Answer:
V=11*7*9=693
Step-by-step explanation:
V=Bh ( B is the base area ( base*height) , and h is the height of the prism)
find B=base*h
B=11*7=77 in²
V=B*h=77*9=693 in³
The volume of the triangular prism is 174.25 in³.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, the triangular base has a base of 11 inches and height of 7 inches.
The formula for finding the volume of a triangular prism is V = (base area x height) / 2.
In this case, the base area of the triangle can be calculated using the formula A = (1/2)bh, where b is the base length and h is the height.
In this case, b = 11 inches and h = 7 inches, so the base area is A = (1/2)(11)(7) = 38.5 inches squared.
Now that we have the base area, we can calculate the volume of the triangular prism: V = (38.5 inches² x 9 inches) / 2 = 174.25 in³.
Therefore, the volume of the triangular prism is 174.25 in³.
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The areas of the squares adjacent to two sides of a right triangle are shown below
Answer:
The area of the square is 85 units^2
Step-by-step explanation:
Okay, here in this question, we are interested in calculating the area of the unknown square.
Kindly note that, since each of the other shapes are squares too, it means that the length of their sides is simply the square root of their areas.
Thus, the length of the squares are ;
√35 units and √50 units respectively
Now to find the area of the larger square, we employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Let’s call the unknown length X
x^2 = (√35)^2 + (√50)^2
x^2 = 35 + 50
x^2 = 85
x = √85 units
Now as we know that the area of a square is simply the length of the side squared,
The area of the biggest square is simply (√85)^2 = 85 units^2
Points A and B are on ⊙O and m∠AOB=76. If △AOB is drawn, find m∠OAB. NO OTHER INFORMATION WAS GIVEN WITH THIS QUESTION!!
Answer:
52°
Step-by-step explanation:
Angle AOB is the a.pex angle of the isosceles triangle AOB.* Then angles at A and B are congruent and each is the complement of half the angle at O:
∠OAB = 90° -(1/2)(76°) = 90° -38°
∠OAB = 52°
_____
* You know ΔAOB is isosceles because OA and OB are both radii of the circle, hence the same length.
Which of the following shows the division problem below in synthetic division form?
Answer: D
Step-by-step explanation:
In synthetic division, if the divisor is an expression like x+3, you should always switch it to if x+3 were equal to 0.
[tex]x+3=0\\x=-3[/tex]
So, you should use -3. The only options with -3 are B and D.
The coefficients for the dividend are 7, -2, and 4, so D is the correct answer.
Hope this helps! If you still have questions, please ask.
I need someone to answer this immediately please. ... The area of a piece of land is 50cm square. Fi d the value of x, if the length
and breadth are given as (x+2) and (x-3)m respectively
options. A. 3
B. 5
C. 7
D. 8
Answer:
x=8
Step-by-step explanation:
Area is equal to
A = l * w
50 = ( x+2) ( x-3)
FOIL
50 = x^2 -3x+2x -6
Combine like terms
50 = x^2 -x -6
Subtract 50 from each side
0 = x^2 -x -56
Factor
What two numbers multiply to -56 and add to -1
-8*7 = -56
-8+7 = -1
0 = ( x-8) ( x+7)
Using the zero product property
x-8 =0 x+7 =0
x = 8 x=-7
Since the length cannot be negative x cannot be negative
x=8
Answer:
8
Step-by-step explanation:
put the 50 under area and continue with like that
how do you know if the solutions to a quadratic equations are inside, outside, on, inside and on, or outside and on the parabola? with the different equality signs?
Answer:
Option (1)
Step-by-step explanation:
Given quadratic equation in this question is,
y < -x²+ 4x + 5
Now we will convert this standard quadratic equation into vertex form,
y < -(x² - 4x) + 5
y < -[x² - 2(2)x + 2²] + 5
y < -(x - 2)²+ 5
This equation is in the form of y < a(x - h)² + k
where (h, k) is the vertex of the parabola.
Therefore, y < -(x - 2)²+ 5 will show the parabola with properties as,
1). Parabola having vertex at (2, 5).
2). Coefficient 'a' is negative, so parabola will open downwards.
3). In the inequality notation of less than, (sign < ) will show the solution area inside the parabola.
[If an inequality has a sign of greater than, solution area will be outside the parabola.]
Therefore, Option (1) will be the answer.
find the equation of a circle which passes through the point (2,-2) and (3,4) and whose centre lies on the line x+y=2
Answer:
Equation of the circle
(x - 0.7)² + (y - 1.3)² = 12.58
Step-by-step explanation:
The formula for the equation of a circle is given as:
(x - a)² + (y - b)² = r²,
where(a, b) is the center of the circle and r = radius of the circle.
a) We are told in the question that the equation of the circle passes through point(2, -2)
Hence,
Substituting 2 for x and -2 for y in the equation of the circle.
(x - a)² + (y - b)² = r²
(2 - a)² +(-2 - b)² = r²
Expanding the bracket
(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²
4 - 2a - 2a +a² +4 +2b +2b +b² = r²
4 - 4a + a² + 4 + 4b + b² = r²
a² + b² -4a + 4b + 4 + 4 = r²
a² + b² -4a + 4b + 8 = r²............Equation 1
We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y
Hence,
Substituting 3 for x and 4 for y in the equation of the circle.
(x - a)² + (y - b)² = r²
(3 - a)² +(4 - b)² = r²
Expanding the bracket
(3 - a) (3 - a) + (4 - b)(4- b) = r²
9 - 3a - 3a +a² +16 -4b -4b +b² = r²
9 -6a + a² + 16 -8b + b² = r²
a² + b² -6a -8b + 9 + 16 = r²
a² + b² -6a -8b + 25 = r²..........Equation 2
The next step would be to subtract Equation 1 from Equation 2
a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²
a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²
Collecting like terms
a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0
2a + 12b -17 = 0
2a + 12b = 17...........Equation 3
Step 2
We are going to have to find the values of a and b in other to get our equation of the circle.
Since the center of the circle(a, b) lies on x + y = 2
Therefore, we have
a + b = 2
a = 2 - b
2a + 12b = 17 ..........Equation 3
Substituting 2 - b for a in
2(2 - b) + 12b = 17
4 - 2b + 12b = 17
4 + 10b = 17
10b = 17 - 4
10b = 13
b = 13/10
b = 1.3
Substituting 1.3 for b in
a + b = 2
a + 1.3 = 2
a = 2 - 1.3
a = 0.7
hence, a = 0.7, b = 1.3
Step 3
We have to find the value of r using points (2, -2)
(x - a)² + (y - b)² = r²
Where x = 2 and y = -2
(-2 - 0.7)² + (-2 - 1.3)² = r²
(-2.7)² + (-3.3)² = r²
1.69 + 10.89 = r²
r² = 12.58
r = √12.58 = 3.55
Step 4
The formula for the equation of a circle is given as:
(x - a)² + (y - b)² = r²,
where(a, b) is the center of the circle and r = radius of the circle
a = 0.7
b = 1.3
r² = 12.58
Equation of the circle =
(x - 0.7)² + (y - 1.3)² = 12.58
Find the slope of the line that contains (6, 2) and (6,-3).
Find the slope of the line through the points (-4,-7) and (4, 3).
Answer:
A. Undefined slope (no slope)
B. [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
A slope is rise over run.
The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.
However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.
Hope this helped!
Match each correlation coefficient, r, to its description.
weak negative
correlation
weak positive
correlation
strong positive
correlation
strong negative
correlation
r = −0.83
arrowRight
r = −0.08
arrowRight
r = 0.96
arrowRight
r = 0.06
arrowRight
Answer:
r = -0.83
strong negative correlation
r = -0.08
weak negative correlation
r = 0.96
strong positive correlation
r = 0.06
weak positive correlation
Step-by-step explanation:
In this question, what we are expected to do is to match the values of the correlation given with the type of correlation in which the values are.
When we talk of correlation, we are simply referring to the extent of agreement between the values in the data field.
Correlation has a value between -1 and +1, meaning it could be negative or positive.
Values closer to the extremes i.e (-1 or +1) indicates strong correlation while values farther away, i.e closer to zero indicates a weak relationship.
Let’s answer the questions specifically now:
r = -0.83
This is closer to -1 and it indicates a strong negative correlation
r = -0.08
This indicates a weak negative correlation as it is closer to zero and farther away form -1
r = 0.96
This indicates a strong positive correlation
r = 0.06
This indicates a weak positive correlation
What is the midpoint of the line segment with endpoints (3.5, 2.2) and (1.5, -4.8)
Answer:
2.5, -1.8
Step-by-step explanation:
½(x¹+x²) ,½(y¹+y²)
½(3.5+1.5) ,½(2.2+(-4.8)
½(5.0), ½(2.2-4.8)
2.5 ,½(-3.6)
2.5, -1.8
Answer: It’s 2.5, -1.3, the other person must’ve misclicked lol
A 450m long field is drawn to a scale 1cm to 90cm.find the lenth of drawing
Answer:
5 cm
Step-by-step explanation:
The length of the drawing will be 450 / 90 = 5 cm.
. Factorize a² +3ab - 5ab - 15b²
Answer:
a² +3ab - 5ab - 15b² = (a+3b) (a-5b)
Step-by-step explanation:
We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,
[tex]a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)[/tex]
Now taking a common from the first two terms and 3b from last two terms, then :
[tex](a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)[/tex]
In the above expression, a factor (a-5b) is in both the terms. It would mean that,
[tex]a(a-5b)+3b(a-5b)=(a+3b)(a-5b)[/tex]
So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).
Write the equation of a circle with center (7, -12) and radius 9.
Answer:
( x-7)^2 + ( y+12) ^2 = 81
Step-by-step explanation:
The equation of a circle can be written in the form
( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-7)^2 + ( y--12) ^2 = 9^2
( x-7)^2 + ( y+12) ^2 = 81
Answer:
(x - 7)² + (y + 12)² = 81
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
Here (h, k) = (7, - 12) and r = 9, thus
(x - 7)² + (y - (- 12))² = 9², that is
(x - 7)² + (y + 12)²= 81
Determine whether the data set is a population or a sample. Explain your reasoning. The salary of each teacher in a school. Choose the correct answer below. A. Sample, because it is a collection of salaries for all teachers in the school comma but there are other schools. B. Population, because it is a subset of all schools in the city. C. Sample, because it is a collection of salaries for some teachers in the school. nothing D. Population, because it is a collection of salaries for all teachers in the school.
Answer:
D. Population, because it is a collection of salaries for all teachers in the school.
Step-by-step explanation:
In research, population refers to a complete set of subjects that share a characteristic and that the researcher is interested in. On the other hand, a sample is a subset of a population and it's usually the one the researcher takes to make a study with.
In this example, we have "The salary of each teacher in a school" since we are taking ALL the teachers of this school, this would be a population. If we were working with the salary of only a portion of the teachers of said school, it would be a sample.
Thus, the right answer is D. Population, because it is a collection of salaries for all teachers in the school.
6x+3y=54 2x+y=18 system of equation using substitution
Answer:
[tex]\boxed{x=R}[/tex], where R stands for all real numbers.
Step-by-step explanation:
Part 1: Solving one equation for its variable
First, we need to solve one of the equations for one of its variables. I will use the second equation.
[tex]2x+y=18[/tex] Subtract [tex]2x[/tex] from both sides to isolate the [tex]y[/tex].
[tex]\boxed{y = -2x + 18}[/tex]
Part 2: Substituting the solved variable value into the other equation
Now, simply substitute this value in the place of the [tex]y[/tex] in the first equation and solve for [tex]x[/tex].
[tex]6x+3(-2x+18) =54[/tex] Distribute the coefficient of the equation.
[tex]6x -6x + 54 = 54[/tex] Simplify the equation.
[tex]0 = 0[/tex]
This answer is perfectly okay to get. This means that your equations have an infinite number of solutions.
Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. Find the measure of each central angle in the circle graph for the following: a.sleeping b.eating
Answer:
C) 118.8; 28.8
Step-by-step explanation:
for eating, it didn't make sense for it to be 288 degrees, so i eliminated the two off the list. For sleeping, it made more sense for it to be a 118.8 degree angle, so I narrowed it down to C.
The central angle for sleeping is 118.8 degrees and the central angle for eating is 28.8 degrees.
What is the central angle of a pie chart?
The angle formed by an arc of the circle at the center of the circle is called central angle of a pie chart.
How to find the central angle of a pie chart?central angle = [tex]\frac{sector}{100}[/tex] × 360
According to the given question
We have a pie chart
In which, time spend by students in different activities is given.
Now,
The measure of central angle for sleeping is given by
Central angle for sleeping = [tex]\frac{sector}{100}[/tex] × 360
⇒ Central angle for sleeping =[tex]\frac{33}{100}[/tex] × 360 = 118.8 degrees.
Similarly,
The measure of central angle for eating is given by
Central angle for eating = [tex]\frac{8}{100}[/tex] × 360 = 28.8 degrees
Hence, first option is correct.
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SIMPLIFY. m2 x m5 x m3=???? PLEASE HELP!!!!
Answer:
[tex]m^{10}[/tex]
Step-by-step explanation:
[tex]m^2m^5m^3\\=m^{2+5+3}\\\\=m^{10}[/tex]
===============================================
Explanation:
I'm assuming you meant to write m^2 * m^5 * m^3
If so, you add the exponents to get 2+5+3 = 10 which is the exponent over the original base m. The base does not change.
The rule I used is a^b*a^c = a^(b+c). We see that the base stays the same at 'a' the whole time.
-----------
A longer way to do this is to expand out m^2 into m*m. We have two copies of m multiplied together.
Similarly, m^5 = m*m*m*m*m. We have five copies now.
Saying m^2*m^5 will have seven copies because
m^2*m^5 = (m*m) times (m*m*m*m*m) = m*m*m*m*m*m*m = m^7
Tacking on m^3 will add on three more copies of m to multiply out, giving 10 copies of m total to multiply. This alternative method is not advised since there is a possibility to lose track and make an error somewhere. The formula in the previous section is preferred. Though I recommend you try this second method out to see how/why the formula works.
Please answer this in two minutes
Answer: 9.9
Step-by-step explanation:
SINE RULE:
7/sin(31) = q / sin(47)
Therefore q = 7 / sin(31) * sin(47)
which equals: 9.9 to the nearest tenth.
Answer:
q = 9.9
Step-by-step explanation:
We can use the rule of sines
sin R sin Q
------------- = ------------
PQ PR
sin 31 sin 47
------------- = ------------
7 q
Using cross products
q sin 31 = 7 sin 47
Divide by sin 31
q = 7 sin 47 / sin 31
q =9.939995043
To the nearest tenth
q = 9.9
Find the Equation of the Parallel Line
of
Instructions: Find the equation of the line through point (-1, 4) and parallel to
5x +y = 4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for ).
y =
Answer:
y = -5x - 1
Step-by-step explanation:
Let the equation of a line parallel to the given line is,
y - y' = m(x - x')
Where m = slope of the line
And line passes through (x', y')
Equation of a line has been given as,
5x + y = 4
y = -5x + 4
Slope of this line = -5
By the property of parallel lines "slope of the parallel lines are same",
m = -5
Parallel line passing through (-1, 4) and slope 'm' = -5 will be,
y - 4 = -5(x + 1)
y - 4 = -5x - 5
y = -5x - 5 + 4
y = -5x - 1
Therefore, equation of the parallel line will be,
y = -5x - 1
You want to install a 1 yd. Wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Answer:
75.36 yd²
Step-by-step explanation:
To solve, you need to consider the walkway and the pool as one circle and find the are. The diameter of this circle is 25 yd. This means that the radius is 12.5 yd.
A = πr²
A = π(12.5)²
A = 156.25π
A = 490.625 yd²
Then, you need to find the area of the pool alone. Since the diameter of the pool is 23 yd., the radius is 11.5 yd.
A = πr²
A = π(11.5)²
A = 132.25π
A = 415.265 yd²
Subtract the two areas to find the are of the walk.
490.625 - 415.265 = 75.36 yd²
The area is 75.36 yd²
n the diagram below, points $A,$ $E,$ and $F$ lie on the same line. If $ABCDE$ is a regular pentagon, and $\angle EFD=90^\circ$, then how many degrees are in the measure of $\angle FDE$?
[asy]
size(5.5cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }
pair a=cis(1,144); pair b=cis(1,72); pair c=cis(1,0); pair d=cis(1,288); pair e=cis(1,216);
pair f=e-(0,2*sin(pi/5)*sin(pi/10));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
label("$A$",a,WNW);
label("$B$",b,ENE);
label("$C$",c,E);
label("$D$",d,ESE);
label("$E$",e,W);
label("$F$",f,WSW);
draw(d--f--a--b--c--d--e);
draw(f+(0,0.1)--f+(0.1,0.1)--f+(0.1,0));
[/asy]
Answer:
18
Step-by-step explanation:
Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.
Sidenote: I hope this answer helps!
The properties of a pentagon and the given right triangle formed by
segments EF and FD give the measure of ∠FDE.
Response:
∠FDE = 18°Which properties of a pentagon can be used to find ∠FDE?The given parameters are;
A, E, F are points on the same line.
ABCDE is a regular pentagon
∠EFD = 90°
Required:
The measure of ∠FDE
Solution:
The points A and E are adjacent points in the pentagon, ABCDE
Therefore;
line AEF is an extension of line side AE to F
Which gives;
∠DEF is an exterior angle of the regular pentagon = [tex]\frac{360 ^{\circ}}{5}[/tex] = 72°∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;
The sum of the acute angles of a right triangle = 90°
Therefore;
∠DEF + ∠FDE = 90°
Which gives;
72° + ∠FDE = 90°
∠FDE = 90° - 72° = 18°
∠FDE = 18°
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7+2x/3=5 what is x?????
The value of x is 3
The above expression in the question is referred to as an Algebraic expression
Step 1: Multiply all through by 3
7+ 2x/3 = 5
7 x 3 + (2x/3) x 3 = 5 x 3
21 + 2x = 5 × 3
21 + 2x = 15
Step 2 : Subtract 21 from both sides21 - 21 + 2x = 15 - 21
2x = -6
Step 3 : Divide both sides by 22x/2 = -6/2
x = -3
Therefore, the value of x is -3
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Solve for y 110 75 100 55
Answer:
y = 100
Step-by-step explanation:
x = 25
x+y + 55 = 180 since it is a straight line
25+y+ 55 = 180
Combine like terms
80+y = 180
Subtract 80 from each side
y = 180-80
y = 100
Which store will give Martina the best deal if she has 60 people in attendance?
Igloo
Tasty
Fred’s
Answer:
Fred's
Step-by-step explanation:
Igloo 1.75(60) + 75 = 180
Tasty 2(60) + 80 = 200
Fred's 1.25(60) + 90 = 151.25
Answer: fred's
Step-by-step explanation:
which explicit formula can be used to find the number of rabbits in the nth generation ?
Answer:
A. an = 3(6)^(n-1)
Step-by-step explanation:
1st generation: n = 1:
a1 = 3*6^(1-1) = 3*6^0
= 3
n = 2:
a2 = 3*6^2-1
= 3*6
=18
n = 3
a3 = 3*6^(3-1)
= 3*6^2
= 106.
The solution is Option A.
The geometric progression is given by the equation aₙ = 3 ( 6 )ⁿ⁻¹ , where n is the number of terms
What is Geometric Progression?
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Let the number of terms be represented as n
Now , the first term a₁ = 3 rabbits
The second term a₂ = 3 x 6 = 18 rabbits
The third term a₃ = 18 x 6 = 108 rabbits
So , the common ratio r = second term / first term
Substituting the values in the equation , we get
Common ratio r = 18/6 = 6
Now , the geometric progression A is given by the equation ,
The nth term of a GP is aₙ = arⁿ⁻¹
Substituting the values in the equation , we get
aₙ = 3 ( 6 )ⁿ⁻¹
Therefore , the value of A is aₙ = 3 ( 6 )ⁿ⁻¹
Hence , the equation is aₙ = 3 ( 6 )ⁿ⁻¹
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What the answer please answer this question now
Answer:
[tex]m\angle Z\approx22.0\textdegree[/tex]
Step-by-step explanation:
First, note that we have a right triangle. Second, we need to find angle Z, and we are given the sides opposite to angle Z and the hypotenuse. Therefore, we can use sine.
Recall that:
[tex]\sin(\theta)=opp/hyp[/tex]
The opposite side is 3 while the hypotenuse is 8. Plug in the numbers and simplify. Use a calculator:
[tex]\sin(\angle Z)=3/8\\\angle Z=\arcsin(3/8)\\\angle Z\approx 22.0243\textdegree[/tex]
first answer get the best marks
Answer:
Choice C
Step-by-step explanation:
[tex] -3.55g \le -28.4 [/tex]
Divide both sides by -3.55; remember that by dividing both sides of an inequality by a negative sign, you need to change the direction of the inequality sign.
[tex] \dfrac{-3.55g}{-3.55} \ge \dfrac{-28.4}{-3.55} [/tex]
[tex] g \ge 8 [/tex]
Answer: Choice C
Answer:
Third answer
Step-by-step explanation:
the sign less than or equal to gets flipped when you divide by a negative
solid circle and points to the right because now it is greater than or equal to.
Suppose an apple picker in China earns an average wage of 45 cents per hour. An apple picker can harvest about 2.0 bushels of apples each hour. One gallon of apple juice requires 40 apples. Each bushel contains about 126 apples. What is the labor cost of one gallon of apple juice in dollars?
Answer:
0.0398 dollars
Step-by-step explanation:
We are told in the question that
An apple picker in China earns an average wage of 45 cents per hour.
Mathematically
1 hour= 45 cents............ Equation 1
An apple picker can harvest about 2.0 bushels of apples each hour.
Mathematically
2.0 bushels = 1 hour ..............Equation 2
We are told that each bushel contains about 126 apples
1 bushel = 126 apples
2 bushels =
126 × 2
= 252 apples
Combining Equation 1 and 2 together,
We can say
An apple picker in 1 hour harvests 2 bushels of apples which is 252 apples and is paid 45 cents
1 hour = 2 bushels of apples
1 hour = 252 apples
1 hour = 45 cents
Hence we can say fro harvesting 252 apples, an apples picker is paid 45 cents
Mathematically,
252 apples = 45 cents
One gallon of apple juice requires 40 apples
We are to calculate the labor cost of one gallon of apple juice in dollars
If : 252 apples = 45 cents
40 apples = X cents
Cross Multiply
40 × 25 = 252 × X
X = (40× 25) ÷ 252
X = 3.984063745 cents
Hence the labor cost of 40 apples = 3.984063745 cents
Approximately = 3.98 cents
Converting 3.98 cents to dollars
100 cents = 1 dollar
3.98 cents =
= 3.98/100
= 0.0398 dollars.
Therefore, the labor cost of one gallon of apple juice in dollars is 0.0398 dollars.
Given the function, f (x) = sq3x+3+3, choose the correct transformation.
Answer:
B.
Step-by-step explanation:
First, let's start from the parent function. The parent function is:
[tex]f(x)=\sqrt{x}[/tex]
The possible transformations are so:
[tex]f(x)=a\sqrt{bx-c} +d[/tex],
where a is the vertical stretch, b is the horizontal stretch, c is the horizontal shift and d is the vertical shift.
From the given equation, we can see that a=1 (so no change), b=3, c=-3 (negative 3), and d=3.
Thus, this is a horizontal stretch by a factor of 3, a shift of 3 to the left (because it's negative), and a vertical shift of 3 upwards (because it's positive).
5 (x+4)=35.please solve it for me
Answer:
3 = x
Step-by-step explanation:
5(x+4) = 35
distribute: 5x + 20 = 35
subtract 20 to both sides
15 = 5x
divide by 5 to make x independent
x=3
20
The average annual energy cost for a certain home is
$4,334. The homeowner plans to spend $25,000 to
install a geothermal heating system. The homeowner
estimates that the average annual energy cost will
then be $2,712. Which of the following inequalities
can be solved to find t, the number of years after
installation at which the total amount of energy cost
savings will exceed the installation cost?
A) 25,000 > (4,334 - 2,712)
B) 25,000 < (4,334 - 2,712)
C) 25,000 - 4,334 > 2,712t
D) 25,000 >
4,332
2,712t
Answer:
This is my first question but I think it's c
Step-by-step explanation:
25,000-4334=20,666
20,666/2712=7.62 which rounds to 8