The mode of the data set is 15.
What is the mode?A data set's mode or modal value is the value that appears the most frequently.
The given data are:
15, 12, 20, 19, 20, 15, 7, 12, 7, 19, 15.
Note that the number 15 occurs 3 times in the data set which is highest than the occurrence of any other number in the data set.
Hence, the mode of the data set is 15.
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Given the coordinates, classify ∆QRT by its sides. Q(-2, -1), R(1, 5), T(-8, -4) Classify:
The given triangle ∆QRT is isosceles triangle.
What is isosceles triangle?
Triangles with two equal sides are referred to as isosceles triangles. Also equal are the two angles that face the two equal sides. To put it another way, "An isosceles triangle is a triangle with two congruent sides." Assume that the sides AB and AC of the triangle ABC are equal, in which case the triangle ABC is an isosceles triangle with B = C. According to the theorem, "if the two sides of a triangle are congruent, then the angle opposite to them is also congruent."
Here the given points are Q(-2,-1) , R(1,5) , T(-8,-4).
Using distance formula
Now , The Distance between the points can be measure as :
D=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
QR = [tex]\sqrt{(1+2)^2+(5+1)^2}[/tex]
=>QR=[tex]\sqrt{3^2+6^2} = \sqrt{9+36} =\sqrt{45}=3\sqrt{5[/tex] unit
Now RT = [tex]\sqrt{(-8-1)^2+(-4-5)^2} =\sqrt{9^2+9^2} \\[/tex]
=>RT=[tex]\sqrt{81+81}=\sqrt{162} = 9\sqrt{2}[/tex] unit
Now TQ = [tex]\sqrt{(-2+8)^2+(-1+4)^2} =\sqrt{6^2+3^2} \\[/tex]
=>TQ=[tex]\sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex] unit.
Here QR=TQ then
Hence the given triangle is isosceles triangle.
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please help it’s urgent
I cant see the full sentence but yes it is because Q and P and both on the M line which is both 20
Mary and Tom bought a gift for their
mother for Mother's Day. Tom paid $28.00,
and Mary paid $12.00. If they wanted to
share the cost of the gift equally, how
much money does Mary owe Tom?
$
Answer:
$8
Step-by-step explanation:
Mary and Tom bought a gift for their mother for Mother's Day. Tom paid $28.00, and Mary paid $12.00. If they wanted to share the cost of the gift equally, how much money does Mary owe Tom?
total paid: 28 + 12 = $40
if they split equally: $40/2 = $20 each
because Mary only paid $12 she owes Tom: 20-12 = $8
Shanice's car is traveling 10 miles per hour slower than twice the speed of Brandon's car. She covers 93 miles in 1 hour 30 minutes. How fast is Brandon driving?
The speed of a body is the distance it travels per unit of time. That means that we can also find out how far an
object moves in a certain amount of time if we know its speed: we use the equation "distance = speed time."
Here, we don't know either Brandon's speed or Shanice's, but since the question asks for Brandon's speed, that's what we'll use as our variable x.
The distance Shanice covers in miles is 93, and the time in hours is 1.5. Her speed is 10 less than twice Brandon's speed.
Shanice's speed is:
x - 10 miles per hour.
Substituting into the equation distance = speed × time gives us
93 = ( x - 10)1.5
First we distribute, to get
93 = 3x -
Then we add 15 to both sides to get
108 = 3x.
Finally we divide by 3 to get
= x.
Brandon is driving at miles per hour.
Check: We can check this answer by considering the situation another way: we can solve for Shanice's speed instead of Brandon's and then check that against Brandon's speed.
The equation for Shanice's speed is simply 2x - 10 = 2(
-10
72 - 10 = 62
So, Shanice is traveling at
miles per hour.
The problem tells us that Shanice is traveling 10 mph slower than twice Brandon's speed;
that would mean that 62 is equal to 2 times 36 minus 10. Is that true? Well, 2 times 36 is 72, minus 10 is 62.
Answer:
Step-by-step explanation: use your brain please you will get it ahhh
please help
1. Draw a triangle.
2. Plot a midsegment of the triangle in the image with number 11. Include work to verify that the segment drawn is the midsegment. Make sure to include the midsegment in the image.
1. Triangle ABC with the vertices, A(0, 2), B(6, 4), and C(4, -2) is drawn and attached below.
2. The midsegment is EF. This is verified using the triangle midsegment theorem which states that EF = 1/2(AC).
What is the Midsegment of a Triangle?The midsegment of a triangle is the line segment that joins the midpoints of two sides of a triangle together. Every triangle typically has three midsegments.
According to the triangle midsegment theorem, the length of the midsegment is half the length of the third side of the triangle that it is parallel to.
What is the Midpoint of a Line?The midpoint of a line is its middle, which can be calculate using the formula:
M(x, y) = [tex](\frac{x_2 - x_1}{2}, \frac{y_2 - y_1}{2})[/tex].
1. The coordinate of the three vertices that is used to draw a triangle are:
A(0, 2), B(6, 4), and C(4, -2).
The triangle is in the attachment below.
2. To plot the midsegment of the triangle, determine the midpoints of AB and BC, then plot the coordinate where both midpoints would be joined.
Midpoint of AB = (x, y) = (0+6)/2, (2+4)/2
= (6/2, 6/2)
= (3, 3) (let this be point E)
Midpoint of AB = (x, y) = (4+6)/2, (−2+4)/2
F = (5, 1)
The midsegment will have the endpoints, E(3, 3) and F(5, 1).
To verify the segment draw is the midsegment according to the triangle midsegment theorem, find the length of the midsegment, EF, and the length of the third side, AC using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
EF = √[(5−3)² + (1−3)²]
EF = √8 units
AC = √[(4−0)² + (−2−2)²]
AC = √32 units
Based on the triangle midsegment theorem:
EF = 1/2(AC)
Plug in the values:
√8 = 1/2(√32)
√8 = 1/2(4√2)
√8 = 2√2
2√2 = 2√2 (true)
This means that EF is a midsegment of triangle ABC.
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HELP ME PLEASEEEEEEEEEE
The rules for transformation of first graph is (x + 4, y + 6).
The rules for transformation of second graph is (x + 4, y + 6).
What is Transformation?Transform the forms on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century. In geometry, object transformations are the foundation for the majority of proofs.
In first graph it is clear that the graph is translated and the rule for first graph is (x + 4, y + 6).
Similarly, the second graph is also translated and the rule is (x+3, y).
Therefore, the rule for first graph is (x + 4, y + 6) and the rule for second graph is (x + 4, y + 6).
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Find the circumference of each of the following circles. Use 3.14 for TT
17 km
32 in
39 m
25 mi
Answer:
a=34π
b=64π
c=39π
d=25π
Step-by-step explanation:
What is the length of the garden?
The length of the garden is 63ft, in the rectangle
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,
Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.
The given perimeter is 210ft
let l be the length and 2/3 of l is the breadth.
We know that 2(a+b) = 210
2(l + 2/3l) = 210
5/3 l = 105
l = 105* 3/5 = 63ft
Hence the length of the garden is 63ft.
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Answer these math questions(put solution) (if you want to answer word problem look in the comments)
1. ( 1.8 + 3.44 ) x 0.75
2. (8.29 - 0.32) ÷ 0.4
3. 7.58 (1.5 x 0.24) ÷ 0.5
4. (16.45-5.05) x (2.46 + 1.24)
5. (7.1 x 2.3) ÷ (1.25 x 0.6)
6. (4.19 + 6.8) ÷ (0.34-0.15)
Solution to the questions are: (1) 3.95
(2)19.92
(3) 5.45
(4) 42.18
(5) 21.77
(6) 57.84
What is Simplify?
Simplify in mathematics is a simple way of bringing down a problem, fraction or word expression into an easier from
1. ( 1.8 + 3.44 ) x 0.75
Simplify the equation using
=(5.24) x 0.75
=3.95
2. (8.29 - 0.32) ÷ 0.4
Rewrite the equation and simplify
=[tex]\frac{8.29 -0.32}{0.4}[/tex]
=[tex]\frac{7.97}{0.4}[/tex]
=19.92
3. 7.58 (1.5 x 0.24) ÷ 0.5
Rewrite the equation and simplify
=[tex]\frac{7.58(1.5 * 0.24) }{0.5}[/tex]
= [tex]\frac{7.58 (0.36)}{0.5}[/tex]
= [tex]\frac{2.728}{0.5}[/tex]
= 5.45
4. (16.45-5.05) x (2.46 + 1.24)
Simplify the equation
=(11.4)x (3.7)
=42.18
5. (7.1 x 2.3) ÷ (1.25 x 0.6)
Rewrite the equation and simplify
= [tex]\frac{7.1 * 2.3}{1.25 * 0.6}[/tex]
= [tex]\frac{16.33}{0.75}[/tex]
= 21.77
6. (4.19 + 6.8) ÷ (0.34-0.15)
Rewrite the equation and simplify
= [tex]\frac{4.19 + 6.8 }{0.34 - 0.15}[/tex]
= [tex]\frac{10.99}{0.19}[/tex]
= 57.84
Therefore, the solution to the equations are ;(1) 3.95
(2)19.92
(3) 5.45
(4) 42.18
(5) 21.77
(6) 57.84
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Please help me!! can't figure it out for some reason
A census was conducted at a school. All of the students were asked how many cars their family owns. The results are below.
3. What is the probability that a randomly chosen student has at least 3 cars? Answer
4. What is the expected number of cars? Answer
5. What is the standard deviation? Answer
Answer: how did u get a pfp
Step-by-step explanation:
A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation?
y = 1,000(1.15)6; 2,313 bacteria
y = 1,000(1.15)7; 2,660 bacteria
y = 1,000(1.5)5; 7,594 bacteria
y = 1,000(1.5)6; 11,391 bacteria
"The population of the culture 6 days after inoculation is 1,000(1.15)^6 ; 2313 bacteria"
Initial inoculated bacteria = 1000
Growing rate of bacteria = 15%
we have to find the population of the culture after 6 days
y = 1000 ( 1 + 15/100)^6
y= 1000 (1.15)^6
y = 1000(2.313060)
y = 2313.06 ≈ 2313
The population of the culture 6 days after inoculation is 2313.
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Select the equation that is true. 12 ÷ 2 = 15 ÷ 5 12 ÷ 3 = 24 ÷ 6 32 ÷ 8 = 21 ÷ 7 30 ÷ 5 = 28 ÷ 4
Answer:
12 ÷ 3 = 24 ÷ 6
Step-by-step explanation:
12/3 = 4 and 24/6 = 4
So 4 = 4
77, 49, 36, 18, _
what is the next number?
what is the rule?
Answer:9
Step-by-step explanation:um
A 70-meter path surrounds a rectangular garden. The width of the garden is two-thirds its length. Find its area (in m2).
The area of the rectangular garden that has a 70-meter path surrounding it is: 1,176 m².
What is the Area of a Rectangle?Area = length × width
Perimeter of a rectangle = length surrounding a rectangular shape = 2(length + width).
Give the following:
Perimeter of the rectangular garden = 70 meter
Length = l
Width = 2/3l
Therefore:
l + 2/3l = 70
5/3l = 70
5l = 3(70)
5l = 210
5l/5 = 210/5
l = 42
Length = l = 42
Width = 2/3l = 2/3(42) = 28
Area of rectangular garden = 42 × 28 = 1,176 m².
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Z-score of 1 to percentile
For the z-score = 1, the percentile = 84.13%
In this question, we need to find the percentile when z-score is 1
We know that a Z-scores is a normalized score that used to compare values relative to their population. z-score represents a specific location in the normal distribution, so that there is a certain area that is to the left of that z-score. The percentile associated to a z-score is nothing but the area to the left of that z-score.
When z = 1 then the percentile would be 84.13%
Therefore, for the z-score = 1, the percentile is 84.13%
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find the perimeter of each figure formed by using six squares tiles. By what percentage is the maximum perimeter more than the minimum one
Answer: no.
Step-by-step explanation: no.
(1 po
3. Your cell phone plan is $35.98/month plus a utilities tax of 6.5% APR. During the year, you go
40 minutes over your plan at a rate of $0.35/minute. How much do you pay for the overages?
The amount that the cell phone owner will pay for the overages is $14.91.
What is the overage?The overage is the difference between the actual usage in minutes and the estimated usage.
For instance, if the plan estimates that the phone usage per year would be 4,000 minutes, but the plan holder uses 4,010 minutes, the extra 10 minutes are regarded as overages.
The opposite of overages is underages. If underages are part of the phone plan, the plan holder will be refunded accordingly.
Usually, overages attract a variable plan rate per minute.
Fixed charge per month = $35.98
Utilities tax APR = 6.5%
Overages = 40 minutes
Rate per overage minute = $0.35
The total charge for overage = $14 ($0.35 x 40)
Interest on the overages = $0.91 ($14 x 6.5%)
Total payment for the overages = $14.91 ($14 + $0.91)
Thus, for going over the plan by 40 minutes at $0.35 plus an APR of 6.5%, you will pay $14.91 for the overages.
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a2- 3x -10 please solve this what will be the factor of it
Step-by-step explanation:
a² - 3x - 10
a(a -3) (x - 10)
Multiply and then simplify, if needed: 3x/ x² - 25 . x²+6x+5/6x²+6x Divide and then simplify, if needed: x²-2x-3/x²+2x+1 ÷ x³ -5x² +6x /x²-3x -4
The simplified form of the expression will be 1 / [2(x - 5)] and [(x - 4) / [x (x - 2)].
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The expression is given below.
⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]
Simplify the expression, then we have
⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]
⇒ [(3x) / (x² - 5²)] · [(x² + 5x + x + 5) / (6x² + 6x)]
⇒ {3x / [(x - 5)(x + 5)]} · {[(x + 5)(x + 1)] / [(6x)(x + 1)]}
⇒ 1 / [2(x - 5)]
The expression is given below.
⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]
Simplify the expression, then we have
⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]
⇒ {[(x - 3)(x + 1)] / [(x + 2)(x + 1)]} · {[(x - 4)(x + 1)] / [x(x - 3)(x - 2)]}
⇒ [(x - 4) / [x (x - 2)]
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murray mixes 2 quarts of liquid A and 8 pints of liquid B to make a compound. How many gallons of compound are produced?
Answer:
1 1/2 gallons
Step-by-step explanation:
there are two pints in one quart so 2 quarts plus 8 pints equals
2 quarts plus 4 quarts, or 6 quarts
there are 4 quarts in one gallon so 6 quarts is the same as 1 gallon and 2 quarts
2 quarts is half of one gallon
Fill in the blanks to create an equation that has infinite solutions
7x+3x+10=-2(_x + _)
Fill in the blanks to create an equation that has no solutions
7x+3x+10=-2(_x + _)
An equation 7x+3x+10= -2[-5x +(-5)] has infinite solutions and an equation 7x+3x+10= -2[-5x + (-4)] has no solution.
Given that:
7x+3x+10 = -2 (_x + _)
=> 10x + 10 = -2 (_x + _)
Putting in the blank -5 so as to satisfy the equation that has an infinite solution.
=> 10x + 10 = -2(-5x + -5)
This is the equation that shows that it has infinite solutions and they are in the same line.
For no solutions
7x+3x+10 = -2 (_x + _)
In no solution, the value of b is not equal to -5.
For equation:
7x+3x+10 = -2 (-5x + b) [If putting value in first blank = -5]
Therefore, -2 (-5x + b) is parallel to 10x+10 for any value of b not equal to -5. Parallel lines never intersect. So solutions are no solution.
Putting the value of b = -4
7x+3x+10 = -2 [-5x + (-4)]
This is the equation that shows that it has infinite solutions and they are in the same line.
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5. On Friday night, Samantha ate a pizza for dinner and had 1/2 of the pizza left over. On Saturday, she ate 2/3 of what was left. How much of the pizza did
Samantha eat on Saturday?
Answer:
∴ Samantha ate [tex]\frac{1}{3}[/tex] of the pizza on Saturday.
Step-by-step explanation:
Fraction of pizza left on Friday = [tex]1-\frac{1}{2}[/tex]
= [tex]\frac{1}{2}[/tex]
∴ Fraction of pizza eaten on Saturday = [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{3}[/tex]
A groundskeeper needs grass seed to cover a circular
field, 290 feet in diameter.
A store sells 50-pound bags of grass seed. One pound
of grass seed covers about 400 square feet of field.
What is the smallest number of bags the
groundskeeper must buy to cover the circular field?
Explain or show your reasoning.
Hint: You can only buy WHOLE bags of grass seed so
you MUST round up!
The smallest number of bags the groundskeeper must buy to cover the circular field is 4.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
The perimeter of the circle = 2πr where r is the radius of the circle.
As per the given,
Diameter of the circular field = 290 feet
Radius = 290/2 = 145
Area of circle = πr² = π(145)²
⇒ 66051.985 feet²
In one bag = 50 pounds
Area cover in one bag = 50 × 400 = 20000
Number of bags needed to cover the whole area
⇒ 66051.985/20000 = 3.3025
Since the number of bags is a whole quantity thus it will round up to 4.
Hence "The smallest number of bags the groundskeeper must buy to cover the circular field is 4".
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Mai picked a mystery number that is less than 30. she says she can show 3 different rectangles on this grid whose area is the same as her mystery number
what could be Mai's mystery number?
Answer:The answer is 4
Step-by-step explanation:BEcause of the mail´s mystery number
The annual profits for a company are given in the following table, where x represents the number of years since 1997, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected profit (in thousands of dollars) for 2006, rounded to the nearest thousand dollars.
Years since 1997 (x) Profits (y)
(in thousands of dollars)
00 131131
11 168168
22 202202
33 193193
44 221221
Regression Equation:
Final Answer:
The linear regression equation for the profit in x years after 1997 is of:
y = 20.5x + 142.
Using this equation, the estimate for the profit in 2006, is of: $326,500.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the data, represented either in a table or in a scatter plot, into a linear regression calculator.
In the context of this problem, these points are given as follows:
(0, 131), (1, 168), (2, 202), (3, 193), (4, 221).
Inserting these points into a calculator, the equation is:
y = 20.5x + 142.
The estimate for the profit in 2006, that is, 9 years after 1997, is of:
y = 20.5(9) + 142 = 326.5 thousand dollars = $326,500.
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Add (7.8 x 10^5) + (2.4 x 10^5).
[tex](7.8*10^5)+(2.4 * 10^5)[/tex]
[tex](7.8 * 100,000) + (2.4 * 100,000)[/tex]
[tex]780,000 + 240,000[/tex]
= 1,020,000
Answer:
1020000
Step-by-step explanation:
(7.8 x 10^5) + (2.4 x 10^5)
780000+240000
1020000
Hopes this helps please mark brainliest
a big storage tank contains 1680 gallons of gasoline. 25 cars filled their tanks with 24 gallons of gas each. 35 trucks put 30 gallons of gas in each of their tanks. how many gallons of gas are left in the big storage tank?
Answer:
30 gallons of gas is left
Step-by-step explanation:
1680 is what we start with
25 filled with 24
25*24=600
35 filled with 30
35*30= 1050
So we take away what we used
600+1050= 1650
We started with 1680
1650 got taken away so
1680-1650= 30
30 gallons are left
Answer:
30 gallons of gas are left in the big storage tank---------------------------------
Initial volume of gas in the storage tank is 1680 gallons.
Cars took:
25 × 24 = 600 gallonsTrucks took:
35 × 30 = 1050 gallonsGas left in the storage tank:
1680 - (600 + 1050) = 1680 - 1650 = 30 gallonsPlease answer I need to turn it in asap morning when please help
Answer:
-7/3
Step-by-step explanation:
(-2-5)/(5-2)
-7/3
Answer:
C.
Step-by-step explanation:
Using Slope formula (y2-y1/x2-x1), we can plug these 2 coordinates in. -2-5/5-2= -7/3.
Or even by simply using rise over run, we can get the slope. Up 7 over 3, and we know that the slope is negative, so we add a negative sign in front.
-Hope this helped
How many kg of an alloy with 90% copper must be added to 6 kg of another alloy with 15% copper to obtain an alloy that is 40% copper?
3 kg of an alloy with 90% copper must be added to 6 kg of another alloy with 15% copper to obtain an alloy that is 40% copper.
Given, we are asked to determine:
How many kg of an alloy with 90% copper must be added to 6 kg of another alloy with 15% copper to obtain an alloy that is 40% copper = ?
convert kg to ounces.
6kg = 211.644 ounces.
90%x+15%(211.644)=40%(211.64+x)
0.9x+0.15(211.64)=0.4(211.64+x)
0.9x+31.7466 = 84.6576 + 0.4x
0.9x - 0.4x = 84.6576 - 31.7466
0.5x = 52.911
x = 52.911/0.5
x = 105.822
now convert ounces to kg.
= 3kg
Hence approximately 3 kg of an alloy with 90% copper must be added to 6 kg of another alloy with 15% copper to obtain an alloy that is 40% copper.
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A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is ?
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2 x in the figure, is?
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is ?
(Type an integer or decimal rounded to the n
meters.
square meters.
cubic meters.
The solution to the questions are:
The width, labelled x in the figure is 87.5 metersThe length, labelled 350-2 x in the figure, is 175 metersThe largest area that can be enclosed is 15312.5 square metersHow to determine the width and the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 350 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (350 - 2x) * x
Evaluate
A = 350x - 2x²
Differentiate and set to 0
350 - 4x = 0
So, we have
4x = 350
Divide by 4
x = 87.5
Recall that
Length = 350 - 2x
So, we have
Length = 350 - 2 x 87.5
Evaluate
Length = 175
The area is then calculated as
Area = Length x Width
So, we have
Area = 175 x 87.5
Evaluate
Area = 15312.5 square meters
Hence, the area is 15312.5 square meters
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