The given expression is
[tex]3\frac{1}{6}+5\frac{2}{3}[/tex]First, we transform each mixed number into a fraction
[tex]\begin{gathered} 3\frac{1}{6}=\frac{3\cdot6+1}{6}=\frac{18+1}{6}=\frac{19}{6} \\ 5\frac{2}{3}=\frac{5\cdot3+2}{3}=\frac{15+2}{3}=\frac{17}{3} \end{gathered}[/tex]We use these fractions to make the sum
[tex]\frac{19}{6}+\frac{17}{3}[/tex]Now, we use the following property
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex][tex]\frac{19\cdot3+17\cdot6}{6\cdot3}=\frac{57+102}{16}=\frac{159}{16}[/tex]Hence, the result is 159/16.A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -16x2 + 261x + 130
Answer
The highest height attained by the rocket = 1194.4 feet
Explanation
The height of the rocket, y, in feet as a function of the time, x in seconds as
y = -16x² + 261x + 130
We are then asked to find the maximum height reached by the rocket
To do this, we would use the differentiation analysis to obtain the maximum of this function.
At maximum point for any function,
The first derivative = (dy/dx) = 0
The second derivative = (d²y/dx²) < 0
y = -16x² + 261x + 130
First derivative
(dy/dx) = -32x + 261 = 0
32x = 261
Divide both sides by 32
(32x/32) = (261/32)
x = 8.15625 s
We can then substitute this value of x (time) into the equation to get the maximum height (y)
y = -16x² + 261x + 130
At x = 8.15625 s,
y = -16 (8.15625)² + 261 (8.15625) + 130
= -1064.39 + 2128.78 + 130
= 1194.39
= 1194.4 feet to the nearest tenth.
Hope this Helps!!!
The function 1 (2) = 4x is used to calculate the litter of piglets born on the farm; x represents the number of female pigs on the farm. Each female pig births 4 piglets. The
farmer will need pens to house all the piglets. One pen can house 8. The number of pens required is written as p(x)=+1, where x is the number of piglets. The farmer
always builds one extra pen. Which of the following functions represents the number of pens as a function of the female pigs?
p(p(x))
p(l(z))
1(p(x))
1 (1 (x))
A function which represents the number of pens as a function of the female pigs is: p(l(z)).
How to determine the function that represents the number of pens?From the information provided, we have the following the following functions:
Function, l(z) = 4x
Where:
l(z) represents the litter of piglets born on the farm.x represents the number of female pigs on the farm.Function, p(x) = x/8 + 1
Where:
p(x) represents the number of pens required.x represents the number of piglets.Next, we would substitute the the litter of piglets born on the farm l(x) into the number of pens required as follows;
p(x) = x/8 + 1
p(l(z)) = 4x/8 + 1
p(l(z)) = 0.5x + 1
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Complete Question:
Function l(z) = 4x is used to calculate the litter of piglets born on the farm; x represents the number of female pigs on the farm. Each female pig births 4 piglets. The farmer will need pens to house all the piglets. One pen can house 8. The number of pens required is written as p(x) = x/8 + 1, where x is the number of piglets. The farmer always builds one extra pen. Which of the following functions represents the number of pens as a function of the female pigs?
p(p(x))
p(l(z))
1(p(x))
1 (1 (x))
3. Select all the expressions that will have a remainder. 377 644 74 – 3 96 = 5 56 – 2
To obtain the term that will give a remainder, we will have to check if the dividend is a multiple of the divisor
Dividends and divisors are the two key ingredients that yield the quotient. The dividend is the number being divided, while the divisor is the number by which the dividend is divided. In other words, given a÷b, a is the dividend and b is the divisor
Looking at
37 ÷ 3 = (12 remainder 1), 37 is not a multiple of 3, so this will give a remainder of 1
64 ÷ 4 = (16 remainder 0), 64 is a multiple of 4, so this will not give a remainder
74 ÷ 3 = (24 remainder 2), 74 is not a multiple of 3, so this will give a remainder of 2
96 ÷ 5 = (19 remainder 1), 95 is not a multiple of 5, so this will give a remainder of 1
56 ÷ 2 = (28 remainder 0), 56 is a multiple of 2, so this will not give a remainder
independent vs dependent equation5х – Зу = 10 бу = kx - 42
We will assume that we want to know if the system of equations is independent or dependent:
[tex]\begin{cases}5x-3y=10\text{ (1)} \\ 6y=kx-42\text{ (2)}\end{cases}[/tex]where k is a real number. We will try to find the solutions to the system, and we will try to give values to k for which the system becomes independent or dependent.
We will use substitution, we solve for the variable x on the first equation to obtain:
[tex]\begin{gathered} 5x-3y=10 \\ 5x=10+3y \\ x=\frac{10+3y}{5} \end{gathered}[/tex]And now we replace it onto the second equation:
[tex]\begin{gathered} 6y=k(\frac{10+3y}{5})-42 \\ 6y=\frac{10k+3ky}{5}-42 \\ 6y=\frac{10k+3ky-210}{5} \\ 30y=10k+3ky-210 \\ 30y-3ky=10k-210 \\ y(30-3k)=10k-210 \\ y=\frac{10k-210}{30-3k} \end{gathered}[/tex]And the value of x will be:
[tex]\begin{gathered} x=\frac{10+3(\frac{10k-210}{30-3k})}{5}=\frac{10+\frac{10k-210}{10-k}}{5} \\ =\frac{10(10-k)+10k-210}{5(10-k)} \\ =\frac{100-10k+10k-210}{50-5k} \\ =-\frac{110}{50-5k} \\ =-\frac{22}{10-k} \end{gathered}[/tex]This means that a solution of the system will be:
[tex]\begin{cases}x=-\frac{55}{10-k} \\ y=\frac{10k-210}{30-3k}\end{cases}[/tex]Now, for finding the values which make the system dependent. This happens when the lines have the same slope, this is, when:
[tex]\begin{gathered} \frac{-5}{-3}=\frac{k}{6} \\ \frac{5}{3}=\frac{k}{6} \\ 30=3k \\ 10=k \end{gathered}[/tex]We did the division of the opposite of the coefficient of x, over the coefficient of y. This means that the system will be independent for each value of k different than 10, and will be dependent for k=10.
Hi, can you help me answer this question please, thank you!
The number of sick days an employee takes per year is believed to be about 12.
The mean purpose of null hypothesis is to verify or disprove the proposed statistical assumptions, also is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.
If you wish to test the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the null hypothesis is "the mean number of sick days an employee takes per year is equal to 12 days".
Then, the correct null hypothesis is:
[tex]H_0\colon\mu=12\text{ days}[/tex]The alternative hypothesis is an alternative to the null hypothesis, then if you want to check the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the alternative hypothesis is "mean number of sick days an employee takes per year is not equal to 12 days".
Then, the correct alternative hypothesis is:
[tex]H_a\colon\mu\ne12\text{ days}[/tex]Which normal distribution has a wider spread: distribution A with a mean of one and a standard deviation of two, or distribution B with a mean of two and a standard deviation of one?
The normal distribution with mean of one and standard deviation of two has the wider spread.
Normal distribution:
Normal distribution defines a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Given,
Here we have the distributions,
Distribution A with a mean of one and a standard deviation of two, or Distribution B with a mean of two and a standard deviation of one
Now, we have to identify the normal distribution has a wider spread.
Here the normal distribution with a mean of 1 and standard deviation of 2 will be wider than a distribution with a mean of 2 and standard deviation of 2.
Because, the distributions with greater standard deviations indicate greater variability/spread of its variables around the mean.
To know more about Normal distribution here.
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The graph of a quadratic function with vertex (0, -1) is shown in the figure below.Find the range and the domain in interval notation please include paranthese or brackets within your answer.
The domain is all the values that the function can take on the x axis, in this case it would be all the real numbers:
[tex]domain\to(-\infty,\infty)[/tex]The range is all the values that the function can take on the y-axis. For this function it will grow from vertex to infinity:
[tex]range\to\lbrack-1,\infty)[/tex]Remember that when intervals are written, parentheses are used for open values and square brackets for exact values.
Use the two-way table on left and right-handed people to create a two-way table that shows the joint and marginal relative frequencies. Drag and drop the numbers to complete the table. Dominant Hand left. right. totalfemale 11. 104. 115Male. 24. 92. 116total. 35. 196. 231 Dominante hand left. rigth. totalfemale maletotalBank:0.0480.1520.1670.3760.3980.4500.4980.5020.5260.84810.104
1st Row (Female)
[tex]\begin{gathered} \frac{11}{231}=0.048 \\ \frac{104}{231}=0.450 \\ \frac{115}{231}=0.498 \end{gathered}[/tex]2nd Row (Male)
[tex]\begin{gathered} \frac{24}{231}=0.104 \\ \frac{92}{231}=0.398 \\ \frac{116}{231}=0.502 \end{gathered}[/tex]Third Row (Total)
[tex]\begin{gathered} \frac{35}{231}=0.156 \\ \frac{196}{231}=0.848 \\ \frac{231}{231}=1 \end{gathered}[/tex]The completed table is given below:
find each unit rate. round to the nearest hundredth if necessary 325 meters in 25 seconds
325 meters in 25 seconds
To find out the unit rate divide the total meters by the total seconds
so
325/25=13 m/sec
therefore
the answer is
13 m/secor 13 m per one secondWhat is the mixed number answer 4 4/9 + 8 7/9
Hello there. To solve this question, we'll have to remember some properties about mixed numbers.
Given the mixed number a b/c, we can write it as and it is the same as
Therefore in the expression:
[tex]4\frac{4}{9}+8\frac{7}{9}[/tex]We rewrite it as
[tex]4+\frac{4}{9}+8+\frac{7}{9}[/tex]Adding the fractions, we have:
[tex]12+\frac{11}{9}=\frac{119}{9}[/tex]And we have to write the answer in mixed fraction form, therefore we perform
[tex]\frac{119}{9}=\frac{117+2}{9}=13\frac{2}{9}[/tex]This is the answer we're looking for.
The ratio of the number of oranges to the number of apples is 1 : 3.21 oranges were added and the ratio became 4 : 5. How many fruitswere there initially?
Answer
There were 15 oranges initially.
There were 45 apples initially.
Hence, there were (15 + 45) = 60 fruits there initially.
Explanation
Let the number of oranges be x
Let the number of apples be y
The ratio of the number of oranges to the number of apples is 1 : 3 implies:
[tex]\begin{gathered} x\colon y=1\colon3 \\ \frac{x}{y}=\frac{1}{3} \\ \text{Cross multiply} \\ y\times1=x\times3 \\ y=3x----i \end{gathered}[/tex]If 21 oranges were added and the ratio became 4 : 5, this implies:
[tex]\begin{gathered} (x+21)\colon y=4\colon5 \\ \frac{x+21}{y}=\frac{4}{5} \\ \text{Cross multiply} \\ 5(x+21)=4\times y \\ 5x+105=4y----ii \end{gathered}[/tex]To know how many fruits were there initially, solve the system of the equations:
[tex]\begin{gathered} \text{Substitute }y=3x\text{ into }ii \\ 5x+105=4(3x) \\ 5x+105=12x \\ \text{Combine the like terms} \\ 12x-5x=105 \\ 7x=105 \\ \text{Divide both sides by 7} \\ \frac{7x}{7}=\frac{105}{7} \\ x=15 \end{gathered}[/tex]x = 15 implies there were 15 oranges initially.
To get y, substitute x = 15 into equation (i):
[tex]\begin{gathered} y=3x----i \\ y=3\times15 \\ y=45 \end{gathered}[/tex]y = 45 implies there were 45 apples initially.
Hence, there were (15 + 45) = 60 fruits there initially.
You have $20,000 that you want to deposit into a savings account. You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?
Problem
You have $20,000 that you want to deposit into a savings account.
You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?
Solution
For this case we need to take in count the compound interest formula given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P= 20000, r= interest rate in fraction and n= number of times that the rate is compounded in a year, t= 5 years and A is the future value
And the simple interest formula:
[tex]A=P(1+rt)[/tex]And compound continuosly:
[tex]A=\text{Pe\textasciicircum{}rt}[/tex]Let's calculate the final amount for each case
Bank A
[tex]A=20000(1+\frac{0.0425}{12})^{12\cdot5}=24726.038[/tex]Bank B
[tex]A=20000(1+\frac{0.06}{2})^{2\cdot5}=26878.328[/tex]Bank C
[tex]A=20000(1+0.055\cdot5)=25500[/tex]Bank D
[tex]A=20000e^{0.04\cdot5}=24428.055[/tex]And the best choice for this case seems to be Bank B since we will have more money at the end of the 5 year
an item is regular priced at $60. Linda bought it on sale for 30% off the regular price. how much did Linda pay?
Given data
*An item is regular priced at $60
*Linda bought is on sale on discount is 30%
Linda pay the price on the item is calculated as
[tex]\begin{gathered} p=60\times30\text{ PERCENT} \\ =60\times0.3 \\ =18 \end{gathered}[/tex]Thus, the charged amount on an item is $18
The table shows the mean number of basketball goals made by four random samples of players from the school teamduring this year's season.Sample #Sample MeanNumber of Goals71243548Is a valid prediction for the mean of the population possible using these samples?A: No, there are not enough samples.B: Yes, the sample means are all less than 10.C: Yes, the variation of the sample means is small.D: No, the variation of the sample means is too great.
Answer:
Step-by-step explanation:
yson does 75 sit-ups during his work out. He wants to increase his sit-ups by 15%. Which represents the new amount of sit-up
Answer:
he does 86 sit ups instead of 75 to increase by 15 percent
Step-by-step explanation:
Answer: The correct answer is 86.25 sit-ups (or round-up to 87 whole sit-ups).
Step-by-step explanation:
S = current amount of sit-ups (75)
S2 = Increased amount of sit-ups by 15%
The equation:
S2 = S + (S x .15)
S2 = 75 + (75 x .15)
S2 = 75 + 11.25
S2 = 86.25 sit-ups
It says. Use the graph of f to determine whether the following statement is true or false. The range of f is [-5,1]
The statement is false because the range is [-5, 1)
EXPLANATION
The range of a function is the set of y-values for which the function is defined.
From the graph given the range is:
-5≤ x < 1
This can be represented by interval notation as :
[ - 5, 1)
Therefore, the statement is false because the range is [-5, 1)
describe the reflection (s) that carry the regular pentagon onto itself.
EXPLANATION:
The reflection that is made on a figure,reverses its position with respect to a line called the axis of reflection.
IMPORTANT NOTE:
To make the reflection of the geometric figure shown in the exercise, we need to know the vertices and coordinates of the figure that allow us to make the corresponding reflection in the Cartesian plane of the pentagon
The minute hand of a clock extends out to the edge of the clock's face, which is a circle of radius 4 inches. What area does the minute hand sweep out between 9:15 and9:35? Round your answer to the nearest hundredth.
To solve the question, we have to make use of the fact that
A minute hand travels 360 degrees in 60 min
From the question given, we are told that the minute hand sweep out between 9:15 and
9:35, thus
There are 20 minutes in between 9:15 and 9:35
Thus
We can get the area using the formula
[tex]\begin{gathered} Area=\frac{\text{minutes turned}}{60}\times\pi r^2 \\ \text{where} \\ r=4\text{ inches} \end{gathered}[/tex]Area will be
[tex]\begin{gathered} \text{Area}=\frac{20}{60}\times\pi\times4^2 \\ \text{Area}=\frac{1}{3}\times\pi\times16 \\ \text{Area}=16.755 \end{gathered}[/tex]Thus, the area will be 16.76 in²
Circle A' is the result of reflecting circle A across the line l.Select all of the correct statements about the unchanged properties of circle A and circle A'. Choose all answers that apply.A: The radii of circle A and circle A' have the same lengthsB: Circle A and circle A' have the same circumference.C: Circle A and circle A' have the same area.D: None of the above.
ANSWER:
A: The radii of circle A and circle A' have the same lengths
B: Circle A and circle A' have the same circumference.
C: Circle A and circle A' have the same area.
STEP-BY-STEP EXPLANATION:
A figure, when reflected, does not lose any of its arithmetic characteristics, since it does not have any type of dilation or change in its figure.
This means that it conserves its radius, and by conserving its radius it conserves the circumference and the area.
Therefore, the correct answers are:
A: The radii of circle A and circle A' have the same lengths
B: Circle A and circle A' have the same circumference.
C: Circle A and circle A' have the same area.
Answer:
A
B
C
Are correct
Step-by-step explanation:
Suppose your bank charges a $7 monthly fee and $0.11 per check. If you write 62 checks in a year, how much money in fees would you expect to pay for the year? Type out acalculations and make sure your final answer is clear.
The cost has a monthly fee and a per check fee.
We can write the bank fee as:
[tex]C(m,c)=7m+0.11c[/tex]m: months, c: number of checks.
If, in a year (m=12 months), you write 62 checks (c=62), the total fee is:
[tex]C(12,62)=7\cdot12+0.11\cdot62=84+6.82=90.82[/tex]You expect to pay a yearly fee of $90.82.
Find the area of the triangle below.9.9 m5.6 m4.4 m7.8 m
the Answer
Step by Step Explanation
The area of the triangle formula is
[tex]A=\frac{h_b\cdot b}{2}[/tex]where
[tex]\begin{gathered} h_b=4.4m \\ b=9.9m \end{gathered}[/tex]Subs, the value in above equation
[tex]\begin{gathered} A=\frac{h_b\cdot b}{2} \\ A=\frac{4.4_{}\cdot21.78}{2} \\ A=21.78 \end{gathered}[/tex]The area of the triangle is 21.78 cm^2
What is the area of the circle below, in terms of ?90 metersO 457O 907O 1807O 81007134
Step 1: Write out the formula
[tex]\begin{gathered} \text{Area of a circle = }\pi r^2 \\ \text{where } \\ r=\text{ the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]r=90m[/tex]Therefore,
[tex]\text{ the area of the circle = }\pi(90)^2=\pi\times8100=8100\pi m^2[/tex]Hence, the area in terms of pi is
[tex]8100\pi[/tex]The last choice is the correct answer
There are 3 consecutive odd integers that sum to –9. What is the least of these integers?
let the three consecutive numbers are,
a , a+ 1 , a+2
sum of the numbers = -9
a + a +1 + a + 2 = -9
3a + 3 = -9
3a = -9 - 3
3a = -12
a = -12/3
a = -4
so the least number is a = -4
thus the answer is -4.
Write the function whose graph is the graph of y=x^3, but is shifted to the right 3 units.y=
The Solution:
Given the function below:
[tex]y=x^3[/tex]When the function is shifted to the right by 3 units, the new function becomes:
[tex]y=(x-3)^3[/tex]Therefore, the correct answer is
[tex]y=(x-3)^3[/tex]1. In the function f(x) = 2x +3, what does the x represent?2. In the function f(x) = 2x + 3, what does the f(x) represent?
a. h(-4) = -13
b. h(t) = 23 , t = 14
c. h(13) = 21
d. h(t) = -33 , t = -14
Model -4 + -2 using counter chipsRed chip = 1 Yellow chip = 1What’s the sum?
Given the following question:
Since both are negatives and we are adding the two together:
We need 4 red chips to represent the negative four (-4)
We need 2 more red chips to present the negative two (-2)
The total sum of -4 + -2 is...
[tex]-4+-2=-6[/tex]To represent the sum using the chips we will place "six red chips."
i don’t know how to put it into an equation
x is the unknown number
The difference of a number and 4: x-4
Twice the difference of a number and 4: 2(x-4)
Twice the difference of a number and 4 equals 3: [tex]2(x-4)=3[/tex]Draw the given angles in standard position. 110 degrees, - 80 degrees
Standard Position of Angles
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.
The ray on the x-axis is called the initial side and the other ray is called the terminal side.
Positive angles are measured counterclockwise, negative angles are measured clockwise.
The angle of 110 degrees is positive so it must be measured counterclockwise. The angle -80 will be drawn clockwise.
The following image shows the required angles:
A bag contains seven green marbles and four yellow marbles.• 2a) If you randomly pick a marble and then pick a second marble without returning the marble to the bag, what is the probability the firstmarble is yellow and the second marble is green?• 3b) If you return the first marble to the bag before picking another marble, what is the probability the first marble is yellow and the secondmarble is green?%DULUa) PIY and G without replacing) = type your answer...$6; b) PIY and G with replacing) = type your answer.4Instructions
a family walked 240 miles in 4 hours yesterday at this rate how many hours will it take to walk another 150 miles
A family walked 240 miles in 4 hours yesterday at this rate how many hours will it take to walk another 150 miles ?
_____________________________________________________
Rate
240 miles / 4 hours = 60 miles / hour
_______________________
Can you see the updates?
_____________________
150 miles ÷ rate = time ( 150 miles)
150 miles ÷ 60 miles/hour = 150/ 60 = 2.5 hours
___________________________________
Total time = 4 h + 2.5 h = 6.5 h
_________________________________
Answer
It will take 2.5 h to walk another 150 miles (in total 240 + 150, 6.5 h )