Given data:
The given amount of liquid fertilizer is f=4.
The given water is w=6 gallons.
4 tablespoons= 6 gallons of water
1 tablespoon= 1.5 gallons of water.
Thus, 1.5 gallons of water is mix with each tablespoon.
the volume of a sphere is 12348 pi in ³ calculate the radius of the sphere
The volume of a sphere is given by the expression:
[tex]V=\frac{4}{3}\pi\cdot r^3[/tex]Where V is the volume and r is the radius of the sphere. Solve this expression for r and replace for the given values to find the radius of the sphere, this way:
[tex]\begin{gathered} V=\frac{4}{3}\pi\cdot r^3 \\ 12348\pi=\frac{4}{3}\pi\cdot r^3 \\ \frac{12348\pi}{\pi}\cdot\frac{3}{4}=r^3 \\ 9261=r^3 \\ r=\sqrt[3]{9261} \\ r=21 \end{gathered}[/tex]The radius of the sphere is 21 inches.
2x+y=21;y=-2x+21please hurry I need this straight away use any method
Answer:
(k, -2k+21) where k is any integer
Explanation:
Given the following simultaneous equation;
2x+y=21 ..... 1
y=-2x+21 ..... 2
Subtitute equation 2 into 1:
2x + (-2x+21) = 21
2x -2x+21 = 21
0x = 21-21
0x = 0
x = 0/0
Since the variables cannot be determined, we will subtitute x = k
Substitute x = k into equation 2;
From 2: y = -2x+21
y = -2k+21
Hence the solution to the system of equation is (k, -2k+21) where k is any integer
For each scenario below, choose the graph that gives the best representation.(A) Carlos is driving on the freeway at a constant speed. He then speeds up to pass a truck, After passing the truck, he exits the freeway and slows down.(B) Rachel is delivering a pizza to Mark's house. She drives at a constant speed toward the house until she hits a traffic jam and has to stop for severalminutes. After, she starts up again and drives at a faster speed than before.
Given:
Given the word problem, we can deduce the following information:
a)
1. Carlos is driving on the freeway at a constant speed.
2. He then speeds up, and exits the freeway and slows down.
Based on hte given information, the graph should have a constant or horizontal line at the first part, increases as he speeds up on the second part, and decreases as he slows down.
Thus the graph should be:
b)
1. Rachel is delivering at a constant speed toward the house until she hits a traffic jam and has to stop for several minutes.
2. She starts up again and drives at a faster speed than before.
So based on the given information, the graph should have a horizontal line at the first part since Rachel is driving at a constant speed. Next, the line should be increasing and higher than the horizontal line since Rachel is driving at a faster speed than before.
Therefore, the graph is:
Given the following frequency table of values, iIs the mean, median, or mode likely to be the best measure of the center for the data set? ValueFrequency211220230240250260270280290300310320330340352363371380392404413Select the correct answer below:ModeMeanMedian
Solution
In the dataset given. The distribution is skewed.
The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution)
Thus, the correct answer is median
The salaries of the employees at four companies are summarized below. Answer the question about them.
Given,
Company A: the range of the salaries is $60000 and the mean salary is $22000.
Company B: the range of the salaries is $58000 and the mean salary is $29000.
Company C: the range of the salaries is $67000 and the mean salary is $27000.
Company D: the range of the salaries is $63000 and the mean salary is $28000.
Required
The company have least average salary and least variability.
a) From the given data, it is clearly seen that the company that have the lowest salary is $22000.
Hence, the company that have the lowest salary is Company A.
b)From the given data, it is clearly seen that the company that have the least salary variability is $58000.
Hence, the company that have the least salary variability is Company B.
Find the median for the scores: 93,69,72,86,72,95,88,74,72,89,89,95,74,79
A set of data is given and it is required to find the median:
[tex]93,69,72,86,72,95,88,74,72,89,89,95,74,79[/tex]Recall that the Median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Hence, to find the median, rearrange the scores either in ascending or descending order.
[tex]69,72,72,72,74,74,79,86,88,89,89,93,95,95[/tex]Next, highlight the two middle numbers since the frequency of the scores is even (14):
[tex]69,72,72,72,74,74,\boxed{79,86},88,89,89,93,95,95[/tex]Find the mean of the two middle numbers to calculate the median for the scores:
[tex]\frac{79+86}{2}=\frac{165}{2}=82.5[/tex]Hence, the median score is 82.5.
The median score is 82.5.
Question 60 state wether the triangle is an isosceles triangle,right triangle, neither of these or both.
Given:
The points of the triangle:
[tex]P_1=(7,2);P_2=(-4,0);P_3=(4,6)[/tex]Required:
To find out if the given triangle is an equilateral triangle or an isosceles triangle or both or none of these.
Explanation:
To find if the triangle is an equilateral triangle or an isosceles triangle we will have to first find the length of the sides by distance formula.
Distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)_^2+(y_2-y_1)^2}[/tex]So applying the distance formula on side P₁P₂
Substituting the value of P₁ and P₂ in the distance formula we get
[tex]P₁P₂=\sqrt{(-4-7)^2+(0-2)^2}=\sqrt{(-11)^2+(-2)^2}=\sqrt{121+4}=\sqrt{125}=5\sqrt{5}[/tex]Now lets find the length of P₂P₃
Substituting the value of P₂ and P₃ in the distance formula we get
[tex]P₂P₃=\sqrt{(4-(-4))^2+(6-0)^2}=\sqrt{(4+4)^2+6^2}=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10[/tex]Now lets find the length of P₁P₃
Substituting the value of P₁ and P₃ in the distance formula we get
[tex]P₁P₃=\sqrt{(4-7)^2+(6-2)^2}=\sqrt{(-3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]S now we have the length of all three sides, that is
[tex]\begin{gathered} l(P₁P₂)=5\sqrt{5} \\ \\ l(P_2P_3)=10 \\ \\ l(P₁P_3)=5 \end{gathered}[/tex]If we add any two sides of triangle then it is greater than the third side so it is a triangle.
[tex]\begin{gathered} 5\sqrt{5}+5>10 \\ 5+10>5\sqrt{5} \\ 5\sqrt{5}+10>5 \end{gathered}[/tex]So it is a valid triangle. But the length of all the sides of triangle are different.
In equilateral triangle all the sides are same.
In isosceles triangle any sides are same.
Since here none of the sides are same so it is neither an equilateral triangle nor an isosceles triangle. It is a Scalene triangle with all three sides different.
Final answer:
The answer is none of these.
you roll a six-sided number cube find theprobabilsty of rolling each of the followingP(1 or 6)
When you roll a six-sided number cube you can get the next set of possible results:
[tex]\lbrace1,2,3,4,5,6\rbrace[/tex]You have a total of 6 possible results.
From the set of possible results you get the set of presults that are 1 or 6:
[tex]\lbrace1,6\rbrace[/tex]You have 2 results that are 1 or 6
The probability of rolling (1 or 6) is: The number of results that are 1 or 6 divided in the total number of possible results:
[tex]P(1or6)=\frac{2}{6}=\frac{1}{3}[/tex]Then, the probability of rolling (1 or 6) is 1/3Graph the function by first finding the relative extrema. f(x) = x² + 4x2-x-4 7 4 6 2
Graph the function by first finding the relative extrema.
__________________________________
f(x) = x^3 + 4x^2 - x - 4
f'(x) = 3x ^2 + 8x -1
c= 3x ^2 + 8x -1
Using the quadratic equation
[tex]x=\frac{-b\text{ }\pm\text{ }^{}\sqrt[]{b^2\text{ -4ac}}}{2a}\text{ = }\frac{-(8)\text{ }\pm\text{ }^{}\sqrt[]{8^2\text{ -4}\cdot3\cdot\text{ (-1)}}}{2\cdot3}[/tex]___________________
They want you to see the extreme points, but the easiest way is to evaluate 0 and check which graph matches
f(0) = 0^3 + 40^2 - 0 - 4
Point (0, -4)
Fill in the table using function rule
Y=6x+2
Using our equation y = 6x + 2, we were able to write out values for our table of function.
Function TableA function table is a table that shows which coordinates should be plotted in the coordinate system, so that you can draw the graph of the function.
Since we have our equation, we can proceed to find what values of y we would have when x is in a certain condition.
Using from -2 to + 5, we can have a good table of function.
When x = -2
y = 6x + 2
y = 6(-2) + 2 = -10
When x = -1
y = 6(-1) + 2 = -4
When x = 0
y = 6(0) + 2 = 2
When x = 1
y = 6(1) + 2 = 8
When x = 2
y = 6(2) + 2 = 14
When x = 3
y = 6(3) + 2 = 20
When x = 4
y = 6(4) + 2 = 26
When x = 5
y = 6(5) + 2 = 32
Using the values above, we have a good function table and can proceed to plot a graph if needed.
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Combine like terms and write each expression in standard form
SOLUTION
From the expression
[tex]x^2-5+2x+x^2[/tex]combining like terms we have to bring the x-squares together, we have
[tex]\begin{gathered} x^2+x^2-5+2x \\ 2x^2-5+2x \end{gathered}[/tex]To write in standard form, the 2x should come before the -5, so we have
[tex]2x^2+2x-5[/tex]Hence the answer is
[tex]2x^2+2x-5[/tex]To which subset of the real numbers does 22‾√ belong?
Ok
Squared root of 2 is a irrational number because it can not be expressed as a fraction.
So the correct choice is Irrational, the last one.
Function gis represented by the equation.g(x)=9(1/3)^x-4Which statement correctly compares the two functions?
So,
As you can see, the function g:
[tex]g(x)=9(\frac{1}{3})^x-4[/tex]Has the same behavior of the graph above.
That's because the rate (1/3) is less than 1, so the graph will decay.
The y- intercept of the function g is obtained when we make x=0:
[tex]\begin{gathered} g(0)=9(\frac{1}{3})^0-4 \\ g(0)=9-4 \\ g(0)=5 \end{gathered}[/tex]If we compare, both y-intercepts seem to be different.
Therefore,
I WILL GIVE BRAINLIEST
Juan bought three and three-fourths pounds of pineapple and three and three-eighths pounds of strawberries for a fruit salad. After eating one and fifteen-sixteenths pounds of the fruit salad, how much was left?
five and three-sixteenths pounds
five and three-eighths pounds
five and nine-sixteenths pounds
seven and twenty-one sixteenths pounds
Salad was left (A) Five and three-sixteenths pounds.
Fraction is the comparison between numbers or mathematical quantities.
Given that, Juan bought pineapple of = (3 + 3/4) pounds = 15/4 pounds
Juan bought strawberries of = (3 + 3/8) pounds = 27/8 pounds
So now the amount total fruit salad = 15/4 + 27/8 = (30+27)/8 = 57/8 pounds
Juan eats = (1+15/16) = 31/16 pounds
Now salad left = 57/8 - 31/16 = (114-31)/16 = 83/16 = (5+3/16) pounds
Hence the correct option is (A).
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what is the distance between -1 1/2 +5. Find absolute value
To find the absolute value of -1 1/2 +5 you make the addition:
You can write the mixed number also as -3/2 (because -1 is equal to -2/2 and -2/2 and 1/2 is -3/2).
You add fractions as follow:
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex]You can write the 5 as 5/1:
[tex]-\frac{3}{2}+\frac{5}{1}=\frac{-3\cdot1+5\cdot2}{2\cdot1}=\frac{-3+10}{2}=\frac{7}{2}[/tex]As the addition of the given numbers is 7/2, the absolute value or the distance is:
[tex]\lvert\pm a\rvert=a[/tex][tex]\lvert-1\frac{1}{2}+5\rvert=\lvert\frac{7}{2}\rvert=\frac{7}{2}[/tex]Then, the distance is 7/2Without graphing, find the slope of the line that goes through each pair of coordinate points. (0,5) and (8,2 ) [Choose ] (2,-1) and (6, 1) [ Choose ] (-3,-2) and (- 1,-5) [ Choose]
Answers:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
Explanation:
The slope of a line that goes through two points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, the slope of a line that goes through (0,5) and (8,2) is equal to:
[tex]m=\frac{2-0}{8-5}=\frac{2}{3}[/tex]The slope of a line that goes through (2, -1) and (6, 1) is:
[tex]m=\frac{1-(-1)}{6-2}=\frac{1+1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]The slope of a line that goes through (-3, -2) and (-1, -5) is:
[tex]m=\frac{-5-(-2)}{-1-(-3)}=\frac{-5+2}{-1+3}=-\frac{3}{2}[/tex]Therefore, the answers are:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
Determine the most specific name for quadrilateral JKLM if the coordinates of the vertices are:J(-4,6), K(-1,2), L(1,6), M(4,2)JL ll KM PROOF:J.5JL is parallel to X-axis.bothvertices have y-coordinate at y = 6.KM Parallel to x axis, bothvertices have y-coordinate aty=2.43KM M1Determine Stopes of JK & LM(If slopes ave ithen sides arparallel):4517-42-8-3-10JK: 31-4,6) K(+1,2)x2 Y2xiyo2-6-4
To finish the demonstration that the quadrilateral JKLM is a rhombus we need to prove that side JK is congruent with side LM.
The length of a segment with endpoints (x1, y1) and (x2, y2) is calculated as follows:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting with points L(1,6) and M(4,2) we get:
[tex]\begin{gathered} LM=\sqrt[]{(4-1)^2+(2-6)^2} \\ LM=\sqrt[]{3^2+(-4)^2} \\ LM=\sqrt[]{9+16^{}} \\ LM=5 \end{gathered}[/tex]Given that opposite sides are parallel, all sides have the same length, and, from the diagram, the quadrilateral is not a square, we conclude that it is a rhombus.
Given that events "A" and "B" are independent, P(A) = 0.80, and P(A and B) = 0.24, what is P(B)?
Answer:
P(B)=0.3
Explanation:
Given two independent events, A and B:
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Substitute the given values:
[tex]\begin{gathered} 0.24=0.8\times P(B) \\ \text{ Divide both sides by 0.8} \\ \frac{0.24}{0.8}=\frac{0.8\times P(B)}{0.8} \\ P(B)=0.3 \end{gathered}[/tex]The probability of event B is 0.3.
it is a graph I will send a picture of it
SOLUTION
The image of f(x) is given in the diagram.
Then the image of the function
[tex]f(x)-1\text{ means the f(x) as b}een\text{ shifted vertically down by one unit }[/tex]Thence the image of f(x)-1 is given below as
Therefore the right option is A
A drawer is filled with 2 black shirts, 7 white shirts, and 11 gray shirts.One shirt is chosen at random from the drawer. Find the probability that it is not a black shirt.Write your answer as a fraction. I need help with this math problem
There is a total of 2 + 7 + 11 = 20 shirts
Mackenzie has a bag that contains 6 red marbles, 4 blue marbles, and 14yellow marbles. If she chooses one marble from the bag, what is theprobability that the marble is not yellow?O A. 7/ 금B.LINdC.soOD.
Probability that the marble is not yellow = 5/12
Explanations:Number of red marbles, N(Red) = 6
Number of blue marbles, N(Blue) = 4
Number of yellow maebles, N(Yellow) = 14
Total number of marbles, N(Total) = N(Red) + N(Blue) + N(Yellow)
N(Total) = 6 + 4 + 14
N(Total) = 24
Probability that the marble chosen is yellow, P(yellow) = N(yellow) / N(Total)
P(yellow) = 14/24
P(yellow) = 7/12
P(yellow) + P(not yellow) = 1
P(not yellow) = 1 - P(yellow)
P(not yellow) = 1 - 7/12
P(not yellow) = 5/12
Probability that the marble is not yellow = 5/12
I would like some help solving this step by step please
in rst the measure of ∠J=90° the measure of ∠H=69° and Hl=88 feet. find the length of JH to the nearest tenth of a foot
From the information provided, we can construct the following triangle;
The measure of angle J is 90 degrees, the measure of angle H is 69 degrees and line HI measures 88 feet. Therefore to calculate line JH;
[tex]\begin{gathered} \cos \theta=\frac{adj}{hyp} \\ \cos 69=\frac{JH}{88} \\ \text{Cross multiply and you'll have;} \\ 88\times\cos 69=JH \\ 88\times0.35836794\ldots=JH \\ 31.5363\ldots=JH \\ JH\approx31.5ft \end{gathered}[/tex]The answer is 31.5 feet (rounded to the nearest tenth of a foot
A travel agency polled its customers about their favorite kind of vacation. The results of the survey are shown in the given two-way frequency table.
Vacation Preferences
Seaside Mountain Historical Sightseeing Total
Female 38 36 32 17 123
Male 43 52 23 19 137
Total 81 88 55 36 260
What is the marginal relative frequency of customers who prefer sightseeing vacations?
A.
0.47
B.
0.21
C.
0.14
D.
0.89
The marginal relative frequency of customers who prefer sightseeing vacations is (C) 0.14
The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.
[tex]Marginal relative frequency = \frac{sightseeing(total)}{Total}[/tex]
= 36/260
= 0.1385
≅ 0.14
Hence, marginal relative frequency of customers who prefer sightseeing vacations is 0.14.
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50 points!
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 3
Hope this helps!
Step-by-step explanation:
ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6[tex]\sqrt{2}[/tex] ) can be [tex]x\sqrt{2}[/tex] while AB and CB are x. Because 6[tex]\sqrt{2}[/tex] is equal to [tex]x\sqrt{2}[/tex], you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD = [tex]x\sqrt{3}[/tex]. CB is equal to 6 so 2x = 6, x = 3.
Simplify. (-3)2 -32 -30
We need to simplify the next given expression:
[tex](-3)^2-3^2-3^0[/tex]Let's solve each term:
[tex](-3)^2=(-3)(-3)=9[/tex][tex]3^2=3\cdot3=9[/tex]Finally, for the last term we need to use the next property:
[tex]a^0=1[/tex]Every whole number with an exponent of 0 will always equal one.
Therefore:
[tex]3^0=1[/tex]Now, we have the next expression:
[tex]9-9-1[/tex][tex]=-1[/tex]Hence, when we simplified the expression the result is -1.
6. Andre is drawing a triangle that is congruent to this one.He begins by constructing an angle congruent to angleLKJ. What is the least amount of additional informationthat Andre needs to construct a triangle congruent tothis one?
The measure of an angle
The measure of two legs
1) Andre can construct a congruent triangle using SAS congruence, knowing the angle congruent to LKJ and with a compass measure two legs of that triangle
2) Sketching out we have:
Notice that either with a protractor or with a compass we can measure congruent angles and based on SAS congruence we need two congruent legs to determine a SAS congruence.
3) Hence, Andre needs at least:
The measure of an angle
The measure of two legs
Need help with figuring out if this is a system of equations
Given:
The system is:
[tex]\begin{cases}{2x+3y+10z=9} \\ {-x+2y+5z=1} \\ {3x+z=5}\end{cases}[/tex]The solution is (2,3,-1)
Find-:
The (2,3,-1) is the solution of function or not
Explanation-:
The solution is (2,3,-1) which means:
[tex]\begin{gathered} x=2 \\ \\ y=3 \\ \\ z=-1 \end{gathered}[/tex]Check the value for the given expression:
[tex]\begin{gathered} 2x+3y+10z=9 \\ \\ 2(2)+3(3)+10(-1)=9 \\ \\ 4+9-10=9 \\ \\ 3\ne9 \end{gathered}[/tex]So, it is not a solution of system.
Give an interval over which the function is increasing. Give an interval over which it is decreasing
one interval where the function is increasing is
(-3;1)
one interval where the function is decreasing is
(1;4)
Area of a triangle Find the area of the triangle below. Be sure to include the correct unit in your answer. Explanation Check 9 cml 19 cm 10 cm A 0 cm X cm² cm³ ?
Given
To find:
The area of the triangle.
Explanation:
It is given that,
That implies,
The area of the triangle is,
[tex]\begin{gathered} A=\frac{1}{2}\times b\times h \\ =\frac{1}{2}\times10\times9 \\ =5\times9 \\ =45cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 45cm
²