According to the problem, the total amount of money we have is $10.
Additionally, we know that the cost of peaches is $2 per pound, and the cost for grapes is $2.50 per pound.
Notice that the cost for grapes is greater than the cost for peaches, that means we'll by fewer pounds of grapes with $10 than for peaches.
For example, if we buy peaches, it would be
[tex]\frac{10}{2}=5[/tex]This means we would be able to buy 5 pounds of peaches.
But, for grapes
[tex]\frac{10}{2.50}=4[/tex]Which means we can by only 4 pounds of grapes.
Therefore, we would be able to buy a greater amount of peaches than grapes.The scatter plot shows the median household income x in thousands of dollars, and the number of adults per 1,000 people with bachelors degree y of 50 U.S states. The line y=4.08x+63.13 is a good fit for this data
So,
The line:
[tex]y=4.08x+63.13[/tex]Is a good fit of the data given.
To predict the number of bachelor's degrees in Mississippi, we replace x by 40.6 and operate:
[tex]\begin{gathered} y=4.08(40.6)+63.13 \\ y=228.778 \end{gathered}[/tex]The number of bachelor's degrees per 1000 people when x=40.6 median income, is predicted as 228.778.
f(x) =-x² + 2x + 6
Find f(-7)
Write the number 0.2 in the form a over b using integers to show that it is a rational number
Hello! Let's solve this exercise:
We have some ways to show it, look:
[tex]\begin{gathered} \frac{a}{b}=0.2 \\ \\ \frac{1}{5}=0.2 \\ \\ \frac{2}{10}=0.2 \end{gathered}[/tex]So, as it can be written as a fraction, is a rational number.
a motorboat travels 456 km in 8 hours going upstream and 783 km in 9 hours going downstream. what is the rate of the boat in still water and what is the rate of current?
How much water must be evaporated from 8 grams of a 30% antiseptic solution to produce a 40% solution?
Answer:
Step-by-step explanation:
8 grams of 30% --> 2.4 grams of AS For 2.4 grams to be 40% --> 6 grams of solution Evaporate 2 grams of water
The graph of function g is a vertical stretch of the graph of function f by a factor of 3. Which equation describes function g?
g(x)=f(x/3)
g(x)=3f(x)
g(x)=f(3x) ,
g(x)=1/3f(x)
Answer:
B) g(x) = 3f(x)Step-by-step explanation:
What is a vertical stretch?Given a function f(x), a new function g(x) = cf(x), where c is a constant, is a vertical stretch of f(x) when c > 1.
In our case the function f(x) is stretched by a factor of 3.
It means c = 3 and therefore:
g(x) = 3f(x)Correct choice is B
Find y if the line through (1, y) and (8, 2) has a slope of 3.
Answer: -19
Step-by-step explanation:
I think I am correct I am sorry if not.
Here is how I got it-
m = 21 / 7 = 3 / 1 = 3
Equation: y = 3x - 22
Answer:
y = -19
Step-by-step explanation:
Pre-SolvingWe are given two points: (1, y) and (8,2).
We want to find the value of y if the slope of the line is 3.
SolvingThe slope (m) can be calculated from two points using the formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We can label the values of the points to avoid any confusion and mistakes.
[tex]x_1 = 1\\y_1=y \\x_2=8\\y_2=2[/tex]
Substitute these values into the formula.
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{2-y}{8-1}[/tex]
Remember that the slope of the line is 3, so we can substitute m as 3.
Replace m as 3.
[tex]3 = \frac{2-y}{8-1}[/tex]
Subtract.
[tex]3 = \frac{2-y}{7}[/tex]
Multiply both sides by 7.
[tex]3 * 7 = 7(\frac{2-y}{7})[/tex]
21 = 2-y
Subtract 2 from both sides.
19 = -y
Divide both sides by -1.
-19 = y
y = - 19.
3. Solve using the Laws of Sines Make a drawing to graphically represent what the following word problem states. to. Two fire watch towers are 30 miles apart, with Station B directly south of Station A. Both stations saw a fire on the mountain to the south. The direction from Station A to the fire was N32 W. The direction from Station B to the fire was N40 ° E. How far (to the nearest mile) is Station B from the fire?
Let's make a diagram to represent the situation
The tower angle is found by using the interior angles theorem
[tex]\begin{gathered} 50+58+T=180 \\ T=180-50-58=72 \end{gathered}[/tex]It is important to know that the given directions are about the North axis, that's why we have to draw a line showing North to then find the interior angles on the base of the triangle formed.
To find the distance between the fire and Station B, we have to use the law of sines.
[tex]\frac{x}{\sin58}=\frac{30}{\sin 72}[/tex]Then, we solve for x
[tex]\begin{gathered} x=\frac{30\cdot\sin 58}{\sin 72} \\ x\approx26.75 \end{gathered}[/tex]Hence, Station B is 26.75 miles far away from the fire.Somebody please answer asap for brainlist please
The thing that the change that takes place in Ulrich and Georg suggested that the authors theme may be A. Wild anger can lead to wild deaths.
What is the story about?The Interlopers is a story about two men who met in a forest and we're fighting over a land. They were trapped under a tree. In the end, they wee killed by a wolf.
It should be noted that the theme was illustrated in the story. This was that anger can bring about death. This was depicted ad Georg and rich fired due o their anger.
In conclusion, the correct option is A.
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Use (60° - 45°) = 15° to find the exact value of cos 15º.vaV2 + V6V-V6(b)(c)4(d)4+ V62
Answer;
[tex]B\text{. }\frac{\sqrt[]{2}+\sqrt[]{6}}{4}[/tex]Explanation;
Given that;
[tex](60^0-45^0)=15^0[/tex]Hence;
[tex]\text{Cos 15}^0=Cos(60^0-45^0)[/tex]According to trigonometry identity;
[tex]\begin{gathered} Cos(60^0-45^0\text{) = Cos60 Cos45 + Sin60Sin45} \\ Cos(60^0-45^0\text{) }=\frac{1}{2}(\frac{1}{\sqrt[]{2}})+\frac{\sqrt[]{3}}{2}(\frac{1}{\sqrt[]{2}}) \end{gathered}[/tex]Evaluate the result by finding the LCM
[tex]Cos(60^0-45^0\text{) }=\frac{1+\sqrt[]{3}}{2\sqrt[]{2}}[/tex]Rationalize;
[tex]\begin{gathered} Cos(60^0-45^0\text{) }=\frac{1+\sqrt[]{3}}{2\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ Cos(60^0-45^0\text{) }=\frac{\sqrt[]{2}(1+\sqrt[]{3})}{2\cdot2} \\ Cos(60^0-45^0\text{) }=\frac{\sqrt[]{2}+\sqrt[]{6}}{4} \end{gathered}[/tex]Hence the required reusult is;
[tex]\frac{\sqrt[]{2}+\sqrt[]{6}}{4}[/tex]The cost in dollars for removing p percent of pollutants from a river in Smith County is Find the cost of removing 20%Cost for removing 20%, in dollars is = _________Find the cost of removing half of the pollutants. Cost for removing half, in dollars is = __________ Find the cost of removing all but 5% of the pollutants. Cost for removing all but 5%, in dollars, is = _________
Given the cost of removing p percent of pollutant from a river is Smith County in dollars as
[tex]C(p)=\frac{71000p}{100-p}[/tex]To find the cost of removing the pollutant for a particular percentage, we will substitute the value of the pollutant in the cost formula above.
Thus, for p equal to 20%
[tex]\begin{gathered} C(20)=\frac{71000\times20}{100-20}=\frac{1420000}{80} \\ C(20)=\text{ \$}17,750 \end{gathered}[/tex]Hence, the cost of removing 20% of the pollutant is $17,750
The cost of removing half of the pollutants is equivalent to the cost of removing 50%, thus, p in percentage is 50%
[tex]\begin{gathered} C(50)=\frac{71000\times50}{100-50}=\frac{3550000}{50} \\ C(50)=\text{ \$}71,000 \end{gathered}[/tex]Hence, the cost of removing half of the pollutants is $71,000
The cost of removing all but 5% of the pollutant is equivalent to the cost of removing 95% of the pollutants. Hence, p is 95
[tex]\begin{gathered} C(95)=\frac{71000\times95}{100-95}=\frac{6745000}{5} \\ C(95)=\text{ \$}1,349,000 \end{gathered}[/tex]Hence, the cost of removing all but 5% of the pollutants is $1,349,000
Marco is a newspaper boy who received a total piecework paycheck of $169.12. He receives 56 cents for every newspaper he delivers. How many newspapers did he deliver?
if he receives 56 cents for each period it means that the multiplication must give the total paid
[tex]0.56\times P=169.12[/tex]where P is the number of newspapers
then, solve for p
[tex]P=\frac{169.12}{56}=302[/tex]he delivered 302 newspapers
Solve the following system of linear equations using elimination. x-y=5 -x-y=-11
Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
The given system of equation :
x - y = 5 ( 1 )
- x - y = - 11 ( 2 )
Add the equation ( 1 ) & ( 2 )
x - y + ( -x - y ) = 5 + ( -11 )
x - y -x - y = 5 - 11
x - x - y - y = -6
0 - 2y = - 6
y = -6/( -2)
y = 3
Substitute the value of y = 3 in the equation ( 1)
x - y = 5
x - 3 = 5
x = 5 + 3
x = 8
Answer : x = 8, y = 3
May I please get help with this math problem it’s so confusing
We have to find the value of z and x.
We assume that lines g and h are parallel.
Then, z and the angle with measure 85° are consecutive interior angles.
As they are conscutive interior angles, their measures add 180°.
Then, we can write:
[tex]\begin{gathered} z+85\degree=180\degree \\ z=180-85 \\ z=95\degree \end{gathered}[/tex]Then, we can relate the angle with measure z with the angle with measure (6x-109). They are vertical angles and, therefore, they have the same measure.
Then, we can write:
[tex]\begin{gathered} z=6x-109 \\ 95=6x-109 \\ 95+109=6x \\ 204=6x \\ x=\frac{204}{6} \\ x=34 \end{gathered}[/tex]Answer: z = 95 and x = 34.
I need help with this practice problem solving. It is trigonometry It asks to graph the function, if you can.. use Desmos to do so..
Notice that f(x) is
[tex]h(x)=\cos (x)[/tex]translated π/6 to the left.
Now, recall that the period of the cotangent is
[tex]\pi\text{.}[/tex]Since f(x) is just a translation, both functions have the same period.
Answer:
plot the graph f on the graphf(x)=|1/2x-2|
• We will determine the domain, range and x ;y intercept then plot the graph
1. The domain is given by :
[tex]\begin{gathered} \text{Domain = }x<0\text{ = (-}\infty\text{ },\text{ 0) } \\ \text{ x >0 = ( 0 },\infty)\text{ } \\ \text{ =(-}\infty;0)\text{ U ( 0 ;}\infty) \end{gathered}[/tex]2. Range is given by :
[tex]\begin{gathered} \text{Range = f(x) }\ge0\text{ } \\ \text{ =}\lbrack0;\infty) \end{gathered}[/tex]3. x - and y -intercept :
[tex]x\text{ - intercept = ( }\frac{1}{4};\text{ 0) }[/tex]4. asymptote :
[tex]\begin{gathered} \text{vertical : }x\text{ = 0 } \\ \text{horizontal : y = 2 } \end{gathered}[/tex]Now that we have the necessary points to plot the f(x) = | 1/2x -2 | , the graph will look as follows :2 is less than or equal to y
Solution
[tex]2\leq y[/tex]Why can the big candy makers produce candy that is less expensive per piece
Answer:
Step-by-step explanation:
The reason behind the big candy makers producing candy that is less expensive per price is that the cost that they have to bear for production will be less in comparison to small candy makers.
bc a lot of people buy their products, so they have enough money to make a profit even if they sell it at a lower cost.
The half life of titanium - 44 , a radioactive isotope, is 63 years. If a substance starts out with 1000 kg of titanium- 44( round all the answers to the nearest hundredth of a kilogram or year) A) how much titanium- 44 will remain after 441 years ? B) how long will it be before there is only 1 kg of titanium- 44 ?
a)
Every 63 years, the amount of titanium halves.
441 years later means how many halving?
441/63 = 7 halving
We start off with 1000 and do 7 halving to get the amount of Titanium-44 after 441 years.
[tex]\begin{gathered} 1000(\frac{1}{2})^7 \\ =7.8125 \end{gathered}[/tex]after 441 years, the amount of titanium remaining would be 7.8125 kg
b)
Let's find the point where the remaining titanium would be 1 kg.
That would be:
[tex]1=1000(\frac{1}{2})^t[/tex]t is the time we are looking for. We can solve this using Ln(natural log):
[tex]\begin{gathered} 1=1000(\frac{1}{2})^t \\ 0.001=\frac{1}{2}^t \\ ln(0.001)=\ln (\frac{1}{2}^t) \\ \\ t=\frac{\ln (0.001)}{\ln (\frac{1}{2})} \\ t=9.965 \end{gathered}[/tex]There is basically 9.965 halving. That would make the years approximately:
9.965 * 63 (half life) = 627.795 years (approx)
WILL MARK BEST ANSWER BRAINLIEST
The system of conics has two solutions.
(x−1)2+(y+4)2=25(x−1)225+(y+4)2100=1
What are the solutions to this system of conics?
Enter your answer by filling in the boxes.
Answer:
(2,0) and (-2,0)
Step-by-step explanation:
pls mark me Brainliest
Answer: (-4,-4) (6,-4)
Step-by-step explanation:
I took the test and it said these were the corrects answers.
in the experiment of the preceding exercise, the subjects were randomly assigned to the different treatments. what is the most important reason for this random assignment?
The most important reason for random assignment on the subjects in the experiment, is because random assignment would be the best way in creating group of subjects to the different treatments.
Note that; the group of subjects are roughly equivalent at the beginning of the experiment.
Using random assignment will allow the allocation of different patients to various treatments at a random order. From this there will be objective results obtained altogether from the experiment under investigation.
Random assignment will eliminate any biasness that may occur when conducting the experiment. It prevents favoritism of any event from occurring. It will ensure that all the different patients have an equal chance of being selected for various treatment.
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A table is in the shape of a regularhexagon. The perimeter of the table is 12 ftfeet. What is the length of each side ofthe tableA 1 ftB 2 ftC 3 ftD 4 ft
Solution:
Given the shape of a hexagon;
The perimeter, P, of a hexagon is;
[tex]\begin{gathered} P=6s \\ \\ \text{ Where }s=side\text{ length} \end{gathered}[/tex]Given;
[tex]\begin{gathered} P=12ft \\ \\ s=\frac{12}{6}ft \\ \\ s=2ft \end{gathered}[/tex]CORRECT OPTION: B
Raphael has an odd-shaped field shown in Figure 13-2. He wants to put a four-strand barbed wire fence around it for his cattle.A. What is the perimeter of the field?b. How many 80-rod rolls of barbed wire does he need topurchase?c. How many acres will be fenced?
Answer: Total perimeter = 9, 962.01 feet
The figure is a composite structure
It contains a rectangle and triangle
The perimeter of a rectangle is given as
Perimeter = 2( length + width)
length of the rectangle = 1500ft
Width of the rectangle = 1390 ft
Perimeter = 2( 1500 + 1390)
Perimeter = 2(2890)
Perimeter = 5780 ft
To calculate the perimeter of a triangle
[tex]\begin{gathered} \text{Perimeter = a + b + }\sqrt[]{a^2+b^2} \\ a\text{ = 1050ft and b = 1390 ft} \\ \text{Perimeter = 1050 + 1390 + }\sqrt[]{1050^2+1390^2} \\ \text{Perimeter = 2440 + }\sqrt[]{1,102,\text{ 500 + 1, 932, 100}} \\ \text{Perimeter = 2400 + }\sqrt[]{3,034,600} \\ \text{Perimeter = 2440 + 1,742,01} \\ \text{Perimeter = }4182.01\text{ f}eet \end{gathered}[/tex]The total perimeter of the field = Perimeter of the rectangle + perimeter of the right triangle
Total perimeter = 5780 + 4182.01
Total perimeter = 9, 962.01 feet
Question 19 of 25 Which of these is a factor in this expression? 6z^4 - 4+9 (y² +9) O A. (y +9 O B. 624 - 4 OC. 9 (y +9 OD. -4+9 (y +9)
1) In this expression, we have already a factored form. So the factor in this expression is 9(y³+9) Because multiplying "distributing it" we'll have the whole expression
6z^4 -4+9(y³+9)
6z^4 -4 +9y³+81
2) 9(y³+9)
The data below show the number of hits on a website per week over a random sample of five weeks. Compute the followingstatistics.
We have a sample that is:
[tex]115,39,160,240,176[/tex]a) We can find the median by first sorting the sample:
[tex]39,115,160,176,240[/tex]The median is the value that has 50% of the values below its values.
In this case, this value is in the third place of the sorted sample and has a value of 160.
b) We have to find the mean.
We can calculate it as:
[tex]\begin{gathered} \bar{x}=\frac{1}{n}\sum_{n\mathop{=}1}^5x_i \\ \\ \bar{x}=\frac{1}{5}(115+39+160+240+176) \\ \\ \bar{x}=\frac{1}{5}(730) \\ \\ \bar{x}=146 \end{gathered}[/tex]c) We have to calculate the variance. To find its value we will use the mean value we have just calculated:
[tex]\begin{gathered} s^2=\frac{1}{n}\sum_{n\mathop{=}1}^5(x_i-\bar{x})^2 \\ \\ s^2=\frac{1}{5}[(115-146)^2+(39-146)^2+(160-146)^2+(240-146)^2+(176-146)^2] \\ \\ s^2=\frac{1}{5}[(-31)^2+(-107)^2+(14)^2+(94)^2+(30)^2] \\ \\ s^2=\frac{1}{5}(961+11449+196+8836+900) \\ \\ s^2=\frac{1}{5}(22342) \\ \\ s^2=4468.4 \end{gathered}[/tex]d) We have to calculate the standard deviation. As we have already calculated the variance, we can calculate it as:
[tex]\begin{gathered} s=\sqrt{s^2} \\ s=\sqrt{4468.4} \\ s\approx66.85 \end{gathered}[/tex]e) We now have to find the coefficient of variation:
[tex]CV=\frac{s}{\bar{x}}=\frac{66.85}{146}\approx0.457876\cdot100\%\approx46\%[/tex]Answer:
a) 160
b) 146
c) 4468.4
d) 66.85
e) 46%
Question 6 (1 point)Below are four scenarios where counting is involved. Select those scenarios in whichPERMUTATIONS are involved. There may be more than one permutation.How many possible ways can a group of 10 runners finish first, second andthird?How many ways can 2 females and 1male be selected for a conference from alarger group of 5 females and males?How many 3 letter arrangements of the word OLDWAYS are there?How many 5-card hands from a standard deck of cards would result in allspades?Previous PageNext PagePage 6 of 12
Step 1: Definition
Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations.
Step 2:
How many possible ways can a group of 10 runners finish first, second and third?
PERMUTATION because it involved arrangement
Step 3:
How many ways can 2 females and 1 male be selected for a conference from a larger group of 5 females and males?
NOT PERMUTATION because it involved selection, hence it is a combination.
Step 4:
How many 3 letter arrangements of the word OLDWAYS are there?
PERMUTATION because it involved arrangement
Step 5:
How many 5-card hands from a standard deck of cards would result in all spades?
NOT PERMUTATION because it involved selection, hence it is a combination.
320000 in decimal form
Answer:
320×10³
Step-by-step explanation:
This is the standard form for the number 320000
hope it helps
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Select all the correct locations on the image.Which statements are logically equivalent to (p q)?
-(p ∧ q ) is logically equivalent to
-pv-q
what is the probability that a student will be in both chemistry and math but not Spanish round to three decimal places
Answer :
3/13
Explanation :
The probablity of an event = favourable outcome / total outcomes
Now in our case,
favorable outcome = 60
Total number of outcomes = 5 + 70 + 5 + 85 + 60 + 15 + 3 + 17 = 260
Therefore,
probablity = 60 / 260
= 3 /13
Find the equation for the line through points (-3,1) and (4,7) use y=Mx+b
A = (-3, 1) and B = (4,7)
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{7-1}{4-(-3)}=\frac{6}{7}[/tex][tex]y=\frac{6}{7}x+b[/tex]Now, for b, using point B
[tex](7)=\frac{6}{7}(4)+b[/tex][tex]b=7-\frac{6}{7}(4)\rightarrow b=\frac{25}{7}[/tex][tex]y=\frac{6}{7}x+\frac{25}{7}[/tex]