Solution:
Given;
[tex]P(-24,-24),Q(-19,-19)[/tex]The distance d(P,Q) is;
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\ x_1=-24,y_1=-24,x_2=-19,y_2=-19 \\ \\ d=\sqrt{(-19-(-24))^2+(-19-(-24))^2} \\ \\ d=\sqrt{50} \\ \\ d=5\sqrt{2} \end{gathered}[/tex]Also, the midpoint, M, is;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \\ M=(\frac{-24+(-19)}{2},\frac{-24+(-19)}{2}) \\ \\ M=(-\frac{43}{2},-\frac{43}{2}) \end{gathered}[/tex]8. Brendan ran a total of 88 miles over the course of 44 track practices.
How many track practices would it take for Brendan to run 1010 miles?
Solve using unit rate?
Mr. Peasley wrote an expression that is equivalent to
20 ÷ 1 + 4 on the board. Which expression could be the one Mr. Peasley wrote?
Responses
A 3 • 12 – 3 • 43 • 12 – 3 • 4
B 36 ÷ 3 • 2 + 1 36 ÷ 3 • 2 + 1
C 5 • 6 + 2 • 3 ÷ 2 • (1 + 5)5 • 6 + 2 • 3 ÷ 2 • (1 + 5)
D 6 + 6 • (10 + 2)
20 ÷ 1 + 4 on the board is 36 ÷ 3 • 2 + 1 36 ÷ 3 • 2 + 1.According to the order of operations, you should execute addition and subtraction last and multiply and division first, proceeding from left to right
How can addition, subtraction, multiplication, and division be calculated?According to the order of operations, you should execute addition and subtraction last and multiply and division first, proceeding from left to right. Divide and multiply from left to right as you continue. After that, add and subtract starting from the left.Remind them, if necessary, that addition and subtraction occur after multiplication and division in the order of operations.Mathematics has created standards (agreements) for how we interpret mathematical expressions in order to avoid these and other potential ambiguities. A writer who intended the contrary interpretation would have to write the sentence differently: 10 (5 2). One of these conventions stipulates that when all of the operations are the same, we go left to right. Therefore, 10 5 3 = 2.To learn more about mathematical expressions refer to:
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40. If you want a poll to have a margin of error of 3.06%, how large will your sample have to be? Round your answer to the nearest whole number. people
Margin of Error:
[tex]=\pm\frac{100}{\sqrt[]{n}}[/tex]ANSWER: 1068
[tex]\begin{gathered} \text{Margin of Error}=\pm\frac{1}{\sqrt[]{n}} \\ 0.0306=\pm\frac{1}{\sqrt[]{n}} \\ \sqrt[]{n}\cdot0.0306=1 \\ \frac{\sqrt[]{n}\cdot0.0306}{0.0306}=\frac{1}{0.0306} \\ \sqrt[]{n}=32.67973856 \\ (\sqrt[]{n})^2=32.67973856^2 \\ n=1,067.965312 \end{gathered}[/tex]Someone please help me. I can't get the right answer
The required value of x will be 44°.
What is an Isosceles Triangle?An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.
We have been given a triangle in the figure
According to the given figure, we can see that the triangle is an isosceles triangle
As per the property of the isosceles triangle, here two angles are the same.
Now, the sum of angles in a triangle as:
⇒ 68° + 68° + x = 180°
⇒ 136° + x = 180°
⇒ x = 180° - 136°
⇒ x = 44°
Therefore, the required value of x will be 44°.
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What is the equation of the line that passes
through the point (-6, -7) and has an
undefined slope?
A line with an undefined slope would be x=___, in which you would put the x value of the coordinate. So, the equation would be x = -6
The vertices of ΔABC are A(7, 3), B(−8, 6), C(0, −5). If ∆ABC is translated along the vector <−9, 5>, what are the coordinates of the vertices of ΔA'B'C' ?
Responses
A'(−2, 8), B'(−17, 11), C'(−9, 0)
A ' ( - 2 , 8 ) , B ' ( - 17 , 11 ) , C ' ( - 9 , 0 )
A'(8, −2), B'(11, −17), C'(0, −9)
A ' ( 8 , - 2 ) , B ' ( 11 , - 17 ) , C ' ( 0 , - 9 )
A'(12, −6), B'(−3, −3), C'(5, −14)
A ' ( 12 , - 6 ) , B ' ( - 3 , - 3 ) , C ' ( 5 , - 14 )
A'(16, −2), B'(1, 1), C'(9, −10)
The coordinates of the vertices of ΔA'B'C' after the transformation are (a) A'(-2, 8), B'(-17, 11), C'(-9, 0)
How to determine the vertices of ΔA'B'C'?The coordinates of the triangle are given as
ΔABC are A(7, 3), B(−8, 6), C(0, −5).
The transformation is given as
∆ABC is translated along the vector <−9, 5>
Mathematically, this can be represented as
(x, y) ⇒ (x - 9, y + 5)
When this is applied on ABC, we have:
ΔA'B'C' = A'(7 - 9, 3 + 5), B'(−8 - 9, 6 + 5), C'(0 - 9, −5 + 5)
Evaluate the computations
ΔA'B'C' = A'(-2, 8), B'(-17, 11), C'(-9, 0)
Hence, the image of the transformation is (a) A'(-2, 8), B'(-17, 11), C'(-9, 0)
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Find the percent change from 32 to 60.
Answer:
87.50%
Step-by-step explanation:
You have to find the difference between the two numbers and divide the result by the first number which is 32. Multiply the answer by 100 to get the answer as a percentage!
Answer:32% of 60 = 87.5
Step-by-step explanation:
simple interest is computed by finding the product of the principal amount, p, and the interest rate, r, and the time t.translate each sentence into an formula
You have that simple interest is computed by the multiplication of p (principal amount), r (interest rate) and t (time).
The previoues sentence can be written algebraically as follow:
I = p x r x t you only have to multiply each factor
where I is the letter for simple interest.
help!! ASAP!! 50 points too whoever helps!!
Answer:720
thats the answer 720
Find the slope and y-intercept of the line below
What is 14 3/4 - 4 1/8
The mixed fraction is express as :
[tex]a\frac{b}{c}=\frac{a\times c+b}{c}[/tex]The given expression is :
[tex]14\frac{3}{4}-4\frac{1}{8}[/tex]Simplify the mixed fraction into decimal form :
[tex]\begin{gathered} 14\frac{3}{4}=\frac{14\times4+3}{4} \\ 14\frac{3}{4}=\frac{59}{4} \\ 14\frac{3}{4}=14.75 \end{gathered}[/tex][tex]\begin{gathered} 4\frac{1}{8}=\frac{4\times8+1}{8} \\ 4\frac{1}{8}=\frac{33}{8} \\ 4\frac{1}{8}=4.125 \end{gathered}[/tex]Substitute the value and then subtarct :
[tex]\begin{gathered} 14\frac{3}{4}-4\frac{1}{8}=14.75-4.125 \\ 14\frac{3}{4}-4\frac{1}{8}=10.625 \end{gathered}[/tex]Answer : 14 3/4 - 4 1/8 = 10.625
Answer:
5/8
Step-by-step explanation:
3/4 can be multiplied by 2 to get 6/8 and now you have common denominators so you do 4 6/8 - 4 1/8
4-4= 0
6/8 - 1/8 = 5/8 so 5/8 is the answer
A number is squared. This is added to fifteen and the product of eight and the number, to give zero.
A number is squared. This is added to fifteen and the product of eight and the number, to give zero.
the algebraic expression is
Let
x ----> the number
x^2+(15+8x)=0
therefore
x^2+8x+15=0
solve the quadratic equation
Solve by using calculator
x=-5 and x=-3
Albert bought 3 rolls of masking tape that cost the same amount of money and an extension cord that cost $5.50. Albert spent less than $10 altogether.Which inequality can be used to find the cost of each roll of masking tape?A.) 3m+5.50<10B.) 3m-5.50<10C.) 3m+5.50>10D.) 3m-5.50>10
Data:
m: cost of the masking tape
As the masking cost the same amount of money: 3m
Then, you add to the cost of the masking the 5.50, you get: 3m+5.50
The symbol to less than is <
You get:
[tex]3m+5.50<10[/tex]Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 20.a. Find the standard deviation for the numbers of peas with green pods in the groups of 20
Given
Probability that a pea has green pods = 0.75
Sample of the offspring peas , n = 20
Find
Standard deviation for the numbers of peas with green pods in the groups of 20
Explanation
as we have given ,
Probability that a pea has green pods , p = 0.75
Probability that a pea do not have green pods , q = 1 - 0.75 = 0.25
n = 20
in binomial distribution ,
standard deviation is given by
[tex]\sqrt{npq}[/tex]so,
[tex]\begin{gathered} S.D=\sqrt{20\times0.75\times0.25} \\ S.D=\sqrt{3.75} \\ S.D=1.93649167\approx1.94 \end{gathered}[/tex]Final Answer
Hence , the standard deviation for the number of peas with green pods in the group of 20 is 1.94
How can I solve the problem 3+4(10-8)
A) (18,-2)
B) (18,2)
C) (15,-2)
D) (15,2)
Answer: Location of T' on the coordinate axis will be (16,7).
T (6,4) → T' (16,7).
Step-by-step explanation:
coordinate vertices of points in rectangle JKLM are:
J (-8,-8)
K (-4,-8)
L (-4,-5)
M (-8,-5)
and coordinate vertices of points in rectangle J'K'L'M' are:
J' (2,-5)
K' (6,-5)
L' (6,-2)
M' (2,-2)
coordinate vertices of points in Quadrilateral STUV are:
S (1,4)
T (6,4)
U (4,6)
V (2,6)
transformation in coordinate vertices from rectangle JKLM to rectangle J'K'L'M' is:
J (-8,-8) → J' (2,-5)
⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.
and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.
similarly for
K (-4,-8) → K' (6,-5)
⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.
and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.
L (-4,-5) → L' (6,-2)
⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.
and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.
M (-8,-5) → M' (2,-2)
⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.
and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.
So, the location of T' of the Quadrilateral S'T'U'V' on the coordinate plane will be:
along x axis the Quadrilateral will shift towards right by 10 units
So, 6 → 6+10=16
and along y axis the Quadrilateral will shift upwards by 3 units
So, 4 → 4+3=7
⇒ T (6,4) → T' (16,7).
Step-by-step explanation:
Enter the number in scientific notatlon. 65,978 Hint: Move the decimal left 4 places.
ANSWER
[tex]6.5978\cdot10^4[/tex]EXPLANATION
We are given the number 65,978.
To put it in scientific notation, we will need to put it in a format such that we have a number between 1 and 10 multiplying a power of ten.
So, to do that, we will move the decimal point from the end of the number (65978.) to just after the first number.
Then the number of times we move it will be the power of 10.
Since we will move it to the left, it will be a positive power.
So, we have that the number becomes:
[tex]6.5978\cdot10^4[/tex]The power is 4 because we moved the decimal four times.
Myra can fill 20 glasses with 2 containers of iced tea. How many glasses can she fill with 3 containers of tea?
Hint: Find the unit rate first!
Answer: 30 glasses
Step-by-step explanation:
Answer:
30 glasses
Step-by-step explanation:
2:20 = 1:10
1:10 x 3 = 3: 30
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-0.125 divided by (-0.5)
Help please
Answer:
Step-by-step explanation:
Since the numbers, we are given are fractions there is this ultimate rule when we divide fractions
the sign changes from division to multiplciation and the second fraction flips
so lets do this
-0.125 = -1/8
-0.5 = -1/2
Now lets put into into an equation
-1/8 * -2 = 1/4
Simone paid $13 for an initial year's subscription to a magazine. The renewal rate is $8 per year. This situation can be represented by the equation y = 8x + 13, where x represents the number of years the subscription is renewed and y represents the total cost, in dollars. Part 1 out of 4 Complete the table of values for this situation. x (number of years renewed) 0 1 2 3 4 y (total cost in dollars) Next
Data Input
Simone paid $13 for an initial year's
The renewal rate is $8 per year
Equation
y = 8x + 13
Table
x (number of years renewed) | (total cost in dollars)
0 -> 13 dollars
1 -> 21 dollars
2 -> 29 dollars
3 -> 37 dollars
4 -> 45 dollars
How many simple random samples of size 3 can be selected from a population of size 7.
By using combination, it can be obtained that
Number of simple random samples of size 3 that can be selected from a population of size 7 = 35
What is combination?
Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.
Here, concept of combination is used
Number of simple random samples of size 3 that can be selected from a population of size 7 = [tex]{7 \choose 3}[/tex] = 35
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During a thunderstorm at a sports event, a detector activates to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table. Lightning detector activates Lightning detector does not activate Row Totals Lightning in area 88% 2% 90% No lightning in area 7% 3% 10% Column Totals 95% 5% 100% What is the ratio of true positives to false positives in this scenario? Round your answer to one decimal place. 0.1 1.5 12.6 44
The answer is 12.6
Step-by-step explanation:
The ratio is calculated with division.
This means we need to do this equation: 88/7.
The answer to 88/7 is 12.57. However, the question states: Round your answer to one decimal place.
This means we round 12.57 up to 12.6.
Answer: its (C) 12.6
Step-by-step explanation:
basically the first person already explained it
the positives are ( lighting detector activates ) column
the true positive its when the detector activates and there is lightning, so 88%
and false positive its when the detector activates but there's no lightning, so 7%
at the end you just divide 88% / 7%
which is 12.57 and you round it
Crispy Clover, a popular vegetarian restaurant, introduced a new menu that has 20\%20%20, percent more dishes than the previous menu. The previous menu had DDD dishes.
The number of dishes the crispy clover has in his new menu can be expressed as D + (1/5)D.
Define expression.A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, and subtraction operations.
Given data -
20% more dishes are available on the new menu than the old one.
D foods were on the previous menu.
As 20% more dishes are added,
Therefore we can also write it as (20/100)D
Now the total dishes in the new menu can be expressed as
= D + (20/100)D
= D + (1/5)D
Therefore the number of dishes the crispy clover has in his new menu can be expressed as D + (1/5)D.
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The complete question is:
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has?
hi can someone help me here
Answer:
[tex]\left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Given endpoints of the diameter of the circle:
(x₁, y₁) = A (7, -3)(x₂, y₂) = B (0, -4)To find the center of the circle, substitute the given endpoints into the midpoint formula:
[tex]\begin{aligned} \implies \textsf{Midpoint} & =\left(\dfrac{0+7}{2},\dfrac{-4-3}{2}\right)\\& =\left(\dfrac{7}{2},-\dfrac{7}{2}\right)\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Substitute the found center and one of the given points (0, -4) into the equation and solve for r²:
[tex]\implies \left(0-\dfrac{7}{2}\right)^2+\left(-4-\left(-\dfrac{7}{2}\right)\right)^2=r^2[/tex]
[tex]\implies \left(-\dfrac{7}{2}\right)^2+\left(-\dfrac{1}{2}\right)^2=r^2[/tex]
[tex]\implies \dfrac{49}{4}+\dfrac{1}{4}=r^2[/tex]
[tex]\implies \dfrac{50}{4}=r^2[/tex]
[tex]\implies r^2=\dfrac{25}{2}[/tex]
Therefore, the equation of the circle is:
[tex]\implies \left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]
The graph of the circle is attached.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
the question is about distance.
what do we use to measure distance ? things like feet, yards, meters, ...
definitely not square feet (areas) or cubic feet (volume).
it is a right-angled triangle. so Pythagoras applies
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle). in our case the 48 ft side.
a and b are the legs. in our case x and x+6.
the saved walking distance is the difference between 48 ft and the sum of the legs (which would be the walking distance, when they cannot get though the lot).
48² = x² + (x + 6)² = x² + x² + 12x + 36
2304 = 2x² + 12x + 36
1152 = x² + 6x + 18
x² + 6x - 1134 = 0
the solution for such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a) =
= (-6 ± sqrt(6² - 4×1×-1134))/(2×1) =
= (-6 ± sqrt(36 + 4536))/2 =
= (-6 ± sqrt(4572))/2 =
= -3 ± sqrt(4572/4) = -3 ± sqrt(1143) =
= -3 ± sqrt(9×127) = -3 ± 3×sqrt(127)
x1 = -3 + 3×sqrt(127) = 30.80828301...
x2 = -3 - 3×sqrt(127) = -36.80828301...
negative numbers for a distance don't make any sense, so
x = 30.80828301... is our solution.
that means the 2 legs are
30.80828301... ft
36.80828301... ft
in total they are
67.61656602... ft
and so they save
67.61656602... - 48 = 19.61656602... ft ≈
≈ 19.617 ft
by walking across the lot.
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
20, 37, 68, --?--2. Solve.3. Sketch.V + F = E + 2IT V 12 andF = 8, find E.
V + F = E + 2
If V=12 and F=8 Find E:
We have to replace the values given of V and F IN THE EXPRESSION:
12 + 8 = E+2
Now, we simply have to solve for E:
12+8 -2 =E
18=E
E=18
Which of the following ratios is equivalent to 25:18?
The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .
In the question ,
it is given that ,
the ratio is 25:18 , we need an equivalent ratio .
the ratio is 25:80 which can be written in fraction as 25/80 .
writing the factors of 25 and 80 .
= (5×5)/(5×16)
we can see that 5 is the common factor in both the numerator and the denominator .
= 5/16
which can be written as
= 5:16
the equivalent ratio is 5:16 .
Therefore , The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .
The given question is incomplete , the complete question is
Which of the following ratio is equivalent to 25:80 ?
(a) 2:5
(b) 8:5
(c) 16:5
(d) 5:16
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Which of the fractions is equivalent to 2/5
Answer:
all the fractions that are equivalent to 2/5 are 4/10, 6/15, 8/20
Step-by-step explanation:
this is all I can rember
A Town has a population of 20000 and grows at 4% every year. What will be the population after 6 years? To the nearest whole number
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=20000(1 + 0.04)^{6} \implies A=2000(1.04)^6\implies A \approx 25306[/tex]
what are the domain and range or this exponentiAl function y=1/6.8×
We want to identify the domain and range of the following function
[tex]\frac{1}{6}\cdot8^x[/tex]Recall that the domain of a function is the set of values for the variable x, for which the function is defined. Note that we can see this function as the product of two different functions
[tex]\frac{1}{6}[/tex]and
[tex]8^x[/tex]Note that the first part (1/6) does not depend on x, so this means that it is always defined. Also, note that 8^x is always defined for any value of x. That is, if you replace x by any number, you will get another number.
So, this means that the the original function is defined for every value of x. So the domain of this function is the set of all real numbers.
If we define the equation
[tex]y=\frac{1}{6}\cdot8^x[/tex]the range is the set of all possible values that y can take. Taking a look at the functions we already identified (1/6, and 8^x) we can see that 1/6 is always a positive number, and we can also see that for every value of x, the number
8^x is always positive.
That means that the product
[tex]\frac{1}{6}\cdot8^x[/tex]is always a positive number. So, this means that the range of the function is all positive real numbers. That is the set of y such that y>0