The standard deviation of the distribution = 1.5°F
Given that the distribution of daily high temperature is approximately normal.
Population mean, [tex]\mu[/tex] = 86°F
Also approximately 95% of all daily high temperatures are between 83°F and 89°F.
So here [tex]X_1[/tex] = 83°F and [tex]X_2[/tex] = 89°F
We have the z - statistic ,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where [tex]\sigma[/tex] is the Standard deviation.
For 95% probability, the z-value for normal distribution is 1.96.
As we consider the positive z-value, take X = [tex]X_2[/tex] = 89°F
So, [tex]z=\frac{x-\mu}{\sigma}[/tex]
⇒ [tex]\sigma = \frac{x-\mu}{z} = \frac{89-86}{1.96} =1.53[/tex] ≈ 1.5°F
So the standard deviation of the distribution = 1.5°F
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Solve the system of equations using elimination: -6x-6y=-42−6x−6y=−42 and -x+2y=8−x+2y=8.
The solution of the equations −6x − 6y = −42 and −x + 2y = 8 will be (2, 5).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The equations are given below.
−6x − 6y = −42 ...1
−x + 2y = 8 ...2
From equation 2, we have
x = 2y − 8
Put the value of x in equation 1, then we have
−6(2y − 8) − 6y = −42
−12y + 48 − 6y = − 42
18y = 90
y = 5
Then the value of x will be
x = 2(5) − 8
x = 10 − 8
x = 2
The solution of the equations −6x − 6y = −42 and −x + 2y = 8 will be (2, 5).
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Please Answer the question in photo [ Brainliest + points ]
Answer:
72
Step-by-step explanation:
Step-by-step explanation:
QC = Qu + UC
Qu= 22
Uc= 70
QC= 22 + 70
QC = 92
The volume of a cuboid having health is double of the height and length is triple of the height is 1296 cm ³ find the area of base.
The area of the base is 216 cm².
The volume of a cuboid is 1296 cm³.
The breadth of the cuboid is double the height of the cuboid and the length of the cuboid is triple the height of the cuboid.
Let the length, breadth, and height of the cuboid be l, b, and h respectively.
Then,
l = 3(h)
b = 2(h)
The volume of a cuboid is given as:
V = l × b × h
1296 = 3(h) × 2(h) × h
1296 = 6 × h³
h³ = 1296 / 6
h³ = 216
h = ∛216
h = ∛(6)³
h = 6 cm
Therefore, the length of the b is l = 3(h) = 3 × 6 = 18 cm
The breadth of the cuboid will be:
b = 2(h)
b = 2 × 6
b = 18 cm
Now the volume of the cuboid is also given as:
Volume = base area of cuboid × height
1296 = base area × 6
base area = 216 cm²
The base area is 216 cm².
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an envelope contains eight bills: two $ 1 bills, two $ 5 bills, two $ 10 bills, and two $ 20 bills. two bills are drawn at random without replacement. what is the probability that their sum is $ 20 or more? (a) 1 4 (b) 2 5 (c) 3 7 (d) 1 2 (e) 2 3
Probability is nothing but the ratio of favorable cases to all possible cases or in simple terms it is the ratio of sample set to all set
We are required to find all the cases in which sum of any two bills is 20$ or more
The total number of bills are two $ 1 bills, two $ 5 bills, two $ 10 bills, and two $ 20 bills.
The total case of drawing any two bills will be =
2 for $ 1 bill x two for 5$ bill x two for 10$ bill x two 20$ bills
=2 x 2x2x2 =16
Hence 16 ways in which two bills can be drawn at random
Cases in which bill can be greater than 20$= (1,20)(20,1)(5,20)(20,5)(10,10)(20,10)(10,20) (20,20)= 8 cases
Hence, total number of possible outcomes = 8
Hence the probability of bill to be 20$ or more= favorable outcome/total outcome
=8/16 =1/2
Hence the probability is 1/2
Disclaimer: the fraction sign is missing in question options
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Find 3/4ab divided by 6/abc. Write the quotient in simplest form.
Answer:
[tex] \sf \large \frac {1}{8}b²c[/tex]
Step-by-step explanation:
3/4ab/6/abc
= 1/8ab²c/a
= 1/8b²c
(a) A pyramid is made above a cuboid with measure 90 cm x 50 cm × 225 cm. If the height of the pyramid including cuboid is 240 cm, find the total volume.
The total volume of the solid = 1,035,000 cm³
What is the Volume of a Pyramid and a Cuboid?Volume of a Pyramid = 1/3(length)(width)(height).
Volume of a cuboid = (length)(width)(height).
Volume of the Pyramid = 1/3(length)(width)(height)
Volume of the Pyramid = 1/3(90)(50)(240 - 225)
Volume of the Pyramid = 1/3(90)(50)(15)
Volume of the Pyramid = 22,500 cm³
Volume of the cuboid = (length)(width)(height)
Volume of the cuboid = (90)(50)(225)
Volume of the cuboid = 1,012,500 cm³
The total volume of the solid = 22,500 + 1,012,500
The total volume of the solid = 1,035,000 cm³
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rick's chore list shows that he is responsible for washing the dishes after dinner this week. last night, he washed 4 plates in 2 minutes. tonight, his grandparents are coming to dinner, and rick will wash 6 plates. if he washes plates at the same rate, how many minutes will it take rick to wash the plates tonight?
Rick will have to wash the plates for three minutes.
By first figuring out the value of a single unit and then multiplying the number by that value, the unitary approach in mathematics can be used to determine the required value.
• The unitary technique can be used to determine how many kilometres can be covered with 2 litres of gasoline, for instance, if a car goes 80 km on 6 l of fuel.
He washed 4 dishes in 2 minutes, thus we need to calculate how long it would take Rick to wash 6 plates. 4 plates, according to the rule, equals 2 minutes. Applying the unitary approach 1 plate in 2/4 of a minute 1 plate Equals 12 minute. 3 minutes equals 6 plates (12 times 6.6 plates).
Therefore, Six dishes will need to be washed in 3 minutes.
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Ava can clean 6 apartments in 4 hours. At this rate, how long will it take Ava to clean 9
apartments?
Answer: 6 hours
Step-by-step explanation: 6 apartments divided by 2 is 3 apartments and 4 hours divided by 2 is 2 hours. 3 apartments per 2 hours. So, 3/2 x 3/3 is 9/6 which is 9 apartments for 6 hours.
(Dividing Rational Numbers MC)
(Dividing Rational Numbers MC)
Solve 0.504 ÷ 8.
−7.496
0.063
0.630
4.032
Solve 0.504 ÷ 8.
−7.496
0.063
0.630
4.032
The correct answer for 0.504 ÷ 8 is option B which is 0.063
How to solve 0.504 ÷ 80.504 / 8 is solved by removing the decimals first and then the division as required.
0.504 / 8
= 504/1000 / 8
= 504 / 8000
= ( 504 / 8 ) * ( 1 / 1000 )
= 63 * ( 1 / 1000 )
= 0.063
What are rational numbers?These are class of numbers that can be represented as fractions inform of two integers. Such numbers while in fractions, the denominator should not be zero and while decimal do not need to approximations to terminate them.
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Determine whether each relationship is linear or exponential. Then write an equation to represent the relationship.
5. The relationship is Linear and the equation is 500 × 1.1 + 500 = 1050.
6. The relation ship is Linear and the equation is 6 × 2/3 = 4
Given,
5. The population of a town = 500
The growth of population expected by the city planner = 1.1
That is, 500 × 1.1 + 500 = 1050
This is a Linear equation.
6. The distance from where the basketball fall down = 6 feet
Basket ball bounce back its previous height = 2/3
That is, 6 × 2/3 = 4
This is a Linear equation.
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15 women can complete a piece of work in 16 days. How many women
should leave so that the work would be finished in 20 days?
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
a. In Euclidean geometry, a line continues in opposite directions forever. As a result, the line will have an infinite length. How does this differ from a line in spherical geometry?
Euclidean geometry differs from spherical geometry because Euclidean geometry is used to set points by the use of plane.
What is Euclidean geometry?Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different axioms and theorems.
Now since Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sphere" are used for the surface together with its 3-dimensional interior.
Euclidean geometry differs from spherical geometry because Euclidean Geometry are known to make use of a plane to be able to set points and lines, but Spherical Geometry are known to make use of spheres to set up points and great circles.
Thus, Euclidean geometry differs from spherical geometry because Euclidean geometry is used to set points by the use of plane.
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Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
(Please help)
2 { 5 5/8 } + 3 { 9 13/16 } ?
Help Please
The equivalent expression for the expression consisting of mixed fraction 2 { 5 5/8 } + 3 { 9 13/16 } is 651/16.
According to the given question.
We have an expression consisting of mixed fractions.
2 { 5 5/8 } + 3 { 9 13/16 }
Since, we convert the mixed fraction into improper fraction by
Step 1: Multiply the denominator with the whole number.
Step 2: Add the numerator to the product obtained from step 1.
Step 3: Write the mixed fraction with the sum obtained from step 2 as the numerator and the denominator of the original fractional part of the mixed fraction.
Therefore, the equivalent expression for the expression 2 { 5 5/8 } + 3 { 9 13/16 } is given by
2{45/8} +3{157/16}
= 90/8 + 471/16
= [180 + 471]/16
= 651/16
Hence, the equivalent expression for the expression consisting of mixed fraction 2 { 5 5/8 } + 3 { 9 13/16 } is 651/16.
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Decimal equivalent to 2/5
Answer:
0.4
Step-b0.y-step explanation:
For the data set {11, 13, 15, 15, 16, 17, 18, 19, 19, 20}, which is greater, the mean or the median?
Answer:
Median
Step-by-step explanation:
Median: (16+17)/2= 16.5
Mean: 11+13+15+15+16+17+18+19+19+20= 163
163/10= 16.3
Median is greater.
can someone help me please
Answer:
1. A, 450 = 2(p+w); 450 = 3(p-w)
2. A, 2 units
3. D, Between step 6 and step 7
Step-by-step explanation:
1. This one is confusing on first glance.
[tex]450 = 2(p+w); 450 = 3(p-w)[/tex] Lets break down this equation.
[tex]2(p+w)[/tex] means, the plane speed, plus the windspeed, will take 2 hours to travel 450 KM. The reason we add the plane speed and the windspeed is because we have a tailwind instead of a headwind, the wind is pushing us forward, adding to the planes speed.
[tex]3(p-w)[/tex] means, the plane speed, minus the windspeed, will take 3 hours to travel 450 KM. We subtract the wind speed from the plan speed because the wind is a headwind, it's pushing us backwards, taking away from the planes speed.
----------------------------------------------------------------------------------------------------------
2. Let set these up as two-sided equations.
[tex](6x+3) + (4x) + (2x + 1) = (5x) + (5x) + (3x+2)[/tex]
Combine like terms
[tex]12x + 4 = 13x + 2[/tex]
Subtract 12x from both sides
[tex]4 = 1x + 2[/tex]
Subtract 2 from both sides
2 = 1x, or x = 2.
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3. Take a look at step 6. You want to get x by itself, to do that, and get rid of the 8, you'd divide both sides by 8 to get [tex]x = -\frac{15}{4}[/tex]
what is 22.652 rounded to the nearest tenth?
Answer:
22.7
This is becuase 6 is closer too 7. Thus we would round too 7.
does anyone know this? this is 8th grade math. (eureka math squared)
Solutions of given exponents are :
1. [tex]9^{18}[/tex] 2. [tex]16x^4[/tex] 3. [tex]\frac{6561}{y^2}[/tex]
What are exponents ?In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as [tex]a^x[/tex]
where, a = the base of function
x = exponential
Important properties of exponential :
[tex](a^n)^m = a^{nm}[/tex][tex](ab)^n = a^n.b^n[/tex][tex](\frac{a}{b})^n = \frac{a^n}{b^n}[/tex][tex]a^0=1[/tex][tex]a^1=a[/tex]According to the question,
1. given, [tex](9^{3})^6[/tex]
use the property, [tex](a^n)^m = a^{nm}[/tex]
[tex](9^{3})^6[/tex] = [tex]9^{3.6} = 9^{18}[/tex]
2. Given, [tex](2x)^4[/tex]
use the property, [tex](ab)^n = a^n.b^n[/tex]
[tex](2x)^4[/tex] = [tex]2^4.x^4 = 16x^4[/tex]
3. Given , [tex](\frac{3^4}{y}) ^{2}[/tex]
use the property, [tex](\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]
[tex](\frac{3^4}{y}) ^{2}[/tex] = [tex]\frac{(3^4)^2}{y^2}[/tex]
now use , [tex](a^n)^m = a^{nm}[/tex]
= [tex]\frac{3^8}{y^2} = \frac{6561}{y^2}[/tex]
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Simplify the following
Need the answer asap
answer:
1.
[tex]9y - 1[/tex]
2.
[tex] { \times }^{3} - { \times }^{2} + \times [/tex]
3.
[tex] - 3 {a}^{2} + a + 2[/tex]
4.
[tex] - { \times }^{2} [/tex]
5.
[tex] - 4 { \times }^{5} + 16 { \times }^{3} - 20 { \times }^{2} [/tex]
6.
[tex]8 { \times }^{3} + 6 { \times }^{2} - 32x + 15[/tex]
7.
[tex] { \times }^{2} - \times - 20[/tex]
8.
[tex]24 { \times }^{2} - 6 \times + 1[/tex]
9.
[tex] { \times }^{2} - 6 \times + 5[/tex]
10.
[tex]10 { \times }^{5} + 3 { \times }^{3} - 2 \times [/tex]
In a certain chemical, the ratio of zinc to copper is 4 to 19 . A jar of the chemical contains 551 grams of copper. How many grams of zinc does it contain?
Answer:
116 g
Step-by-step explanation:
Zn:Cu = 4:19
so 551 x (4/19) = 116
A group of friends wants to go to the amusement park. They have $235.75 to spend on parking and admission. Parking is $6.25, and tickets cost $25.50 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
The equation for the number of people is 25.50x + 6.25 = 235.75 and the number of people who can go to the amusement park are 9.
Step-by-step explanation:
We have,
Spend on parking and admission = $235.75
Spend on parking = $6.25
Cost of ticket per person = $25.50
Let number of number of people = x
Now,
According to the question;
25.50x + 6.25 = 235.75
So, this the equation for number of number of people.
Now,
25.50x + 6.25 = 235.75
25.50x = 229.50
x = 9
So, number of number of people is 9, which we find out using the above mentioned equation.
Hence, we can say that the equation for the number of people is 25.50x + 6.25 = 235.75 and the number of people who can go to the amusement park are 9.
The number of people who can go to the amusement park is 9 they have $235.75 to spend on parking and admission. Parking is $6.25.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A group of friends wants to go to the amusement park. They have $235.75 to spend on parking and admission.
Parking is $6.25, and tickets cost $25.50 per person, including tax.
Let x be the number of people
6.25 + 25.50x = 235.75
25.50x = 235.75 - 6.25
25.50x = 229.5
x = 9
Thus, the number of people who can go to the amusement park is 9 they have $235.75 to spend on parking and admission. Parking is $6.25.
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Please help me as soon as possible major grade due today
Answer:
51/8
Step-by-step explanation:
each bracelet length as a fraction will be 51/8 inches if the artist uses the 51 inches of the string to make 8 bracelets
A line has a slope of 1 and passes through the point (-5, 4). What is its equation in
slope-intercept form?
Answer:
y = x + 9
Step-by-step explanation:
y = mx + b Use the x and y from the point (-5,4) and the slope to find b. They you can write the equation. An ordered pair is in the form of (x,y)
y = mx + b
4 = (1)(-5) + b
4 = -5 + b Add 5 to both sides of the equation
9 = b
Now write the equation
y = x + 9
PLEASE HELP ASAP
R is the midpoint of HS. N is the midpoint of RS and RN=5cm. What is the length of HS
Answer: 20 cm
Step-by-step explanation: if the length of R-N= 5cm therefore you multiply 5 by each dot so H-O is 5 cm, H-R is 10 cm, H-N is 15 cm, and H-S is 20 cm.
City A and City B are 312
miles apart. John leaves City B, driving towards City A at an average rate of 80
miles per hour. Pat leaves City A at the same time, driving towards City B in her antique auto, averaging 24
miles per hour. How long will it take them to meet?
Pat and John will meet in 3 hours.
How to calculate the value?It should be noted that speed = Distance / Time
The appropriate equation will be:
80t + 24t = 312
104t = 312
t = 312/104
t = 3. hours
Therefore, it will take them 3 hours to meet.
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If m ∠ E F G = 35 ° and m ∠ G F H = 63 ° , what is m ∠ E F H ?
Answer:
28°
Step-by-step explanation:
63 -35 = 28
please help with this question, thank you!!
Answer:
2.1 cm (nearest tenth)
Step-by-step explanation:
The radius (r) of a circle is the distance between its center and its circumference. Therefore, from inspection of the given circle:
⇒ r = OX = OY = OA
Given:
AB = 3.5 cmOA = r⇒ AB = OA + OB
⇒ 3.5 = r + OB
⇒ OB = 3.5 - r
As OX = OY and AB is perpendicular to XY then XB = BY.
As XY = 3 cm:
⇒ XB = BY = 1.5 cm
Therefore, for ΔOBX:
Leg a = OB = (3.5 - r) cmLeg b = XB = 1.5 cmHypotenuse = OX = r cmPythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Use Pythagoras Theorem and the defined sides of ΔOBX to find r:
[tex]\implies OB^2+XB^2=OX^2[/tex]
[tex]\implies (3.5-r)^2+1.5^2=r^2[/tex]
[tex]\implies 12.25-7r+r^2+2.25=r^2[/tex]
[tex]\implies 14.5-7r+r^2=r^2[/tex]
[tex]\implies 14.5-7r+r^2-r^2=r^2-r^2[/tex]
[tex]\implies 14.5-7r=0[/tex]
[tex]\implies 14.5=7r[/tex]
[tex]\implies 7r=14.5[/tex]
[tex]\implies \dfrac{7r}{7}=\dfrac{14.5}{7}[/tex]
[tex]\implies r=2.07142857...\: \sf cm[/tex]
Therefore, the radius of the circle is 2.1 cm (nearest tenth).
henery works at a pet shelter after school. he purchases a large package of dog treats. he sets aside 10 treats and distributes the rest equally among the 15 dogs in the shelter. if each dog received 4 treats, write and solve an equation to find the number of treats t that were in the original package
An equation to find the number of treats t that was in the original package is t=10+4(15).
First, you set aside the 10 and that is the start of your equation.
We need to find an equation to find the number of treats t that was in the original package.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, t=10+4(15)
⇒t=10+60
⇒t=70
Therefore, an equation to find the number of treats t that was in the original package is t=10+4(15).
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