to find the total Jimmy spent at the farmers market, let's add up the groceries he bought
but note, he bought some in multiples so we need to multiply the cost by the number of units he bought
onions = 3 units
apples = 5 units
potatoes = 7 units
[tex]\begin{gathered} onions=0.48\times3units=1.44 \\ \text{apples}=0.78\times5units=3.9 \\ \text{potatoes}=0.63\times7units=4.41 \\ \text{total}=\text{ 1.44+3.9+4.41} \\ \text{total}=9.75 \end{gathered}[/tex]from the summation above, Jimmy spent a total of $9.75 at the farmers market.
575 mL = ______ L
Please help me
SOLUTION
[tex]undefined[/tex]what is the solution of the system:y = 1/2x + 4-x+2y=8
Given the following system of equations:
[tex]\begin{cases}y=\frac{1}{2}x+4 \\ -x+2y=8\end{cases}[/tex]notice that we can use the first equation and substitute it on the second equation to get the following:
[tex]-x+2(\frac{1}{2}x+4)=8[/tex]then, solving for 'x', we get:
[tex]\begin{gathered} -x+2(\frac{1}{2}x+4)=8 \\ \Rightarrow-x+x+8=8 \\ \Rightarrow8=8 \end{gathered}[/tex]since the variable x was eliminated in the process of solving for it, we have that both equations represent the same line, therefore, there are infinite solutions for the system
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015. 3 significant digits in the final answer.
The projected world population in 2015 is 8.71 billion
Here, we want to use an exponential model to find the world's population in the given year
Generally, we can have the exponential model as;
[tex]P=I(1+r)^t[/tex]where P represents the population in the year 2015
I represents the population in 1987
r is the annual growth percentage = 2% = 2/100 = 0.02
t is the difference in the number of years = 2015-1987 = 28
Substituting these values, we have;
[tex]\begin{gathered} P=5,000,000,000(1+0.02)^{28} \\ \\ P=5,000,000,000(1.02)^{28} \\ \\ P\text{ = 8,705,121,030.86965} \end{gathered}[/tex]Which to 3 significant digits is 8.71 billion
Tamie uses2/3of a cup of water with a pound of flour to make a paste for a sculpture she is creating.How many cups of water does she need to mix with 1 pound of flour to create the same paste?
Given:
Amuount of cup of water used = ⅔ cup
Amount of pound of flour used = ⅙ pound
To find cups of water she needs to mix with 1 pound of flour to create the same paste, we have:
[tex]\begin{gathered} \frac{2}{3}\text{cup}=\frac{1}{6}\text{ pound} \\ \\ x\text{ cup = 1 pound} \end{gathered}[/tex]Let's solve for x:
[tex]\begin{gathered} x=\frac{\frac{2}{3}\ast1}{\frac{1}{6}} \\ \\ x=\frac{\frac{2}{3}}{\frac{1}{6}} \\ \\ x=\frac{2}{3}\div\frac{1}{6} \\ \\ x=\frac{2}{3}\ast\frac{6}{1} \\ \\ x=\frac{2\ast6}{3\ast1} \\ \\ x=\frac{12}{3} \\ \\ x=4 \end{gathered}[/tex]Therefore, she will need to mix 4 cups of water to with 1 pound of floor to create the same paste
I need help with my homework question please. I’m not good at all with word problems
Answer:
[tex]A\text{ = \$1,498.38}[/tex]Explanation:
Here, we want to get the total amount in the account
From the given question:
P is the deposited amount which is $800
r is the interest rate which is 8% = 8/100 = 0.08
t is the number of years which is 8 years
n is the number of times interest is compounded yearly which is semi-annually which means twice (2)
Now, we need to get A
Substituting the values above, we have it that:
[tex]\begin{gathered} A\text{ = 800(1 + }\frac{0.08}{2})^{8\times2} \\ \\ A\text{ = \$1,498.38} \end{gathered}[/tex]David is investing his money. He thinks that he should make $12 for every $100 he invests. How much does he expect to make on an investment of $4300?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
principal = $4300
rate:
$12 ===> $100
final amount = ?
Step 02:
final amount:
$12 --------- $100
x --------- $4300
interest = (4300 * 12 / 100) = $516
final amount = $4300 + $516 = $4816
The answer is:
the distance between -2 1/2 - (-3)
The distance between -2 1/2 - (-3)
-2 1/2 + 3
1/2
______________________
Answer
1/2
Peter takes 5 minutes to make a sandwich and 10 minutes to make dumplings. If he plans tospend no more than 1 hour making food, what inequality represents the number of sandwichesand dumplings Peter can make? What is the graph of the solution set?
Let x be the number of sandwiches Peter makes and let y be the number of dumplingshe makes.
Since he takes 5 minutes per sandwich, the total time he uses to make them is
[tex]5x[/tex]The total times he uses to make dumplings is
[tex]10y[/tex]The total time he spends preparing food is the sum of the two things, that is
[tex]5x+10y[/tex]He wants to spend no more than an hour to make the food, this means the time he is willing to spend making food is less or equal to 60 minutes. (We have to put the hour in minutes, so that the units are the same). Then the inequality representing the number and sandwiches that Peter can make in that time is
[tex]5x+10y\leq60[/tex]To graph the solution set for this inequality we first graph the line that represents this situation, that is, the line
[tex]5x+10y=60[/tex]whose graph is
Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). Whengraphed, the function gives a line with a slope of 1.65. See the figure below.If the monthly cost for 16 HCF is $49.67, what is the monthly cost for 11 HCF?
Given:
The function gives a line with a slope of 1.65.
The monthly cost for 16 HCF is $49.67.
Required:
To find the monthly cost for 11 HCF.
Explanation:
The slope-intercept form of line is
[tex]y=mx+b[/tex]We know the slope is 1.65.
And since 16 HCF costs $49.67, we have a point on the line. (16, 49.67)
Plugging this information into our equation, we get:
[tex]\begin{gathered} 49.67=1.65(16)+b \\ \\ b=49.67-26.4 \\ \\ b=23.27 \end{gathered}[/tex]Now
[tex]y=1.65x+23.27[/tex]If we want to know how much 11 HCF costs, we just have to plug that into our equation as the x-value.
[tex]\begin{gathered} y=1.65(11)+23.27 \\ \\ y=18.15+23.27 \\ \\ y=41.42 \end{gathered}[/tex]Final Answer:
The monthly cost for 11 HCF is $41.42
the diameter of a cylindrical water tank is 8 ft and height is 12ft what is rge exact volume of the tank. write your answer in terms of n
Given:
The diameter of cylinder is d = 8 ft.
The height of cylinder is h = 12 ft.
Explanation:
The formula for the volume of cylinder is,
[tex]V=\frac{\pi d^2h}{4}[/tex](a)
Substitute the values in the formula to determine the volume of cylinder.
[tex]\begin{gathered} V=\frac{\pi\cdot(8)^2\cdot12}{4} \\ =192\pi\text{ ft\textasciicircum{}3} \end{gathered}[/tex]So exact volume of cylinder (in terms of pi) is,
[tex]192\pi\text{ ft\textasciicircum{}3}[/tex](b)
Determine the approximate volume of cylinder.
[tex]\begin{gathered} V=192\pi \\ =603.185 \\ \approx603.19\text{ ft\textasciicircum{}3} \end{gathered}[/tex]So approximate volume of cylinder is 603.19 ft^3.
What is the volume of the cylinder not the nearest hundredths
The volume of the cylinder is 402.18 cm³
Explanations:The volume of a cylinder is given by the formula:
[tex]V\text{ =}\pi r^2h[/tex]where V represents the volume of the cylinder
h represents the height of the cylinder
r represents the radius of the cylinder
π = 3.142
From the diagram shown:
Height = 8 cm
Diameter = 8 cm
Radius, r = diameter / 2
r = 8/2
r = 4 cm
Substituting the values of π, r, and h into the formula given above:
[tex]\begin{gathered} V\text{ = 3.14}2\text{ }\times4^2\times8 \\ V\text{ = 3.142 }\times16\times8 \\ V\text{ = }402.18 \end{gathered}[/tex]The volume of the cylinder is 402.18 cm³
Evaluate using the values given y-x-x; use x=5 and y=4
Given the expression:
[tex]y-x-x[/tex]First, you can simplify both x-terms:
[tex]y-2x[/tex]Replace the expression with the given values for y and x and solve
[tex]\begin{gathered} y-2x=4-2\cdot5 \\ 4-10=-6 \end{gathered}[/tex]The result of the expression when y=4 and x=5 is 6
Mr. Keys has a herd of 250 cows on his 1,400 acre farm, and 4/5 of his cows have a calf at theirside. How many cows do not have a calf at their side?
We want to find the number of cows that do not have a calf at their side. For doing so, we remember that the total of cows that have a calf at their side is 4/5 of the total population, and thus, the number is given by:
[tex]\frac{4}{5}(250)=\frac{1000}{5}=200[/tex]This means that 200 cows have a calf at their side, and thus, just 50 cows do not have a calf at their side.
I brought a car for 21,990 dollars the blue book value of the car is 43000 what is the percent of change between the blue book value and purchase price ?
Answer:
- 48.86% or a decrease of 48.86%.
Step-by-step explanation:
Considering the blue book value the original value and the purchase price the new value, the percent of change is:
P = (21,990 - 43000)/43000*100
P = -48.86%.
The percent of change is - 48.86% or a decrease of 48.86%.
solve the system of linear equations by substitution y=3x-1 and y=x-7
We have the system of equations:
[tex]\begin{gathered} y=3x-1 \\ y=x-7 \end{gathered}[/tex]Since we have two equations that are equal to y, we can set them equal to each other.
[tex]3x-1=x-7[/tex]Lets add 1 to both sides of the equation.
[tex]3x=x-6[/tex]Subtract x from both sides of the equation.
[tex]2x=-6[/tex]Divide both sides of the equation by 2.
[tex]x=-3[/tex]Now, we can substitute x = -3 back into either equation in order to find its corresponding y-value.
[tex]y=3(-3)-1[/tex]Simplify this equation...
[tex]\begin{gathered} y=-9-1 \\ y=-10 \end{gathered}[/tex]The solution to this system of linear equations is (-3, -10).
find the measure of Arc vrt
The first step to calculate the measure of the arc is to determine the angle VR. To do that we need to understand that the angles UV, VQ and QR are suplementary, which means that their sum is equal to 180 degrees. So we have:
[tex]\begin{gathered} \measuredangle UV+\measuredangle VQ+\measuredangle QR=180 \\ 54+95+\measuredangle QR=180 \\ 149+\measuredangle QR=180 \\ \measuredangle QR=180-149 \\ \measuredangle QR=31 \end{gathered}[/tex]The angle QR is equal to 31 degrees, with this we can find the angle VR, because it is the sum of VQ and QR.
[tex]\begin{gathered} \measuredangle VR=\measuredangle VQ+\measuredangle QR \\ \measuredangle VR=95+31=126 \end{gathered}[/tex]The arc measure is equal to 126 degrees.
Suppose that a certain alloy is made by mixing 300 g of an alloy that contain 72% copper with 20 g of pure copper a) how many grams of copper in the resulting mixture b) in what percentage of the resulting mixture is copper
Mass of the alloy = 300 g
Percentage composition of copper in the alloy = 72%
Mass of copper in the alloy = (72/100) x 300
Mass of copper in the alloy = 216 g
The alloy was mixed with 20 g of pure corper
a) Mass of copper in the resulting mixture = (Mass of copper in the alloy) + (Mass of pure corper)
Mass of copper in the resulting mixture = 216 g + 20 g
Mass of copper in the resulting mixture = 236 g
b) In what percentage of the resulting mixture is copper
The mass of the resulting mixture = 300 g + 20 g = 320 g
Percentage of copper in the resulting mixture =
(Mass of copper in the resulting mixture / mass of the resulting mixture) x 100%
Percentage of copper in the resulting mixture = (236 / 320) x 100%
Percentage of copper in the resulting mixture = 73.75%
-За - 8 + 2а = 13what is the value of a?
The initial expression is:
-3a - 8 + 2a = 13
We can sum the similar terms as:
- 3a + 2a - 8 = 13
- a - 8 = 13
Adding 8 on both sides:
- a - 8 + 8 = 13 + 8
- a = 21
Multiplying by -1 on both sides:
- a * (-1) = 21*(-1)
a = - 21
Answer: -21
An electronics manufacturer has 180 capacitors, and the same number of capacitors is needed for eachcircuit board made. The manufacturer uses the capacitors to make 45 circuit boards.Identify and interpret the intercepts, then use the intercepts to graph the line.The y-intercept isThe x-intercept iscapacitors remaining.which means that the manufacturer (select) with capacitors.which means that when boards have been made, there are
Answer:
The y-intercept is 180 which means that the manufacturer has started with 0 capacitors.
The x-intercept is 45, which means that when 45 boards have been made, there are 0 capacitors remaining.
Explanation:
The electronic manufacturer has 180 capacitors. It means that at the beginning when there are 0 circuit boards made, the electronic manufacturer has 180 capacitors remaining.
It means that the y-intercept is 180 which means that the manufacturer has started with 0 capacitors.
On the other hand, they need 180 capacitors to make 45 circuit boards. So, if they made 45 circuit boards, they will have 0 capacitors remaining.
It means that when y ( capacitors remaining) is 0, x (circuit boards made) is 45.
So, the x-intercept is 45, which means that when 45 boards have been made, there are 0 capacitors remaining.
So, the graph that represents the situation is:
Find the root rounded to three significant digits. 77,975
we have that
cubic root of 77,975=42.722
but remember that
rounded to three significant digits
so
42.7
Simplify q^5 q^3 uq Write your answer with only positive exponents
To answer this question we will use the following properties:
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n}, \\ ab=ba\text{.} \end{gathered}[/tex]Using the second property we get:
[tex]q^5q^3uq=q^5q^3qu\text{.}[/tex]Finally, using the first property we get:
[tex]\begin{gathered} q^5q^3uq=q^{5+3}qu=q^8qu \\ =q^{8+1}u=q^9u\text{.} \end{gathered}[/tex]Answer:
[tex]q^9u\text{.}[/tex]
For males in a certain town, the systolic blood pressure is normally distributed with a mean of and a standard deviation of 8. If 428 males from the town are randomly selected to participate in a study, how many of them would be expected to have a systolic blood pressure higher than 114, to the nearest whole number?
Answer
In a group of 428 males in the town, the number of males expected to have a systolic blood pressure higher than 114 is 331.
Explanation
To answer this, we need to first obtain the probability of a male person having a systolic blood pressure higher than 114.
Since it is a normal distribution, we will used the normal distribution tables to obtain the probability after standardizing the score.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ
x = The value = 114
μ = Mean = 120
σ = Standard deviation = 8
z = (x - μ)/σ
z = (114 - 120)/8 = (-6/8) = -0.75
P(x > 114) = P(z > -0.75)
= 1 - P(z ≤ -0.75)
= 1 - 0.227
= 0.773
So,
Probability of a male person having systolic blood pressure higher than 114 = 0.773
In a group of 428 males, we now need to find the expected number of people that will have a systolic blood pressure higher than 114.
Expected value = np
n = Number of variables = 428 males
p = Probability = 0.773
Expected value = np = (428) (0.773) = 330.8 = 331 to the nearest whole number.
Hope this Helps!!!
What is the domain of the graph 1? What is the range of graph 1? What is the domain of graph 2and what is the range of graph 2
EXPLANATION
Graph 1)
Domain: All real numbers
Range: All real numbers
Graph 2)
Domain: -1≤ x≤ 5
Range: -1≤ y ≤ 2
5.2. Gene bought a yacht for $320,000. Salestax is 6%. What is the price of the yachtincluding sales tax?OA $192,0001B$320,600OC $339,2001OD $380,000
ñTriangle ABC is rotated to create the image A'B'C'.Which rule describes the transformation?yCH4.(x,y) - (x, y)(x, y) - (y,x)(x, y) - (-x, y)(x, y) - (y, -x)SEEBA А2345X5 4 -3 -2 -1AB5Save and ExitNextSubmitUnmark this question
Assuming that there is an triangle ABC and it is rotated to create a new image, A'B'C', we can check each of the presented rules.
1° - (x,y) - (x,y)
In this rule, every X will stil be the same X after the change. And so will the Y. This rule does not bring any change at all.
2° - (x,y) - (y,x)
In this rule , the coordinates X will become Y, and vice versa. It will mirror the image through an x=y line. This is not a rotation!!!
3° - (x,y) - (-x,y)
In this rule, the value of each X will become -X, and Y will keep unchanged. This rule just mirror the image through Y-axis.
4° - (x,y) - (y,-x)
In this rule, every point will have the X-values becoming the Y-axis value, in the oposite sigh. And for the Y-values, it will just become the X-axis. In this rule, what we got is a clockwise rotation.
What is 64,646,480,523x789
Given: The expression-
[tex]64,646,480,523\times789[/tex]Required: To simplify the expression.
Explanation: The multiplication of two numbers can be performed by making two rows and then multiplying each numbered row-wise. The final rows are then added together for the answer.
Hence, multiplying the numbers as-
[tex]51,006,073,132,647[/tex]Final Answer: The final Answer is 51,006,073,132,647.
The equation y = 6.75x models the cost, in dollars, to purchase x pounds of steak at grocery store 1. This table shows the cost to buy different weights ofsteak at grocery store 2.Cost of Steak at Grocery Store 2Weight (pounds)23Cost$14.50$21.75$36.25$65.2559Which statement is true?
To answer this question we need to know how much does it cost to purchase steak per pound in the second grocery.
To do this we can calculate the slope of the points in the table, remember that the slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the first to rows of the table we have
[tex]\begin{gathered} m=\frac{21.75-14.5}{3-2} \\ =\frac{7.25}{1} \\ =7.25 \end{gathered}[/tex]Hence, in the second grocery we pay $7.25 per pound.
Now, from the equation given for the first grocery store we know we pay $6.75 per pound.
From this prices we notice that the cost of steak at grocery store 1 is $0.5
less per pound than at grocery store 2.
Therefore the answer is D.
What is the doubling time of prices which are increasing by 5 percent per year? doubling time =(include units)
What is the doubling time of prices which are increasing by 5 percent per year:
Since it is doubling, it must increase by 100%.
100 divided by 5 = 20
1 year ----> 5 %
x ------> 100 %
[tex]x=\frac{100}{5}=20[/tex][tex]100\div5=20\text{yrs}[/tex]Therefore the doubling time = 20yrs
In right ABC, AN is the altitude to the hypotenuse. FindBN, AN, and AC,if AB =2 5 in, and NC= 1 in.
From the statement of the problem, we have:
• a right triangle △ABC,
,• the altitude to the hypotenuse is denoted AN,
,• AB = 2√5 in,
,• NC = 1 in.
Using the data above, we draw the following diagram:
We must compute BN, AN and AC.
To solve this problem, we will use Pitagoras Theorem, which states that:
[tex]h^2=a^2+b^2\text{.}[/tex]Where h is the hypotenuse, a and b the sides of a right triangle.
(I) From the picture, we see that we have two sub right triangles:
1) △ANC with sides:
• h = AC,
,• a = ,NC = 1,,
,• b = NA.
2) △ANB with sides:
• h = ,AB = 2√5,,
,• a = BN,
,• b = NA,
Replacing the data of the triangles in Pitagoras, Theorem, we get the following equations:
[tex]\begin{cases}AC^2=1^2+NA^2, \\ (2\sqrt[]{5})^2=BN^2+NA^2\text{.}\end{cases}\Rightarrow\begin{cases}NA^2=AC^2-1, \\ NA^2=20-BN^2\text{.}\end{cases}[/tex]Equalling the last two equations, we have:
[tex]\begin{gathered} AC^2-1=20-BN^2.^{} \\ AC^2=21-BN^2\text{.} \end{gathered}[/tex](II) To find the values of AC and BN we need another equation. We find that equation applying the Pigatoras Theorem to the sides of the bigger right triangle:
3) △ABC has sides:
• h = BC = ,BN + 1,,
,• a = AC,
,• b = ,AB = 2√5,,
Replacing these data in Pitagoras Theorem, we have:
[tex]\begin{gathered} \mleft(BN+1\mright)^2=(2\sqrt[]{5})^2+AC^2 \\ (BN+1)^2=20+AC^2, \\ AC^2=(BN+1)^2-20. \end{gathered}[/tex]Equalling the last equation to the one from (I), we have:
[tex]\begin{gathered} 21-BN^2=(BN+1)^2-20, \\ 21-BN^2=BN^2+2BN+1-20 \\ 2BN^2+2BN-40=0, \\ BN^2+BN-20=0. \end{gathered}[/tex](III) Solving for BN the last quadratic equation, we get two values:
[tex]\begin{gathered} BN=4, \\ BN=-5. \end{gathered}[/tex]Because BN is a length, we must discard the negative value. So we have:
[tex]BN=4.[/tex]Replacing this value in the equation for AC, we get:
[tex]\begin{gathered} AC^2=21-4^2, \\ AC^2=5, \\ AC=\sqrt[]{5}. \end{gathered}[/tex]Finally, replacing the value of AC in the equation of NA, we get:
[tex]\begin{gathered} NA^2=(\sqrt[]{5})^2-1, \\ NA^2=5-1, \\ NA=\sqrt[]{4}, \\ AN=NA=2. \end{gathered}[/tex]Answers
The lengths of the sides are:
• BN = 4 in,
,• AN = 2 in,
,• AC = √5 in.
The radius of a circle is 16 miles. What is the circle's circumference?r = 16 miUse 3.14 for π.
Given:
a.) The radius of a circle is 16 miles.
b.) Use 3.14 for π
For us to be able to determine the circumference of the circle using the radius, we will be using the following formula:
[tex]\text{ Circumference = 2\pi r}[/tex]Where,
r = radius of the circle
We get,
[tex]\text{ Circumference = 2\lparen3.14\rparen\lparen16\rparen = 100.48 miles}[/tex]Therefore, the circumference of the circle is 100.48 miles.
Explanation:
The circumference of a circle is equal to
π, which is a number ≈3.14, multiplied by the diameter of the circle.
Therefore, C=πd.
We know that the circumference, C, is 16π, so we can say that:
16π=πd
We can divide both sides by π to see that 16=d.
We now know that the diameter of the circle is 16.
We also know that the diameter has twice the length of the radius.
In equation form: 2r=d
2r=16
r=8
Note that since 2r=d, the equation C=2πr holds and can be used in place of C=πd.