The probability that Tara selects 1 pen and then 1 marker is 6/30 (option b).
To solve this problem, we need to first find the total number of ways that Tara can select two items from the box without replacement.
In this case, we have n = 6 (3 pens, 2 markers, and 1 highlighter) and r = 2. Therefore, the total number of ways that Tara can select two items is:
6C2 = 6! / 2! (6 - 2)! = 15
Next, we need to find the number of ways that Tara can select a pen first and then a marker.
Therefore, the number of ways to select a pen first is 3, and the number of ways to select a marker second is 2. The total number of ways to select a pen first and then a marker is:
3 x 2 = 6
Finally, we can find the probability of selecting a pen first and then a marker by dividing the number of ways to select a pen first and then a marker by the total number of ways to select two items:
6 / 15 = 2 / 5
Therefore, the correct answer is option B) 6/30, which can be simplified to 2/5.
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in a specific city there are 1350 people per square mile the city is shaped like a rectangle has a length of 12 miles and a width of eight what is the population of the city?
To find the population of the city, we need to find the total number of people living in the city. We know that there are 1350 people per square mile, so we can find the total number of people by multiplying the number of square miles in the city by the number of people per square mile.
The area of the city is the length times the width, so:
Area = Length x Width
Area = 12 miles x 8 miles
Area = 96 square miles
Now, we can find the population by multiplying the area by the number of people per square mile:
Population = Area x People per square mile
Population = 96 square miles x 1350 people per square mile
Population = 129,600 people
Therefore, the population of the city is 129,600 people.
Hope this helps!
Given that event E has a probability of 0.31, the probability of the complement of event E
Explanation: We subtract the given value from 1
1-0.31 = 0.69
The complement of an event is the complete opposite.
Example: heads vs tails
please solve and explain
The length of curve DE is equal to 26.25 units.
What is Pythagorean theorem?In Mathematics and Geometry, Pythagorean's theorem is modeled by the following mathematical expression:
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
In order to determine the length of the hypotenuse in this right-angled triangle, we would have to apply Pythagorean's theorem as follows;
AC² + BC² = AB²
20² + 15² = AB²
AB² = 400 + 225
AB = √625
AB = 25 units.
For the length of curve DE, we have:
DE = 105% of AB
DE = 1.05 × 25
DE = 26.25 units.
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Jayla's math certificate is 19 centimeters tall and 29 centimeters wide. Jayla wants to put the certificate in a fancy frame that costs $0.03 per centimeter. How much will it cost to frame Jayla's math certificate?
Answer: It will cost $2.88 to frame Jayla's math certificate with the fancy frame.
Step-by-step explanation: To calculate the cost of framing Jayla's math certificate, we need to determine the perimeter of the certificate, which is the sum of the lengths of all four sides.
Perimeter = 2 × (height + width)
Perimeter = 2 × (19 + 29)
Perimeter = 2 × 48
Perimeter = 96 centimeters
So the perimeter of the certificate is 96 centimeters.
To find the cost of framing, we need to multiply the perimeter by the cost per centimeter of the fancy frame:
Cost = perimeter × cost per centimeter
Cost = 96 × $0.03
Cost = $2.88
Therefore, it will cost $2.88 to frame Jayla's math certificate with the fancy frame.
Im stuck on this question
An image of a right rectangular prism is shown. A rectangular prism with dimensions of 4.5 centimeters by 6 centimeters by 4 centimeters. What is the surface area of the prism? 138 cm2 169 cm2 31 cm2 69 cm2
The prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.
What is the meaning of surface area?A three-dimensional object's surface area is the sum of all its faces.
The formula for the surface area of a right rectangular prism is:
surface area = 2lw + 2lh + 2wh
where l, w, and h are the prism's length, breadth, and height, respectively.
When we substitute the provided values, we get:
Surface Area = 2(4.5)(6) + 2(4.5)(4) + 2(6)(4)
Surface Area = 54 + 36 + 48
surface area = 138 [tex]cm^{2}[/tex]
As a result, the prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.
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answer correctly
Spirit
The coordinates of point P are (6.4, 18, -12).
What is the coordinate of point?A coordinate of a point refers to a set of values that specify the position of that point in a particular reference system or coordinate system. Coordinates are used to uniquely identify the location of a point in a geometric space, such as a plane or a three-dimensional space.
According to the given information:
To find the coordinates of point P, we can use the concept of vector comparison. We are given that the ratio of vector AB to vector AP is 6:4.
Let's denote the coordinates of point P as (x, y, z).
Given:
AB vector = (10, 2, -6)
B coordinates = (4, 6, -8)
AB:AP = 6:4
We can calculate the coordinates of point P as follows:
Since AB:AP = 6:4, we can express this as a vector equation:
(10, 2, -6) / (x - 4, y - 6, z + 8) = 6/4
Now we can cross-multiply to get:
10 / (x - 4) = 6/4
2 / (y - 6) = 6/4
-6 / (z + 8) = 6/4
Simplifying further, we have:
10(x - 4) = 6 * 4
2(y - 6) = 6 * 4
-6(z + 8) = 6 * 4
Expanding the equations, we get:
10x - 40 = 24
2y - 12 = 24
-6z - 48 = 24
Solving these equations, we get:
10x = 64
2y = 36
-6z = 72
Dividing by the respective coefficients, we get:
x = 6.4
y = 18
z = -12
So, the coordinates of point P are (6.4, 18, -12).
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of 100 patients selected at random from a clinic, 33 were found to have high blood pressure. construct a 95% confidence interval for the percentage of all patients at this clinic that have high blood pressure.
We can say with 95% certainty that the genuine rate of all patients at this clinic who have high blood pressure is between 24% and 42%.
To develop a 95% certainty interim for the rate of all patients at this clinic that have tall blood weight, we will utilize the equation:
CI = p ± z*(p*(1-p)/n))
where p is the sampling extent, z is the z-score related to the required certainty level (in this case, 1.96 for 95% certainty), and n is the test measure.
We are given that out of a test of 100 patients, 33 have high blood weight. In this manner, the test extent is:
p = 33/100 = 0.33
Utilizing the equation over, we will calculate the edge of the mistake:
Arduino
ME = z*(p*(1-p)/n)) = 1.96*(0.33*(1-0.33)/100)) ≈ 0.09
At that point, we are able to develop the 95% certainty interim:
CI = p ± ME = 0.33 ± 0.09 = (0.24, 0.42)
Hence, able to say with 95% certainty that the genuine rate of all patients at this clinic who have high blood weight is between 24% and 42%.
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MAKE THE FOLLOWING STATEMENTS ABOUT EXPONENTS TRUE.
--- When multiplying polynomials with the same base,
[Select]
the coefficients.
---
When dividing polynomials with the same base, [Select]
[Select]
[Select]
✓the coefficients.
--- When raising a power to a power, distribute the exponent by [Select]
and applying the exponent to the coefficient.
--- When raising anything to the Zero power, the answer will be [Select]
-- When raising anything to the 1st power, the answer will be [Select]
exponents and
exponents and
exponents
--- When trying to leave a variable without a negative exponent, you should flip the position of the variable
to the reciprocal and [Select]
✓the negative exponent.
Where will the parabola intersect the line? What equation did you solve to find the intersection? Question content area bottom
Part 1 Use the equation to find the intersection.
The parabola will intersect the line at____enter your response here.
From the graph of the parabola, line, and the given values we found out that the parabola will intersect the line at coordinates ([tex]2\sqrt{14}[/tex],7).
What is a parabola and how do we obtain the equations of the same?A parabola is a type of curve that can be described as a symmetrical U-shape. The generalized equation of a parabola is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are constant values.This equation represents a vertical parabola with its vertex at the point [tex](-b/2a, c - b^2/4a)[/tex] and an axis of symmetry that is parallel to the y-axis.This equation represents a parabola that opens to the right or left, with its vertex at the point [tex](c - b^2/4a, -b/2a)[/tex] and an axis of symmetry that is parallel to the x-axis. The specific coefficients in the equation depend on the particular characteristics of the parabola, such as its vertex, axis of symmetry, and whether it opens up or down or left or right.As the parabola is originating from the origin and opens at the y-axis, hence:
Equation of parabola = [tex]x^{2} =4ay[/tex] {where a =2} .....................(1)Equation of the line=[tex]y-7=0[/tex].............................................(2)From equation 2 we obtain y=7 and will put this value in 1.After computing the above values in 1 we get: [tex]x^{2} =4*2*7\\x=\sqrt{4*2*7}\\ x=2\sqrt{14}[/tex] and y=7So the coordinates at which the parabola intersects the line is [tex](2\sqrt{14} ,7)[/tex]To know more about the parabola visit:
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Find the marginal revenue curve under monopoly market. 1. When the demand curve is P = -5Q + 25, the Marginal Revenue curve is MR = Q+ 2. When the demand curve is P = -0.5Q + 12, the Marginal Revenue curve is MR = Q +
The marginal revenue curves for the given demand curves are: MR = -0.5 Q + 12 In a monopoly market, the marginal revenue curve is always below the demand curve. This is because a monopolist can only increase their revenue by decreasing the price of their product, and therefore they must lower the price for all units sold, not just the last one.
For the first demand curve, P = -5Q + 25, the marginal revenue curve can be found by taking the derivative of the demand curve with respect to Q. This gives us:
MR = dP/d Q = -5
So the marginal revenue curve is a horizontal line at MR = -5. Adding the intercept of the demand curve at P = 25, we get:
MR = -5Q + 25
For the second demand curve, P = -0.5Q + 12, the marginal revenue curve can be found in the same way:
MR = dP/dQ = -0.5
So the marginal revenue curve is a horizontal line at MR = -0.5. Adding the intercept of the demand curve at P = 12, we get:
MR = -0.5Q + 12
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In this polygon, all angles are right angles.
What is the area of the polygon? Show your work.
The area of the polygon is solved to be 1044 squared cm
How to find the are of the c]polygonThe area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas
Section 1 has dimensions:
length * width = 46 * 14 = 644
section 2 has dimensions:
length = 46 - 21 = 25
width = 30 - 14 = 16
Area = 25 * 16 = 400
Area of the composite figure
section 1 + section 2
= 644 + 400
= 1044 squared cm
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A packet of chips cost $9.99 if the price decreases by 12% what will the new price be
If the price of the packet of chips decreases by 12%, the new price will be:
New price = $9.99 - (12/100) x $9.99
New price = $9.99 - $1.199
New price = $8.791
Therefore, the new price of the packet of chips will be $8.791.
What is the first step in constructing a circumscribed circle around triangle XYZ? Construct a line parallel to segment YZ. Construct the perpendicular bisector of segment XY. Construct a copy of angle X. Construct the angle bisector of angle Y.
Answer: Construct the perpendicular bisector of segment XY
Step-by-step explanation:
Construct the perpendicular bisector of segment XYI am pretty sure this is the answer. I assume you r taking flvs just like me. this is the answer because to construct a circumscribed circle u will need to draw a perpendicular bisector to the sides of the polygon. Which o think is the first step.
PLEASE HELP MY MOMS GONNA KICK MT BUTT AND I JUST DONT GET THIS!!!Add.
(2h + 8) + (9h² + 2h)
apply the half-angle identities for sine and cosine to rewrite or evaluate the following expression.
[tex]tan(\frac{11\pi}{12} )[/tex]
Answer: We can use the halfangle formula for the tangent to answer this question. Using this formula we get that [tex]$\tan\left(\frac{11\pi}{12}\right) = \sqrt{3} - 2[/tex].
Step by Step Explanation: The half angle formula for tangent is [tex]$\tan\left(\frac{A}{2}\right) = \frac{\sin(A)}{1+\cos(A)}[/tex] . So
[tex]$\tan\left(\frac{11\pi}{12}\right)[/tex]
[tex]$= \frac{\sin(\frac{11\pi}{6})}{1+\cos(\frac{11\pi}{6})}[/tex]
[tex]$= \frac{\sin(2\pi - \frac{\pi}{6})}{1+\cos(2\pi - \frac{\pi}{6})}[/tex]
[tex]$ = \frac{-\sin(\frac{\pi}{6})}{1+\cos(\frac{\pi}{6})}[/tex]
[tex]$= \frac{-1/2}{1 + \sqrt{3}/2}[/tex]
[tex]$= -\frac{1}{2+\sqrt{3}}[/tex]
[tex]$= - \frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}[/tex]
[tex]= - \frac{2 -\sqrt{3}}{4-3}}[/tex]
[tex]= \sqrt{3} -2[/tex]
What are the half angle identitiesThese are some of the common halfangle identities:
[tex]\cos(A/2) = \sqrt{\frac{1+\cos(A)}{2}[/tex]
[tex]\sin(A/2) = \sqrt{\frac{1-\cos(A)}{2}[/tex]
[tex]\tan(A/2) = \frac{\sin(A)}{1+\cos(A)} = \frac{1 - \cos(A)}{\sin(A)}[/tex]
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A cylindrical can holds three balls. The balls touch the top, bottom and sides of the can. The radius of one ball is 6 cm. Find the volume of the remaining space inside the cylinder. Use 3.14 for π. please someone help me.
Answer:
16286.01632
Step-by-step explanation:
V=πr2h=π·122·36≈16286.01632
Last week, Austin's Diner sold 2 milkshakes with whipped cream on top and 23 milkshakes without whipped cream. What percentage of the milkshakes had whipped cream?
Answer:
8%
Step-by-step explanation:
You want to know what percentage of milkshakes had whipped cream if 2 had whipped cream and 23 didn't.
PercentageThe fraction of the total number that had whipped cream is ...
2/(2+23) = 2/25
The percentage is found by multiplying the fraction by 100%:
2/25 × 100% = 8%
8% of the milkshakes had whipped cream.
A circle has a diameter of 28 centimeters.
Estimate the area of the circle. Use
3.14
or
22
7
for
π
.
What is the volume of the rectangular prism?
A rectangular prism has a length of 10.4 millimeters, a width of 5 millimeters, and a height of 8 millimeters.
The area of the given circle is 616 sq.cm.
The volume of rectangular prism is 416 mm³
What is a circle?A circle is a particular type of ellipse when the eccentricity is zero and both foci are present. The locus of points drawn equally apart from the centre is also referred to as a circle. The radius of a circle is the separation between its centre and its periphery. The circle's diameter, which is equal to twice its radius, is the line that splits the circle into two equal pieces.
What is area of circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m², cm², etc.
Area of Circle = πr² or πd²/4, square units
where π = 22/7 or 3.14
according to question,
Area = pi times the radius squared
A = pi * r²
A = 22/7 * 14²
A = 22/7 * 196
A = 4,312 / 7
A = 616 sq. cm.
V = l*w*h
To determine the volume, multiply all three dimensions together.
For Connexus users Rectangular prisms and volume quiz part 2:
l * w * h = 8 * 5 * 10.4 = 416
the volume of rectangular prism is 416 mm³
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Convert the rectangular coordinates (-3√3, 0) into polar form. Express the angle
using radians in terms of over the interval 0 ≤ 0 < 27, with a positive value of r.
The polar form of the rectangular coordinates (-3√3, 0) is r = 3√3 and θ = 0
To convert the rectangular coordinates (-3√3, 0) into polar form, we can use the following equations:
r = √(x² + y²)
θ = tan⁻¹(y/x)
In this case, x = -3√3 and y = 0, so we have:
r = √((-3√3)² + 0²) = 3√3
θ = tan⁻¹(0/(-3√3)) = tan⁻¹(0) = 0
Since the angle is given in radians over the interval 0 ≤ θ < 2π (which is equivalent to 0 ≤ θ < 6.28318), we need to add 2π to θ if it is negative, to ensure that θ is in the specified interval.
However, in this case, θ is already equal to 0, which is within the specified interval.
Therefore, the polar form of the rectangular coordinates (-3√3, 0) is:
r = 3√3
θ = 0 (in radians, over the interval 0 ≤ θ < 2π)
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Joe wants to answer the with a river. He marks off two right triangles as shown in the figure. The base of the larger triangle has a length of 55 M and the base of the smaller triangle has a length of 26 m. The height of the smaller triangle is 21.4m. How wide is the river? Round your answer to the nearest meter. (The figure is not drawn to scale)
The width of the river is approximately 45m.
How to calculate the width of the river?Let's say the illustration may be explained as follows:
The big right triangle is located inside the river, with its base extending down one of its sides and its height spanning its breadth.
The base of the little right triangle lies on the opposite bank of the river, outside of it.
Triangles don't cross over one another. Their bases' endpoints contact, as does the end of their hypotenuses.
Let's assume the two right triangles are similar (which means they have proportional sides).
H1/B1 = H2/ B2
which is H1/55 = 21.4/26
=21.4/26 x 55
= 45.27
It is the larger triangle is the width of the river
If the smaller triangle represents the land on one side of the river and the larger triangle includes both the land and the river, we need to find the width of the river by subtracting the base of the smaller triangle from the base of the larger triangle:
Width of the river = 55 - 26 = 29 meters
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. While shopping, Sofia finds a dress she likes at a discounted price. The price on the tag before the discount is p dollars. She must pay sales tax on the discounted price of the dress. Sofia calculates that she must pay p-0.15p+ 0.07(0.85p) to buy the dress. What does 0.85p represent?
The 0.85p in the expression represents the price of the dress after removing the discount
What does 0.85p represent in the equation?From the question, we have the following parameters that can be used in our computation:
Sofia calculates that she must pay the following to buy the dress
p - 0.15p + 0.07(0.85p)
The 0.85p in the expression represents the price of the dress after removing the discount
Hence, 0.85 is the discounted price
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a jet tank is in the shape of a rectangular prism. The tank is 18 inches wide, 12 inches deep and 23 inches tall How many squares inches of glass was used to make the tank if there is no top.
The tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass cutting process.
The tank has four vertical rectangular sides, a bottom, and no top. Since there is no top, we do not need to include the area of any glass for the top of the tank.
The area of each rectangular side is given by multiplying the height by the width. The area of the bottom is given by multiplying the length by the width. Therefore, the total area of glass used to make the tank is:
Area = 2(height x width) + 2(height x length) + (length x width)
Substituting the given values, we get:
Area = 2(23 x 18) + 2(23 x 12) + (18 x 12)
Area = 1,656 + 1,656 + 216
Area = 3,528
Therefore, the tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass-cutting process.
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how do I do 3 + 2n = 7
In the given equation which is 3 + 2n = 7, the value of n = 2.
For, further explanation to find the value of the variable in the given equation, we can solve the given equation by transferring the non-variable digits to one side either to L.H.S or R.H.S.
Given equation = 2n + 3 =7
In the above equation, the variable is 'n' and the non-variable digits are '3' and '7'. To find the value of 'n', we can transfer the non-variable digits to the R.H.S (Right Hand Side) as shown below:
2n + 3 = 7
2n = 7 - 3
2n = 4
n = [tex]\frac{4}{2}[/tex]
n = 2.
So, from the above solution the value of 'n' is 2.
Given question is incomplete/incorrect, I assume the given question was to "obtain the value of n from the linear equation 3 + 2n = 7"
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A 4-cup bottle of soda costs $6.80. What is the price per pint?
Answer: $0.85
:)
hope this hellps
Answer:
$3.40 per pint
Step-by-step explanation:
4 cups is equal to 2 pints, as there are 4 cups in 2 pints.
So let's set up an equation:
6.80/2
3.40
A pitcher contains 3 quarts of iced
tea. John is going to pour the iced tea
into glasses that each hold 1½ cups.
How many glasses will John fill?
John will be able to fill 8 glasses with iced tea.
How many cups are in 3 quarts of iced tea?To convert quarts to cups, we need to multiply the number of quarts by 4, since 1 quart is equal to 4 cups. So, 3 quarts of iced tea is equivalent to 3 x 4 = 12 cups of iced tea.
Since each glass holds 1½ cups of iced tea, John will need to divide the total cups of iced tea by the capacity of each glass: 12 cups / 1.5 cups/glass = 8 glasses.
Therefore, John will fill 8 glasses with iced tea.
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For a trip of x miles, a taxi company charges f(x)=2. 20+0. 6[4x] dollars A. ) What is the cost of a 2. 7-mile trip?
If a taxi company charges f(x)=2. 20+0. 6[4x] dollars, the cost of a 2.7-mile trip is $8.68.
To find the cost of a 2.7-mile trip using the given function f(x) = 2.20 + 0.6[4x], we substitute x = 2.7 in the function.
f(2.7) = 2.20 + 0.6[4(2.7)]
f(2.7) = 2.20 + 0.6[10.8]
f(2.7) = 2.20 + 6.48
f(2.7) = 8.68
The function f(x) = 2.20 + 0.6[4x] represents the cost of a taxi ride based on the distance traveled. The first term 2.20 represents the base fare, which is added to the cost regardless of the distance.
The second term 0.6[4x] represents the variable cost, which is calculated by multiplying the distance traveled by 4 and then by 0.6. This function helps the customers to calculate their fare in advance and plan their expenses accordingly.
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Samuel is folding his laundry. The table shows the proportional relationship between the number of shirts he folds and the time, in minutes, it takes him to fold them.
Number of Shirts 2 4 ?
Time (minutes) 0.4 0.8 3
How many shirts can Samuel fold in 3 minutes?
21 shirts
15 shirts
8 shirts
6 shirts
I’d say 30 shirts.
Step-by-step explanation:
30 seconds = 3 shirts 1 minute 30 seconds = 9 shirts 30 seconds per each 3 shirts.
shirts: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30minutes: .5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5
Answer:
15 (B).
Step-by-step explanation:
I took the test.
HELP PLEASE I NEED THIS DONE ASAP
Answer:5
Step-by-step explanation:
it would be 5 because
Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours.
The equation 3t = 5(3 – t) can be used to find the time it took Stu to hike one way.
How long did it take Stu to hike the trail one way?
hours
How long is the trail?
miles
What is the total distance Stu traveled?
miles
HELP PLEASE !!!!!
Subtract.
(9w² + 3w) - (6w² + w)
Answer:
3w²+2w
Step-by-step explanation:
(9w² +3w)-(6w²+w)
=9w²+3w-6w²-w
collecting like terms
=9w²-6w²+3w-w
=3w²+2w
=w(2+3w)