is a product of the daily rental cost and the number of days the car is rented.
The total cost for the weekly plan is an addition operation since the car is rented for 7 days (weekly cost) and 1 day (daily cost).
Day Week
Rental cost per $48 $312
1 week = 7 days
Total rental cost for
8 days $384 ($48 x 8) $360 ($312 + $48)
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100 pts answer fast and brainliest
Answer:
1 c
2 d
3 a
4 b
5 e
Step-by-step explanation:
scale factor > 1 => expansion
scale factor < 1 => contraction
scale factor = 1 => no change
scale factor is (-) => opposite site
Determine f(3) for f(x)
A. 9
B. 19
C. 22
D. 27
Dario walks from his house to a comic book store along the route shown. Distances in the coordinate plane are in units of miles. How many miles does Dario walk to reach the comic book store
The distance walked by Dario from to reach comic book store is 1.4 miles.
What is distance?Displacement and distance are two terms that, while they appear to imply the same thing, have quite different definitions and meanings. Displacement is the measurement of "how much space an item has covered while it has been in motion," whereas distance is the indication of "how much ground an object has covered during its motion." Let's examine the distinction between displacement and distance in this essay.
For the given route we have:
House to jewelry store:
0.2 - (-0.5) = 0.2 + 0.5 = 0.7 miles.
Jewelry store to bank:
0.6 - 0.2 = 0.4 miles.
Bank to comic book store:
-0.5 -(-0.8) = -0.5 + 0.8 = 0.3 miles.
House to comic book store:
0.7 + 0.4 + 0.3 = 1.4 miles.
Hence, the distance walked by Dario from to reach comic book store is 1.4 miles.
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The complete question is:
Please help, this was due yesterday!!!!!
Answer:
x =65°( being alternate angel)
PLSSS HELPPP QUICK
What is the product of the monomial x and the
trinomial 2x² -5x+1?
PLEASE HELP LATE HOMEWORK
The number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.
What is meant by intersection?
In mathematics, the intersection of two sets A and B is a new set that contains all the elements that are common to both sets. In symbols, the intersection of A and B is denoted by A ∩ B, and it is defined as:
A ∩ B = {x : x ∈ A and x ∈ B}
Let A represent the set of students who have a cell phone, and B represent the set of students who have a tablet. The intersection of A and B, denoted by A ∩ B, represents the set of students who have both a cell phone and a tablet. Therefore, we want to find the cardinality (or size) of the set A ∩ B.
From the frequency table, we know that the total number of seventh graders surveyed is 100. We also know that there are 32 students who have a cell phone (i.e., |A| = 32) and 70 students who have a tablet (i.e., |B| = 70). We are given that 19 students who have a cell phone do not have a tablet, which means that there are 32 - 19 = 13 students who have both a cell phone and a tablet (i.e., |A ∩ B| = 13).
Therefore, the number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.
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HELP ME PLS I LITERATELY CANT
Katya owns two cockatoos, an older white cockatoo and a younger Galah cockatoo. At present, the sum of the cockatoos' ages is 44 years. In n years, where n > 0, the white cockatoo's age will be four times the Galah cockatoo's age. If n is an integer, determine the possible present ages of each cockatoo.
The possible present ages of each cockatoo, given the sum of the cockatoos would be Galah cockatoo is currently 10 years old and the white cockatoo would be 34 years old
How to find the ages of the cockatoos?Let's use variables to represent the present ages of the two cockatoos. Let W be the present age of the white cockatoo and G be the present age of the Galah cockatoo. We're given that the sum of their ages is 44 years:
W + G = 44 (1)
In n years, the white cockatoo will be W + n years old, and the Galah cockatoo will be G + n years old:
W + n = 4(G + n) (2)
Since n > 0, 5G - 44 must be positive. We can try different values of G to find possible integer values for n.
For G = 8:
44 - 5(8) = 4
4 = -3n
n is not an integer.
For G = 10:
44 - 5(10) = -6
-6 = -3n
n = 2
So one possibility is that the Galah cockatoo is currently 10 years old. In this case, the white cockatoo would be 34 years old (since W + G = 44).
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The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten.
The volume of the solid with a hole in the shape of a rectangular prism passing through the center of a cylinder with a radius of 10 yards is approximately 1410 cubic yards, rounded to the nearest ten.
The cylinder with the hole can be viewed as the difference of two solids: the cylinder and the rectangular prism. The volume of the cylinder is given by the formula V_cyl = π[tex]r^2h[/tex], where r is the radius and h is the height.
The height of the cylinder is equal to the height of the rectangular prism that passes through its center. The height of the rectangular prism is given as 12 yards, which is also the diameter of the cylinder. Therefore, the height of the cylinder is h = 12/2 = 6 yards.
The volume of the cylinder is therefore V_cyl = π[tex](10)^2(6)[/tex] = 600π cubic yards.
The rectangular prism has a length of 20 yards, a width of 10 yards, and a height of 12 yards. Therefore, its volume is V_prism = 20 × 10 × 12 = 2400 cubic yards.
The volume of the solid with the hole is then:
V = V_cyl - V_prism = 600π - 2400 = 600(π - 4) ≈ 1412.2 cubic yards.
Therefore, the volume of the solid is approximately 1410 cubic yards.
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Helena sketches a circular backyard skating pond that fits into a square section of her yard. In her sketch, what is the area of the shaded region?
Answer:
The area of the shaded region equals 21.43 sq. units.
Step-by-step explanation:
Why do we use area?When calculating how much material is needed to cover a wooden table, how many tiles are needed to tile the floor, how much space is needed for a parking lot, how much paint is needed for the walls, etc., we employ the notion of area.
Given, A circle is circumscribed in the square,
Area of shaded region = area of square - area of circle
Area of square = Side²
= 10 × 10 = 100 sq. units,
Area of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 unitsArea of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 units
Area of circle = 22/7 × 5 × 5
= 78.57 sq. units
Area of shaded region = 100 - 78.57,
Area of shaded region = 21.43 sq. units
How to calculate Standard Error of the Y intercept and standard error of the slope, given the table below, without the SE coefficient given.
Answer:
Step-by-step explanation:
the stabdard error is given with the se coefficient snf the y slope