Answer: 10
Step-by-step explanation:
2+4+4= 10
The first quartile of a data set is 32, and the third quartile is 52. Which of
these values in the data set is an outlier?
Answer: As we know that the formula of outlier is
IQR = Q3 - Q1
= 52 - 32
= 20
52 + 1.5(20) = 82...
so anything above 82 is an outlier
now
32 - 1.5(20) = 2.
..anything below 2 is an outlier
so...the 83 is outlier
so correct option is D
hope it helps
Step-by-step explanation:
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 7.5%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $825. How much was the hotel charge in each city before tax?
The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.
Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500 (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825 (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.
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1 bag of pretzels cost four dollars. Five bags of pretzels cost $12.00. Which has the lower unit price??
Answer:
The 5 bags of pretzels.
Step-by-step explanation:
Because if you were to buy 5 individual bags you would end up paying $20.00, instead of $12.00
Answer:
The second option
Step-by-step explanation:
In order to find the unit price of each, consider the quotient of amount of money per bag:
Case 1:
$4/ 1 bag
Case2:
$12 / 5 bags = $2.4 / 1 bag
Therefore, the second option is the one with lower unit price.
Simplify be using distributive property: 3(4x -3) + 5(2x - 1)
Answer:
25
Step-by-step explanation:
Dwight's club has 35 members. Its
rules require that 60% of them must
be present for any vote. At leas how
many members must be present to have
a vote?
Answer:
21 memebers must be present
Step-by-step explanation:
First we have to convert the percent to decimal form for an easier calculation. Do this by taking 60 and dividing by 100.
You should get 0.60, now just multiply .60 by 35 and you'll get the answer of 21.
Does (4, 0) make the equation y = 6x true?
Answer: No
Step-by-step explanation: it would be (0,4)
Nina can ride her bike 63,360 ft. In 3,400 seconds, Sophia can ride her bike 10 million 1 hour. What is Nina's rate per hour if there are 5'280 ft. in a mile? Which girl bikes faster?
A grey squirrel population was introduced in a certain county of Great Britain 30 years ago. Biologists observe that the population doubles every 6 years, and now the population is 100,000. what is the formula
Answer:
The formula for the gray squirrel population is \(n = 3125\cdot 2^{\frac{t}{6} }\).
Step-by-step explanation:
The statement indicates that gray squirrel population increases geometrically, population is doubled every 6 years. That is:
\(\frac{n_{t+6}}{n_{t}} = 2\) (1)
If the population after 30 years is 100000, then we construct the following relationship:
\(\frac{n_{6}}{n_{o}} \cdot \frac{n_{12}}{n_{6}}\cdot \frac{n_{18}}{n_{12}}\cdot \frac{n_{24}}{n_{18}}\cdot \frac{n_{30}}{n_{24}} = 2^{5}\)
\(n_{30} = 2^{5}\cdot n_{o}\)
\(n_{o} = \frac{n_{30}}{2^{5}}\) (2)
\(n_{o} = \frac{100000}{2^{5}}\)
\(n_{o} = 3125\)
A geometric progression for the grey squirrel population is defined by the following formula:
\(n = 3125\cdot 2^{\frac{t}{6} }\) (3)
Where:
\(t\) - Time, measured in years.
\(n\) - Population of gray squirrels.
Which rule explains why these triangles are
congruent?
U
T
V
W
AAS
ASA
SAS
SSS
These triangles
cannot be proven
congruent.
These triangles can be proven congruent by using ASA RULE.
What is congruent triangles and its rules ?
When two triangles are congruent, their three sides and their three angles match precisely.
If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.
ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.
Main Body:
In ΔTUV and ΔTWV
VT =VT ----(1)
∠VTU=∠TVW -----(2)
As TUVW is a parallelogram
so, ∠T = ∠U
hence, ∠TVU =∠VTW ----(3)
taking equation 1, 2,3
therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.
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Which picture best illustrates the following postulate?
“The intersection of two planes is a line."
B
C
A
none of the choices
The correct answer is B
Explanation:
In mathematics and related areas, a plane is a surface. This implies if there are two planes intersected, there should be two surfaces that pass across each other. Also, this bidimensional. This feature only occurs in option B because this is the only one that shows the two planes and their intersection, while options A and C show only one plane. Moreover, the intersection of planes forms a defined lined, which is shown in the region, in which the two surfaces met. This implies option B shows the postulate.
Which of the following are disadvantages of the mode?
For many sets of data there are multiple modes.
The mode is affected by extremely large and small values.
For many sets of data there is no mode.
the mode can only be computed for interval-level data or higher
The disadvantages of the mode are: For many sets of data there is no mode.
The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.
However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.
The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.
The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.
The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.
The correct option is: For many sets of data there is no mode.
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Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
I will ONLY give you a brainliest of you answer this questions CORRECTLY!
Answer:
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
Step-by-step explanation:
Surface area of a cylinder = 2πrh+2πr² = 2π(rh+r²)
Cylinder A = 2π(rh+r²)
Cylinder B = 2π((2r)(2h)+(2r)²) = 2π(4rh+4r²)=2π(4(rh+r²))
To find how many times greater Cylinder B's surface area is than Cylinder A's surface area, divide:
\(\frac{Cylinder B}{Cylinder A}\)
=2π(4(rh+r²))/2π(rh+r²)
(divide top and bottom by 2π)
=4(rh+r²)/(rh+r²)
(divide top and bottom by (rh+r²))
=4
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
what is the length of segment kl
33 √3 is the length of segment KL.
The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).
Tanθ = Perpendicular / Base
In the above ΔKJL
According to ∠J,
KL = Perpendicular
KJ = Base
⇒Tan 60° = KJ/KL
⇒Tan 60° = KJ / 33
⇒KJ = Tan 60° × 33 [ Tan 60°= √3 ]
⇒KJ = √3 × 33
⇒KJ = 33√3 m
Hence, 33 √3 is the length of segment KL.
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Identify the dependent and independent variables.
To lease my car, I had to put down $2500, plus I pay $299 per month for 5 years.
The dependent variable is the total cost of leasing the car while the independent variable is the number of months that the car is leased.
What is the independent variable?We know that when we talk about the independent variable, we have to look at the variable that changes and as this variable changing, there would be a change in another variable.
In the case that we have here, we can see that as the number of months is changing, so does the total cost. As such, the total cost would be the dependent variable while the number months would be the independent variable.
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What is the equation of the line in slope-intercept form?
Line on a coordinate plane. Line runs through points begin ordered pair negative 3 comma 0 end ordered pair and begin ordered pair 0 comma 4.
Enter your answer in the boxes.
y =
x +
Answer: x= 3 y=0
x= 0 y=4
Step-by-step explanation: Because the x value is the first number like (3,0) in this 3 is the first number. Y is the second. HOPE IT HELPS!
Answer:
y= 4/3x+4
Step-by-step explanation:
hit me wit that brainliest
Determine the initial investment, PV, for a future value of 6500 dollars if the nominal rate of interest is 5.9 percent compounded quarterly for 12 years? FV = PV(1 + r/n) ^ntPv = ________ (Be sure to give 2 decimal places of accuracy.)
Answer: PV = 3218.69
Explanation:
The formula for calculating compound interest is expressed as
FV = PV(1 + r/n) ^nt
Where
FV is the future value
PV is the initial value
r is the interest rate
n is the number of compounding periods in a year
t is the number of years
From the information given,
FV = 6500
r = 5.9% = 5.9/100 = 0.059
n = 4 because it was compounded quarterly
t = 12
By substituting these values into the formula,
6500 = PV(1 + 0.059/4)^4 * 12
6500 = PV(1.01475)^48
PV = 6500/(1.01475)^48
PV = 3218.69
Which of the following is not equivalent to 23 + ( − 27 ) − 16 − ( − 32 )
The expression that is not equivalent is 23 + (-27) + 16 + 32. Option C
What is PEDMAS?PEDMAS is described as a mathematical acronym that represents the arithmetic operations in the other of their usage in calculation.
They are;
ParenthesesExponentDivisionMultiplicationAdditionSubtractionFrom the information given, we have that;
23 + ( − 27 ) − 16 − ( − 32 )
expand the parentheses, we get;
23 - 27 - 16 + 32
Add the values
23 - 27 - 16
Now, subtract the values
-20
Hence, the value is -20
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The complete question
Which of the following is not equivalent to 23 + ( − 27 ) − 16 − ( − 32 )
23 - 27 - 16 + 3223 - 27 - 16- (-32)23 + (-27) + 16 + 3223 + (-27) + (-16)- (-32)Delia had several packages of jellybeans. She opened them all and had 684 jellybeans. If each package has 76 jellybeans, how many packages of jellybeans did she open?
Answer:
9 packages
Step-by-step explanation:
you would divide 684 by 76 which equals 9
Answer:
9
Step-by-step explanation:
684 divided by 76 equals 9
2/5 is closet to 0 1/2 or 1
Answer:
2/5 is closest to 1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
2/5 = 0.4
1/2 = 0.5
Therefore closer to 1/2
A research organization studying families in various countries reported the following data for the amount of time that children spent with their fathers each day. What is the mode and the median, respectively? Country Time with Dad (minutes) Belgium 30 Canada 44 China 54 Finland 50 Germany 36 Nigeria 42 Sweden 46 United States 42 A. 42, 42 B. 42, 43 C. 43, 42 D. 43,43
Answer:B. 42, 43
Step-by-step explanation:
STEP 1 Listing out the data set
Country Time with dad
Belgium 30
Canada 44
China 54
Finland 50
Germany 36
Nigeria 42
Sweden 46
United States 42
STEP 2--- finding the mode and median
Mode----The mode of this data set is the number that occurs most frequently in this research date.
Time with dad in ascending order is given as 30, 36, 42, 42, 44,46,50,54
The number that occurred the most is 42 = mode
Median The median is the middle value in a data set
Since these data set is an even number, we take the average of the two middle numbers
Arranging in ascending order, we have
30, 36, 42, 42, 44, 46, 50, 54---------------42 and 44 are the middle numbers
42+ 44/2 =43
Therefore mode and median are 42 and 43 respectively
Tim has 2/3 cup of chocolate syrup. If he uses 1/9 cup of chocolate syrup for each serving of chocolate milk, how many servings of chocolate milk can he make
Answer:
6 servings
Step-by-step explanation:
Each serving Tim uses 1/9 cup. So, after using the amount of syrup reduces and repeated subtraction is division.
\(\frac{2}{3}\) ÷ \(\frac{1}{9}\)
\(=\dfrac{2}{3}*\dfrac{9}{1}\)
= 2 *3
= 6
Needing to find the answer to this question attached. Thank you
\(\sin \theta -1 =0\\\\\ \implies \sin \theta = 1\\\\ \implies \theta = \dfrac{\pi}2 + 2\pi n\\\\\text{For n =0,}\\\\\theta = \dfrac{\pi}2\)
Why are these triangles similar?
A. Angle-Angle similarity
B. Side-Angle-Side Similarity
C. Side-Side-Side similarity
D. The triangle are not similar
The reason these triangles are similar is A. Angle-Angle similarity.
How can Angle-Angle similarity prove triangular similarity ?Angle-Angle similarity, also known as AA similarity, states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
In the figure that we are given, we see two angles that are similar as shown on the diagram. These angles are on the different triangles and yet are congruent which means that the triangles are similar.
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Evaluate the expression for u = –8. Simplify your answer. –8 u
9514 1404 393
Answer:
64
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
-8u = -8(-8) = 64
Calc question — related rates
The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
How to determine rate?The volume of the liquid in the bowl is given by the following integral:
\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)
where r = radius of the bowl and y = height of the liquid.
The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:
r = √{(4/(8-x)) - 1}² + 1²
The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:
h = (4/(8-x)) - 1
Substituting these equations into the volume integral:
\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)
Evaluate this integral using the following steps:
Expand the parentheses in the integrand.
Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.
Integrate each part separately.
The integral of the square root term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)
The integral of the linear term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)
Substituting these formulas into the integral:
V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h
Evaluating this integral:
V = π { 16/27 (8-h)³ - 16/18 (8-h)² }
The rate of change of the volume of the liquid is given by:
dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }
The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.
Substituting these values into the equation for dV/dt:
dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π
Solving this equation for the rate of change of the depth of the liquid:
dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹
Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
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Write the expression without using exponents.
(−9x)4
The expression (-9x)^4 can be represented as -6561x^3 without using exponents.
To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.
(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)
To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:
(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2
So, by substituting this result back into the original expression, we get:
(-9x)^4 = 81x^2 * (-9x) = -6561 x^3
Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.
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12. The ratios of the side lengths of a triangle are 7:9:12. The perimeter is 56. What are the lengths of the sides?
Answer:
7+9+12 = 28
doubling each side makes them 14 + 18 + 24 which equals 56
Step-by-step explanation:
Step-by-step explanation:
here's your solution
==> ratio of sides of traingle are given = 7:9:12
==> perimeter of traingle = 56
==> let the ratio be X
==> now , 7x + 9x + 12x = 56
==> 28x = 56
==> x = 56/28
==> x = 2
... length of sides = 7x = 14
.....9x = 18
12x = 24
. length of. sides = 14 ,18 ,.24
\(hope \: it \: helps\)
Dylan and Eric were the lead scorers in a basketball game. Dylan scored p points in the second period of the game. Eric scored as many points as Dylan in the same period of the game. a) Write an expression for Eric's score in terms of p. points b) If Dylan scored 18 points in the second period, how many points did Eric score?
I think the answers 3048_&8_9_)_)_
Skylar went shopping for a new video game. To find the total plus tax, she multiplied the price of the video game by 1.0775. What percent tax did she pay?
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
A third grade teacher is creating a ball tossing competition and has divided her students into three teams. She wants to find the best location to place the basket
so that each team has to throw the ball the same distance. Plot the point that is equidistant from all three teams.
Answer:
Is there a location drawn cause I'm pretty sure without a visual you wont be able to plot here.