Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, the mean of Xochitl's finishing times is 84 seconds and the standard deviation is 2.5 seconds, so the interval that represents the middle 68% of her finishing times is:
[84 - 2.5, 84 + 2.5] = [81.5, 86.5]
So, we can conclude that the middle 68% of Xochitl's finishing times in the 400 meter race fall between 81.5 and 86.5 seconds.
Step-by-step explanation:
tom works for a company
his normal rate of pay is £15 per hour
Answer:
£ 185
Step-by-step explanation:
Tama po yan promise
In parallelogram QRST,m/R=63.7.what is m/S?
The measure of m∠S is 116.3.
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
Parallelogram QRST.
m∠R = 63.7
Now,
We see that,
m∠R and m∠T are opposite angles.
So,
m∠T = 63.7 _____(1)
And,
m∠Q and m∠S are opposite angles.
So,
m∠Q = m∠S ______(2)
Now,
The sum of the four angles is 360.
So,
m∠R + m∠T + m∠Q + m∠S = 360
From (1) and (2),
63.7 + 63.7 + 2m∠S = 360
127.4 + 2m∠S = 360
2m∠S = 360 - 127.4
2m∠S = 232.6
m∠S = 232.6/2
m∠S = 116.3
Thus,
The measure of m∠S is 116.3.
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A new helium tank holds 14.9 ft3 of helium. 0.5 ft3 of helium is needed to fill a foil balloon. This function can be used to find the amount of helium left in the tank (h) after each balloon (b) is filled
The table is
Balloon Helium in the tank
1 14.4
2 13.9
3 13.4
4 12.9
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
Given function is h = 14.9 - 0.5b .....(i)
Where b is the number of ballon.
Putting b = 1 in equation (i)
h(1) = 14.9 - 0.5×1
h(1) = 14.4
Putting b =2 in equation (i)
h(2) = 14.9 - 0.5×2
h(2) = 13.9
Putting b = 3 in equation (i)
h(3) = 14.9 - 0.5×3
h(3) = 13.4
Putting b = 4 in equation (i)
h(4) = 14.9 - 0.5×4
h(4) = 12.9
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7. Mr. and Mrs. Quigley just moved into a new home with a lot of land. They need to plant grass seed The problem is that they are not sure how to figure the new amount that they need. At their old house they knew that the lawn was 10 ft by 20 ft. and needed 5 pounds of seed. Their new lawn is 100 # by 50 ft. How will knowing the amount of seed needed from their old house help them with Buying seed for the new lawn? How much will they need? Show all work
Answer: Seed needed for the new lawn = 125 pounds
Step-by-step explanation:
Knowing the amount of seed needed for their old lawn will help Mr. and Mrs. Quigley calculate the amount of seed needed for their new lawn based on the size of the area.
First, let's calculate the area of the old lawn:
Area = length × width
Area = 10 ft × 20 ft
Area = 200 square feet
Next, we can determine the seed requirement per square foot for the old lawn:
Seed requirement per square foot = total seed needed ÷ area of the lawn
Seed requirement per square foot = 5 pounds ÷ 200 square feet
Seed requirement per square foot = 0.025 pounds per square foot
Now, let's calculate the area of the new lawn:
Area = length × width
Area = 100 ft × 50 ft
Area = 5000 square feet
To find the amount of seed needed for the new lawn, we can multiply the seed requirement per square foot by the area of the new lawn:
Seed needed for the new lawn = Seed requirement per square foot × area of the new lawn
Seed needed for the new lawn = 0.025 pounds per square foot × 5000 square feet
Therefore, Mr. and Mrs. Quigley will need 125 pounds of grass seed for their new lawn based on the calculations using the information from their old lawn.
If a tap drips at 0.15 litres per second,how long will it take to drip 30 litres
Answer:
3 min 20 seconds
Step-by-step explanation:
30÷0.15= 200 seconds
= 3 min 20 seconds
It is solving for, the elimination
The total number of 2 pointers was 4.
The total number of 3 pointers was 11
How to solve Simultaneous Linear Equations?Let the number of 2 pointers be x
Let the number of 3 pointers be y
Since the total points was 41, then we have;
2x + 3y = 41 -------(1)
Total basket was 15. Thus;
x + y = 15 --------(2)
Multiply eq 2 by 2 and eq 1 by 1 to get;
2x + 3y = 41 -------(3)
2x + 2y = 30 --------(4)
Subtract eq 4 from eq 3 to get;
y = 11
Thus;
x = 15 - 11
x = 4
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Find the measure of missing angle
y> -2x - 3
Y <4/3x +3
The solution to the inequality is a coordinate of (-1.8, 0.6)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y> -2x - 3
Y <4/3x +3
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, the shaded area has a coordinate of (-1.8, 0.6)
Hence, the solution is (-1.8, 0.6)
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27. Which situation can be correctly summarized by the equation, y = 5x + 15?
The base area of a rectangular tank is 300 cm square. The capacity of the tank is 6 litres. Peter fills the tank with water up to 4/5 of its height. What is the height of the water leve?
Answer: 1 liters = 1000 cm^36 liters = 6000 cm^3Height
Step-by-step explanation:
1 liters = 1000 cm^36 liters = 6000 cm^3Height
what is the value of 1000m in ft?
1000 meters is equal to 3280.84 feet. To convert from meters to feet, you must multiply the number of meters by 3.28084. This is due to the fact that a meter is slightly longer than a foot.
One meter is equivalent to 3.28084 feet. Therefore, to compute 1,000 meters in feet, you must multiply 1,000 meters by 3.28084. Doing this calculation yields a result of 3,280.84 feet. The meter is the primary unit of measurement for length in the International System of Units, or SI. The SI base unit for length is the meter, which is defined as the length of the path travelled by light in a vacuum in 1/299,792,458 seconds. In other words, the meter is the distance light travels in a vacuum in 1/299,792,458 of a second. The meter is also referred to as the "meter of the air," since it is the length of the path travelled by light in the air in the same time.The foot is a unit of length in the British Imperial and US customary systems of measurement, and is equivalent to 1/3 of a yard. One foot is equal to 0.3048 meters.
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please answer this question
The domain of the relation include the following: A. {1, 2, 3, 6}.
How to determine of this relation?In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain:
Domain = {1, 2, 3, 6}.
In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {1, 2, 3, 6}.
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Give three solutions to the equation
y
=
1
2
x
+
1
. Give your solutions as ordered pairs, using reduced fractions or integers for coordinates.
The three solutions to the equation are (0, 1), (1, 12) and (2, 25)
How to determine the three solutions to the equationFrom the question, we have the following parameters that can be used in our computation:
y = 12x + 1
Next, we set x to 0, 1 and 2
Substitute the known values in the above equation, so, we have the following representation
y = 12 * 0 + 1
y = 1
y = 12 * 1 + 1
y = 13
y = 12 * 2 + 1
y = 25
As an ordered pair, we have
(0, 1), (1, 12) and (2, 25)
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secx - 2 = 0
Please solve the problem and show the work.
Answer:
x = 60 degrees (if x < 90 degrees).
Step-by-step explanation:
secx - 2 = 0
secx = 2
Now sec x = 1/cos x
So,
1/cosx = 2
cos x = 1/2
x = 60 degrees.
You toss two dimes 24 times and record the results. Use the table to find the experimental probability of tossing two tails.
Answer:
I cannot give you the answer because I need the table with the records.
Step-by-step explanation:
MARKING BRAINLIEST! please help asap, show your work then choose the correct answer, thank you
Answer:
lower right option
Step-by-step explanation:
using the properties of logarithms
• loga + logb ⇔ log(ab)
• loga - logb ⇔ log ([tex]\frac{a}{b}[/tex] )
• log[tex]x^{n}[/tex] = nlogx
• lne = 1
given
a[tex]e^{bt}[/tex] = c ( take ln of both sides )
ln a[tex]e^{bt}[/tex] = lnc
lna + ln[tex]e^{bt}[/tex] = lnc
lna + bt lne = lnc ( subtract lna from both sides )
bt = lnc - lna
bt = ln ([tex]\frac{c}{a}[/tex] ) ← divide both sides by b
t = [tex]\frac{ln(\frac{c}{a}) }{b}[/tex]
Julieta has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 204 square meters. Solve for the dimensions (length and width) of the field.
The dimensions of the field are length is 12 m and width is 17m or length is 17m and width is 17m.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that Julieta has 58 m of fencing to build a four-sided fence around a rectangular plot of land.
2(L+W)=58
2L+2W=58
Now area of the land is 204 square meters.
LW=204
L=204/W
Now plug in this L in above equation.
2(204/W)+2W=58
408/W+2W=58
2W²+408-58W=0
2(W²-29W+204)=0
(W-17)(W-12)=0
W=17
Now plug in W as 17 in L
L=204/17=12
Hence, the dimensions of the field are length is 12 m and width is 17m or length is 17m and width is 17m.
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Mmusi borrows an amount of money from Aggie. After two years, Mmusi pays back money, plus 18% simple interest per year. He has to pay back an amount of R4080 much money did he borrow from Aggie?
The required, Mmusi borrowed R3000 from Aggie as per the given conditions.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.
Amount = Principal [1 + rate×time]
Let's call the amount Mmusi borrowed from Aggie "P".
After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P
So if he has to pay back R4080, we can set up an equation to solve for P:
1.36P = 4080
To find P, we can divide both sides by 1.36:
P = 4080 / 1.36 = 3000
So Mmusi borrowed R3000 from Aggie.
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Una mujer de negocios desea invertir $30,000 en fondos diferentes que producen ganancias anuales del
13% y 15% respectivamente.
¿Cuánto debe invertir en cada fondo para obtener ganancias de $4,350 después de un año?
The businesswoman must invest $7,500 in the 13% fund and $22,500 in the 15% fund to earn a return of $4,350 after one year.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
We can use substitution or elimination method to solve when there are more than one equation.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Let's denote,
The amount invested in the 13% fund = x
The amount invested in the 15% fund = y.
Now,
The total amount invested = $30,000,
i.e
x + y = 30000 _____(1)
The total return after one year = $4,350.
Which can be expressed as,
0.13x + 0.15y = 4350 _____(2)
Use the substitution method.
From (1),
x + y = 30000
y = 30000 - x _____(3)
Substituting y in (2)
0.13x + 0.15(30000 - x) = 4350
Solving for x.
0.13x + 4500 - 0.15x = 4350
-0.02x = -150
x = 7500
And,
y = 30000 - x
y = 30000 - 7500
y = 22500
Thus,
The businesswoman must invest $7,500 in the 13% fund and $22,500 in the 15% fund to earn a return of $4,350 after one year.
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The complete question.
A businesswoman wants to invest $30,000 in different funds that produce annual returns of 13% and 15% respectively. How much must she invest in each fund to earn a return of $4,350 after one year?
in the metric system each millimeter increment is equal to
In the Metric System , each millimeter increment is equal to the 1/10 or 0.1 of a centimeter .
The Metric System is defined as a standardized system of measurements which is used in many countries around the world.
In the Metric System, there are different units of length, which include millimeters (mm) and centimeters (cm).
we know that , 1 centimeter is equivalent to 10 millimeters. This means that each millimeter increment is equal to 0.1 of a centimeter.
For Example, if we measure a length of 50 millimeters, we can convert it to centimeters by dividing 50 by 10, which gives you a length of 5 centimeters.
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The given question is incomplete , the complete question is
In the metric system each millimeter increment is equal to ____ of a centimeter .
A triangle has sides with lengths of 32 millimeters, 60 millimeters, and 64 millimeters. Is it a right triangle?
Answer:
Yes it is a right triangle
Step-by-step explanation:
These side lengths correspond to a Pythagorean triple, specifically 8-15-17, which is a set of three positive integers that satisfies the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, also known as the hypotenuse.
In this triangle, 32^2 + 60^2 = 8^2 + 15^2 = 17^2, which confirms that it is indeed a right triangle.
Evan runs a circular loop around his neighborhood after he ran a lap he calculated that he had run 744 feet what is the diameter across this loop
The diameter across this loop was 236.6 feet
What is the perimeter?Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.
Perimeter = Sum of length of the all the sides
However, if we assume that Evan ran around the loop's outer edge and not inside the loop,
we can use the formula for the circumference of a circle,
which is C = πd,
where C is the circumference, d is the diameter, and π is approximately 3.14.
We can rearrange the formula to solve for the diameter,
which is d = C/π.
Plugging in the given value for the circumference, we get:
d = 744/π ≈ 236.6 feet
Therefore, if Evan ran around the outer edge of the loop, the diameter of the circle is approximately 236.6 feet.
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Carmen is a contestant on the kids' game show, Spend or Switch! When she makes it up on
stage, host Guy Granger takes out a stack of one hundred-dollar bills. He divides the bills
evenly among all 5 contestants on stage. Each contestant receives 4 one hundred-dollar bills.
Which equation can you use to find the number of bills b in Guy Granger's stack?
b-5=4
5b= 4
bills
5
= 4
b + 5 = 4
olve this equation for b to find the number of bills in Guy Granger's stack.
The equation we need to use to find the number of bills in Guy Granger's stack is 5b = 4, where b is the number of bills.
What is an Equation ?
An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
This equation represents the fact that each of the 5 contestants received 4 one hundred-dollar bills, so the total number of bills is
= 4 x 5
= 20
To solve for b, we need to divide both sides of the equation by 5:
5b / 5 = 4 / 5
b = 4 / 5
So, the number of bills in Guy Granger's stack is 4 / 5 * 100 = 80.
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please help worth 100 points
Two rival dry cleaners both advertise their prices. Store A's prices are modeled by the expression 25x-9 where x is the number of items brought in. Store B's prices are modeled by the expression 5(5x+8), where x is the number of items brought in. When do the two stores charge the same rate? Write the equation and show the work to justify your response.
Answer: never
Step-by-step explanation:
Store A's prices are represented by the expression 25x-9
Store B's prices are represented by the expression 5(5x+8)
To find when the 2 stores charge the same rate , we set the expression equal and solve for x
25x-9 = 5(5x+8)
25x -9 = 25x + 40
Subtract 25x on both sides
-9 = 40
We cannot solve for x
So , the price of two stores never be same
Two stores never charge the same rate
Find x. Round your answer to the nearest tenth of a degree
Find the 8th term of the geometric sequence 10, -20, 40, ...
Answer:
-1280
Step-by-step explanation:
10×(-2)= -20
-20×(-2)= 40
4th term: 40×(-2)= -80
5th term: -80×(-2)= 160
6th term: 160×(-2)= -320
7th term: -320×(-2)= 640
8th term: 640×(-2)= -1280
what is the value of 5(2 x -4) - 2y if x = -2 and y =6
Answer:
-52
Step-by-step explanation:
If x = -2 and y = 6, then we can substitute those values into the expression:
5(2 x - 4) - 2y = 5(2(-2) - 4) - 2(6)
= 5(-4 - 4) - 2(6)
= 5(-8) - 2(6)
= -40 - 12
= -52
So, the value of the expression 5(2 x - 4) - 2y when x = -2 and y = 6 is -52.
how to count to 20 in spanish?
Counting to 20 in Spanish is a relatively straightforward process. The first step is to learn the numbers from 1 to 10, which are:
1 - uno
2 - dos
3 - tres
4 - cuatro
5 - cinco
6 - seis
7 - siete
8 - ocho
9 - nueve
10 - diez
Once you have these numbers memorized, it's easy to continue counting up to 20. Simply add the numbers from 11 to 19 to the base number, diez.
11 - once (diez + uno)
12 - doce (diez + dos)
13 - trece (diez + tres)
14 - catorce (diez + cuatro)
15 - quince (diez + cinco)
16 - dieciséis (diez + seis)
17 - diecisiete (diez + siete)
18 - dieciocho (diez + ocho)
19 - diecinueve (diez + nueve)
20 - veinte
As you can see, the only exception is the number 15, which has its own unique word, "quince." Other than that, all of the numbers from 11 to 19 follow the same pattern of adding "diez" to the appropriate digit. And once you reach 20, you're done! It's important to note that Spanish has gendered nouns, so when counting objects, you will need to use the appropriate article and adjective to match the gender of the noun. For example, if you are counting "dogs," you would say "uno perro," but if you were counting "cats," you would say "una gata."
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Answer:
1 uno
2 dos
3 tres
4 cuatro
5 cinco
6 seis
7 siete
8 ocho
9 nueve
10 diez
11 once
12 doce
13 trece
14 catorce
15 quince
16 dieciséis
17 diecisiete
18 dieciocho
19 diecinueve
20 veinte
Step-by-step explanation:
The following sample space could represent which reapeted expirement
S[WW,WL,LW,LL]
The given sample space could represent a win and loss game by flipping a coin twice, where win represent the outcome head and loss represent the outcome tail.
What is a Sample Space?A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.
The subset of the sample space are events.
Given sample space is S = {WW, WL, LW, LL}
This can be interpreted as the outcomes in a random experiment, which has only two possibilities, either win or loss.
Suppose that we flip a coin two times.
Possible outcomes are,
HH : head appears twice
HT : head appears at first and tail appears second
TH : tail appears first and then head appears
TT : tail appears twice
Let the outcome head represent the win and tail represent the loss.
Possible outcomes are then WW, WL, LW, LL.
Hence the given sample space can be a possible outcomes of flipping a coin twice.
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for one weekend each year before school begins, people can buy clothing without paying any sales tax. Nora is shopping for new outfits to wear to school. She also has a coupon that will take 5% off of each item she buys.
Part A: Write an equation for the amount of money (c) that Nora would spend, after the discount is applied, on a shirt that cost (d) dollars.
Part B: Nora can spend a total of $57 on clothes at this store. What is the total value of the clothes that Nora can buy at the store, in dollars, before the discount is taken?
Answer:
Part A:
The equation for the amount of money Nora would spend after the discount is applied on a shirt that costs d dollars is:
c = d - 0.05d
c = 0.95d
Part B:
Let x be the total value of the clothes Nora can buy before the discount is taken.
After the discount is applied, she can spend a total of $57, so we have:
0.95x = 57
x = 60
Therefore, Nora can buy a total of $60 worth of clothes before the discount is taken.