First, you can know how many minutes are 8 hours using the rule of three like this
[tex]\begin{gathered} 1\text{ hour}\rightarrow60\text{ minutes} \\ 8\text{ hours }\rightarrow\text{ x minutes} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{8\text{ hours }\ast\text{ 60 minutes}}{1\text{ hour}} \\ x=480\text{ minutes} \end{gathered}[/tex]Now, using the rule of three again, you can find out how many gifts Dracula would wrap in 8 hours if she wrapped 3 gifts every 20 minutes
[tex]\begin{gathered} 20\text{ minutes}\rightarrow3\text{ presents} \\ 480\text{ minutes}\rightarrow x\text{presents} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{480\text{ minutes}\ast3\text{ presents}}{20\text{ minutes}} \\ x=\frac{1440}{20}\text{ presents} \\ x=72\text{ presents} \end{gathered}[/tex]Therefore, Dracula would wrap 72 gifts in 8 hours if he wrapped 3 gifts in 20 minutes
A normally distributed set of 250 values has amean of 88 and a standard deviation of 15.What percent of the values are expected tobe below 78?
We have a sample of size n=250. They are normally distributed with mean 88 and standard deviation of 15.
We have to find how many values from the sample are expected to be below 78.
We can calculate the z-score for 78 as:
[tex]z=\frac{X-\mu}{\sigma}=\frac{78-88}{15}=-\frac{10}{15}=-\frac{2}{3}\approx-0.67[/tex]Then, we can calculate the percentage of values below 78 as the probability P(z<-0.67):
[tex]P(X<78)=P(z<-0.67)=0.25249\approx25\%[/tex]This percentage is independent of the sample size: it is the same percentage for 100 numbers, 250 numbers or 1000 numbers.
For 250, 63 numbers are expected to be below 78, as 0.25*250=63 approximately.
Answer: 25%
assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute.if 1 adult female is randomly selected find the probability that her pulse rate is less than 81 beats per minute.
SOLUTION:
[tex]Z\text{ score = }\frac{\text{ Raw score - Mean Score}}{\text{Standard Deviation}}[/tex][tex]\begin{gathered} Z\text{ score = }\frac{81\text{ - 74}}{12.5} \\ \\ Z\text{ score = }\frac{7}{12.5} \\ \\ Z\text{ score = 0.56} \end{gathered}[/tex]From the Z-score probability table;
P < 81 = 0.7123
CONCLUSION:
If one adult female is randomly selected, the probability that her pulse rate is less than 81 beats per minute is 0.7123
One less than five times a number is 39. Find the number.
Answer: x = 8
5x - 1 = 39
isolate and divide to get x
x = 8
1. The department store’s annual profit from the sale of a certain toy is given by the function 8000 30,000(2) 0.4x y where y is the annual profit in dollars and x denotes the number of years the toy has been on the market. Calculate the store’s annual profit for (a) x = 3 (b) x = 5 (c) x = 15 2. It is estimated that the population P of a certain country is given by the function P(t) 4,000,000(1.02) r where t is the number of years after 1989. If this trend continues, what will the population be 20 years after 1989? 3. The projected population of a city is given by 20 125,000(1.11) t P , where t is the number of years after 1995. What is the projected population in 2015? 4. Suppose $900 is placed in a saving account that earns interest at the rate 4.5% compounded semiannually. (a) What is the value of the account at the end of five years? (b) If the account has earned interest at the rate of 4.5% compounded semiannually, what would be the value after five years?
Part A:
Given 900 dollars
Interest rate = 4.5%
Value at the end of 5 years
900 × 4.5% × 5 = $226.62
900 + 226.62 = 1,126.62
= 1,126.62 after 5 years
Part B: Given 900 dollars is placed in a saving account
interest rate = 4.5% semiannually (which means twice a year)
We need to find the value after 5 years
Since it's semiannually it's twice a year
5 × 2 = 10
900 × 4.5% (interest rate) × 10
900 × 4.5% × 10 = 510.29
510.29 + 900(intital amount) = 1,410.29
= $1,410.29 after 5 years
15,60, 240, fine the 6th term
Notice that the sequence has a common ratio of 4:
[tex]\begin{gathered} 15\times4=60 \\ 60\times4=240 \end{gathered}[/tex]The n-th term of a sequence with first term equal to a and common ratio r is:
[tex]a\cdot r^{n-1}[/tex]The first term of this sequence is 15 and the common ratio is 4, then the nth term is:
[tex]15\cdot4^{n-1}[/tex]Substitute n=6 to find the 6th term:
[tex]15\cdot4^{6-1}=15\cdot4^5=15\cdot1024=15,360[/tex]Therefore, the 6th term of the sequence, is:
[tex]15,360[/tex]Question is in picture
Please help me I’m confused
In triangle, value of QS = 12 ft .
What is a triangle answer?
A triangle is a three-sided polygon in geometry with three edges and three vertices. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles.A triangle is a polygon with three sides. The three vertices that make up its three sides also create its three angles. Any triangle with three vertices is represented below by the symbols A B C: several triangular types: The sides of a scalene triangle are not all the same length.ΔPQR and ΔQSR ,
QS/SR = PO/OS
y/9 = 16/12
12 * y = 16 * 9
y = 16 * 9 /12
y = 12
value of QS = 12ft
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total amount = P (1 + i)t
Ryan has an eight–year loan for $6,000. He is being charged an interest rate of 5 percent, compounded annually. Calculate the total amount that he will pay.
According to the compound interest concept, the total amount he will be paid is $8,864.73
Compound interest:
The general form of the compound interest is,
A = P(1 + r/n)ⁿˣ
where
A = Accrued amount (principal + interest)
P = Principal amount
r = Annual nominal interest rate as a decimal
R = Annual nominal interest rate as a percent
r = R/100
n = number of compounding periods per unit of time
x = time in decimal years;
Given,
Ryan has an eight–year loan for $6,000. He is being charged an interest rate of 5 percent, compounded annually.
Here we need to find the total amount he will pay.
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)ⁿˣ
A = 6,000.00(1 + 0.05/1)⁽¹⁾⁽⁸⁾
A = 6,000.00(1 + 0.05)⁸
A = $8,864.73
Therefore, the total amount that he will pay is $ 8,864.73
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Explain how the following ordered pairs represent or doesn't represent a function - {(-3, 5), (-2, 5), (-1, 5), (0, 5), (1, 5). (2, 5)8 function a function a. For every x value there is one y value - not a c. For every y value, there is one x value - function b. For every x value, there is only one y value - d. . For every y value, there is one x value - not a function
The way in which the given ordered pairs represent a function is: b. For every x value, there is only one y value - a function.
What is a function?A function simply refers to a mathematical expression (equation) which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable (x-value) to an output variable (y-value).
In this context, we can reasonably infer and logically deduce that these ordered pairs represent a function because it has different input variables (x-values) for different or the same output variables (y-values).
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Help me wolf this System of equations by the addition/elimination method
Given the system of equations
[tex]\begin{cases}x+y=-3 \\ 3x+4y=-7\end{cases}[/tex]Solve by elimination method as shown below.
Multiply the first equation by 3 and subtract it from the second equation,
[tex]\begin{gathered} 3(x+y)=3(-3) \\ \Rightarrow3x+3y=-9 \end{gathered}[/tex]Then,
[tex]\begin{gathered} \Rightarrow(3x+4y)-(3x+3y)=-7-(-9) \\ \Rightarrow y=-7+9=2 \\ \Rightarrow y=2 \end{gathered}[/tex]Use the value of y in the first equation,
[tex]\begin{gathered} y=2 \\ \Rightarrow x+2=-3 \\ \Rightarrow x=-5 \end{gathered}[/tex]Therefore, the answers are x=-5 and y=2, (x,y)=(-5,2)
Runners at a cross-country meet run 2 miles south and then 4 miles west from the starting line. Determine the shortest straight path they must run to get back to the starting line. Brainliest and 20 points
Answer:
√20 miles
Step-by-step explanation:
a² + b² = c²
|
? | 2 miles ↓
|
------------------------------
← 4 miles
2² + 4² = c²
4 + 16 = c²
20 = c²
√20 = c
I hope this helps!
The length of the straight path they must run to get back to the starting line is 4.47 miles.
What is displacement?Displacement [x] of an object is the length of the straight line joining the initial and final position of the object. Mathematically, displacement can be written as-
Δx = x[2] - x[1]
Now -
Δx = vΔt {[v] is velocity}
So we can write -
vΔt = x[2] - x[1]
Given are the runners at a cross-country meet such that they ran 2 miles to south and then 4 miles to west from the starting line.
We can find the straight path they must run to get back to the starting line using the Pythagoras theorem. The base will be equal to distance ran towards south and height will be equal to the distance ran towards west. The length of the hypotenuse will be equal to that of displacement or the straight path they must run to get back to the starting line. Using Pythagoras theorem -
[h]² = [b]² + [p]²
[h]² = (2 x 2) + (4 x 4)
[h]² = 4 + 16
[h]² = 20
[h] = 4.47 miles
Therefore, the length of the straight path they must run to get back to the starting line is 4.47 miles.
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The value of gold is always changing. Last year, Max had a 0.2-ounce piece of gold appraised at $148.96. This year he had a 0.24-ouncepiece of gold appraised at $222.84. How much had the price of gold per ounce changed between Max's appraisals?O A. $73.88
The value of gold is always changing. Last year, Max had a 0.2-ounce piece of gold appraised at $148.96. This year he had a 0.24-ounce
piece of gold appraised at $222.84. How much had the price of gold per ounce changed between Max's appraisals?
O A. $73.88
last year
w=0.2 ounces
price= $148.96
this year
w=0.24 ounces
price=$222.84
Let's find the price per ounce for the last year
[tex]\begin{gathered} w=0.2\text{ ounces} \\ \text{price}=148.96 \\ \text{price per ounce=}\frac{148.96}{0.2}=744.8\text{ per ounce} \\ \end{gathered}[/tex]Now for this year
[tex]\begin{gathered} w=0.24\text{ ounces} \\ \text{price}=222.84 \\ \text{the price per ounce is=}\frac{222.84}{0.24}=928.5\text{ per ounce} \end{gathered}[/tex]Now, the change
[tex]\begin{gathered} \text{change =final pric- initial price} \\ \text{change}=928.5\text{ \$/ounce -744.8 per ounce} \\ \text{change}=183.7\text{ \$/ounce} \end{gathered}[/tex]so the answer is $183.7
Ethan surveyed the first 22 celebrities to arrive at the movie premiere.Is this sample of celebrities likely to be representative
No, the sample of celebrities is not likely to be representative
Here, we should understand if the sample collected is likely to be representative or not
We need to understand what is meant by a representative sample or representative sampling
When a sampling is representative, it means that the sample that we have obtained looks like the population in which we are taking the sample from
Now, from what we have selected as a sample, we only considered the early comers while we have left out the late comers
What this mean in this case is that whatever sample we have is in fact not representative of the total
So we conclude that the sample of celebrities is not likely to be representative
how do you do this help
Step-by-step explanation:
you can use proportions to convert molecules to moles and then moles to grams.
To convert molecules to moles, use the Avogadro number (6,022 × 10²³ atoms)
The proportion is:
1 : Avogadro number = x : number of molecules
so
1 : 6,022 × 10²³ = x : 4,5 × 10²⁴
solve. x = 7,47 moles
From the moles you can get the grams of SO2. To find grams, first find the mass of SO2.
S = 32,06
O2 = (16×2) = 32
so mass of SO2 is 64,06
Now use the proportion:
mass of SO2 : 1 = moles : x
so
64,06 : 1 = 7,47 : x
solve. x = 0,11 grams
find the product 6000×50
The product of 6000 and 50 can be found below
Do (-6) raised to -4 power equal -6 to the -4 power
Yes. (-6) raised to -4 power equal -6 to the -4 power
What is exponentiation ?
Exponentiation is a mathematical operation, written as [tex]b^{n}[/tex], involving two numbers, the base b and the power n it is read as b raised to n.
We have asked that whether [tex](-6)^{-4}[/tex] is equal to [tex]-6^{-4}[/tex]
Now we solve both the sides to show that they are equal
[tex](-6)^{-4}=(\frac{-1}{6} )^{4}[/tex]
Now for the right hand side
[tex]-6^{-4} =\frac{-1}{6} ^{-4}[/tex]
Both the values are same
Hence, Yes. (-6) raised to -4 power equal -6 to the -4 power
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There are 300 eighth graders at Wilson Middle School. In the class president election, 192 students voted for Luke, 60 students voted for Alice, and 48 students voted for Chris. What percent of eighth graders voted for Luke?
The percent of eighth graders who voted for Luke is 64 %.
Given that:-
Number of eighth graders who voted for Luke = 192
Number of eighth graders who voted for Alice = 60
Number of eighth graders who voted for Chris = 48
Total number of eighth graders at Wilson Middle School = 300
We have to find the percent of eighth graders who voted for Luke.
We know that:-
Percent of eighth graders who voted for Luke =
(Number of eighth graders who voted for Luke/Total number of eighth graders)*100
Hence, we can write,
Percent of eighth graders who voted for Luke = (192/300)*100 = 64 %
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10x + 2y = - 12 Find the slope and y-intercept of the line with the equation Om = 6, b= 5 Om=-6, b = -5 O m=-5, b=-6 Om= 5, B = 6
Answer: m = -5 and b = -6
Given that 10x + 2y = -12
The slope - intercept form of equation is written as
y = mx + b
where m = slope and b = intercept
This equation can be re-arrange as
2y = -12 - 10x
2y = -10x - 12
Divide all through by 2
2y/2 = -10x/2 - 12/2
y = -5x - 6
From, y = mx + b
m = -5 and b = -6
The PTA was doing a fundraiser and bought 500 megaphones to sell for a pep rally. The profit (p) from the sale of megaphones can be represented by: p(m) = 3.5m-875. Which of the following represents the range in the context of the situation?i. p(m) >= -875 where p(m) is all real numbersii. {-875,-871.5, -868, -864.5, ...875}iii. 0 <= m <= 500a. IIb. Ic. IIId. I, II
Since the profit equation has been given to us as
[tex]p(m)=3.5m-875[/tex]Where m is the number of megaphones sold.
Since m can only take integer values from zero and above.
When no megaphone was sold, p(m)=p(0)=-875
Therefore, the range is;
[tex]p(m)\ge-875[/tex]However p(m) is not all real numbers.
When 500 megaphones were sold, the profit is;
[tex]3.5(500)-875=875[/tex]This is the correct range.
Therefore, the range is represented as;
[tex]\mleft\lbrace-875,-871.5,\ldots,875\mright\rbrace[/tex]Thus the correct option is a. II
MULTIPLE CHOICE QUESTION 2. Problem set: One jug of powdered plant teod treate an area of 138 aquare feet of flowers. How many Jugs would be needed to treat an area of 168 square yerde? what is your answer? 9 there are square feet there are 2.5 square feet wa 6 there are 12 square feet Belutien there are 3 square feet Newt 13
To answer how many Jugs would be needed to treat an are of 168 square feet, we can use proportional relationships:
[tex]\begin{gathered} \frac{138}{1}=\frac{168}{x} \\ 138x=168 \\ x=\frac{168}{138}=\frac{28}{23}=1.22\text{ jugs} \end{gathered}[/tex]Write a linear function (y=Mx+b) or exponential function that models the data
We are given a data set and we are asked to write the model that fits the data. We notice that for each step of "x" the values of "y" increase by the same amount. That means that the data follow a linear model, therefore, we will use:
[tex]y=mx+b[/tex]Where:
[tex]\begin{gathered} m=\text{ slope} \\ b=\text{ y-intercept} \end{gathered}[/tex]To determine the slope "m" we will use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex](x_1,y_1),(x_2,y_2)[/tex]Are data points. From the table we choose the following points:
[tex]\begin{gathered} (x_1,y_1)=(-8,47) \\ (x_2,y_2)=(-7,40) \end{gathered}[/tex]Now, we substitute in the equation for the slope:
[tex]m=\frac{40-47}{-7-(-8)}[/tex]Solving the operations:
[tex]m=\frac{-7}{-7+8}=-7[/tex]Therefore, the slope is -7. Substituting in the equation of the line we get:
[tex]y=-7x+b[/tex]Now, we substitute one of the points to get the value of "b". We will substitute the value x = -8, y = 47, we get:
[tex]47=-7(-8)+b[/tex]Solving the product:
[tex]47=56+b[/tex]Now we subtract 56 from both sides:
[tex]\begin{gathered} 47-56=56-56+b \\ -9=b \end{gathered}[/tex]Now, we substitute the value of "b" in the equation of the line:
[tex]y=-7x-9[/tex]And thus we get the line equation.
In the function, the slope will be multiplied by 1/2, and the y-value of the y-intercept will be increased by 3 units. Which of the following graphs best represents the new function?
Answer
Option Y is correct.
Explanation
We are told that the slope is multiplied by (1/2) and the y-intercept is increased by 3 units.
The original graph has a y-intercept (point where the graph crosses the y-axis) at point y = 1. Adding 3 units to that, changes the y-intercept to y = 4.
And that leaves options X and Y as viable answers.
But the original graph is positive sloping, and multiplying the slope by (1/2) only spreads the graph out more along the y-axis, it doesn't change the direction of the graph like option X has been changed to be negative sloping. This would only happen if the slope was multiplied by a negative number.
So, this leaves us with only Option Y as the viable answer.
And to be absolutely sure, we can go further and calculate the slope of the original graph and the graph in option Y.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For the original question,
(x₁, y₁) and (x₂, y₂) are (0, 1) and (-1, -1)
[tex]\text{Slope = }\frac{-1-1}{-1-0}=\frac{-2}{-1}=2[/tex]For the option Y,
(x₁, y₁) and (x₂, y₂) are (0, 4) and (-1, 3)
[tex]\text{Slope = }\frac{3-4}{-1-0}=\frac{-1}{-1}=1[/tex]1 is indeed half of 2. This confrims our answer.
Hope this Helps!!!
Mrs. Valdez can type 438 words in 6 minutes. How many minutes does it take to type 512 words
Answer:
7 [tex]\frac{1}{73}[/tex]
Step-by-step explanation:
Set up a proportion
[tex]\frac{words}{minutes}[/tex] = [tex]\frac{words}{minutes}[/tex]
[tex]\frac{438}{6}[/tex] = [tex]\frac{512}{m}[/tex] Cross multiply
438m = 6(512)
438 m = 3072 Divide both sides by 438
m = 7 [tex]\frac{1}{73}[/tex]
15.) In the accompanying diagram, ABC is a straight line and
BE bisects 4DBC. If m4ABD = 2x and m4DBE = 2x + 15,
find m4ABD.
Jake and Mia sold muffins at the bake sale. Jake collected $38 for selling a number of chocolate and blueberry muffins, while Mia collected $20 for selling
the same type of muffins. The following system of equations represents the scenario where is the price of a chocolate muffin and y is the price of a
blueberry muffin. What does the coefficient 3 represent?
(No Calculator)
8x+3y=38
2x+6y=20
Answer:
The number of blueberry muffins Jake sold.
Step-by-step explanation:
Since Jake sold $38 of muffins, we know that 3 pertains to Jake.
Y is the price of a blueberry muffin, so 3 must be how many blueberry muffins were sold.
I need help on this question I need the answer only :)
Step 1
Given;
Step 2
[tex]\sqrt[3]{48y^4}=2y\sqrt[3]{6y}[/tex][tex]\begin{gathered} 14(2y\sqrt[3]{6y})=28y(\sqrt[3]{6y}) \\ 17y(\sqrt[3]{6y}) \end{gathered}[/tex]Thus;
[tex]17y(\sqrt[3]{6y})-28y(\sqrt[3]{6y})=-11y(\sqrt[3]{6y)}[/tex]Answer;
Select the values that make the inequality t < -3 true.
(Numbers written in order from least to greatest going across.)
The order from least to greatest to satisfy the inequality t < -3 is (-∞, -2).
What is called the inequality?Inequality is just a mathematical statement which uses the inequality symbol to show the relationship between two expressions. Both sides of the an inequality sign have different expressions. It implies that expression on the left should be greater or smaller than expression on the right, or vice versa.For the given question,
The inequality is given as;
t < -3
For the inequality to be true the value of 't' must be less than -3.
Thus, the values will range between.
(-∞, -2)
Where, -∞ represents the least value and -2 shows the greatest value for 't'.
Thus, the order from least to greatest to satisfy the inequality t < -3 is (-∞, -2).
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Find the slope of the line passing through the given points, when possible. (If an answer is undefined, enter UNDEFINED.)
(−12, 5) and (−20, 6)
Answer:
y= -1/8x+3.5
Step-by-step explanation:
Plot your points and draw a line thru them. Find the slope: -1/8. Find the y-int: 3.5.
y = mx+b where x and y are variables, m is the slope and b is the y-int
y=-1/8x+3.5
Hope that helps
68,74,66,78,72,80,74
which best describes what 74 represents in this data set?
1)mean and mode
2)mode only
3)median and mode
4)median only
74 is the median and mode of the data set, that is, option 3.
Here, we are given a set of observations- 68, 74, 66, 78, 72, 80, 74
Mean = sum of all observations/ number of observations
Thus, the mean of the data is-
Mean = (68 + 74 + 66 + 78 + 72 + 80 + 74)/ 7
= 512/ 7
= 73.14
Now, to calculate the median of the data, we arrange it in ascending order-
66, 68, 72, 74, 74, 78, 80
Since, the number of observations are odd, the median will be the (n+1)/2th term.
= (7+1)/2
= 4th term
The 4th term is 74. Thus, the median is 74.
Now, the mode is that observation that appears the maximum number of times.
Here, all the numbers appear only once, except 74 which appears twice. Thus, the mode is 74.
Hence, we find that 74 is the median and mode of the data set, that is, option 3.
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help me pleasee!!
thank you
The cost of manufacturing C(x) = 2658 in a day is $2658
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here, it is given from the part A of solution :
the linear function that models the situation is C(x) = 75x + 1908
Now, for cost of manufacturing C(x) = 2658 the value of x will be :
C(x) = 75x + 1908
2658 = 75x + 1908
75x = 2658-1908
75x = 750
x = 10
Therefore, the cost of manufacturing C(x) = 2658 in a day is $2658
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x+y=8you can find more solutions by replacing x with other values and then solving for y for example let x = 6. what is y?
Given
[tex]x+y=8[/tex]Set x=6; then,
[tex]\begin{gathered} x=6 \\ \Rightarrow6+y=8 \\ \Rightarrow y=8-6 \\ \Rightarrow y=2 \end{gathered}[/tex]If x=6, y=2
