Final answer:
To find the liters for 5 cups of water, divide 5 by 4.22, according to the conversion rate obtained from the given table.
Explanation:
To calculate the number of liters used if Saloman used 5 cups of water, we need to determine how many cups are in a liter. According to the unit conversion provided, 1 liter is equivalent to approximately 4.22 cups. To find the number of liters from the number of cups, we should divide the total cups by the number of cups per liter. Therefore, to find the liters for 5 cups, we divide 5 by 4.22.
The calculation is: 5 cups ÷ 4.22 cups/liter = number of liters.
Given the frequency table, what percentage of the students that like rock are also in grades 11–12? Round to the nearest whole percent.
Band Preference for School Dance
Rap Rock Country Row totals
Grades 9–10 40 30 55 125
Grades 11–12 60 25 35 120
Column totals 100 55 90 245
a. 10%
b. 21%
c. 25%
d. 45%
Answer:
d. 45%
Step-by-step explanation:
In total there are 30 + 25 = 55 students in total that like rock. From these there are 25 who are in grades 11-12. This makes that (25/55) * 100% = 45.45% of the students that like rock are in grades 11-12.
Answer: d. 45%
Step-by-step explanation:
According to the frequency table there are 30 sudents who like rock in grades 9-10 and 25 students that like rock and are in grades 11-12.
25 ÷ 55 = n ÷ 100
25 · 100 = 55 · n
2500 ÷ 55 = n n = 45.454545 n = 45%
55 is the total amount of students that like rock
25 is the total amount of students that like rock in grades 11-12
100 is the total percentage
1. Bill Jones is an employee of Soccer Supply Company. Find Jones’ net pay for the first week of November.
A. $749.03
B. $230.97
C. $792.03
D. $905.03
2. Bill Jones is an employee of Soccer Supply Company. Find Jones’ total deductions for the first week of November.
A. $230.97
B. $187.97
C. $74.97
D. $134.97
Use the picture for both questions if some can answer both in one shot. I thank everyone in advance.
Net pay is the gross pay after all the deductions.
1. Net pay = 980 - 156.00 - 60.76 - 14.21 = 749.03
The answer is A.
2. Total deductions = Gross pay - Net Pay:
980 - 749.03 = 230.97
The answer is A.
Answer:
A. $749.03
A. $230.97
Step-by-step explanation:
Jones's total deductions are :
[tex]156+60.76+14.21=230.97[/tex] dollars
His gross pay = $980
Net pay = gross pay - deductions
Net pay = [tex]980-230.97=749.03[/tex] dollars
Part A: Net pay is : A. $749.03
Part B : total deductions are : A. $230.97
Which of the relations given by the following sets of ordered pairs is not a function?
Select one:
a. {(5,2),(4,2),(3,2),(2,2),(1,2)}
{
(
5
,
2
)
,
(
4
,
2
)
,
(
3
,
2
)
,
(
2
,
2
)
,
(
1
,
2
)
}
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
{
(
−
4
,
−
2
)
,
(
−
1
,
−
1
)
,
(
3
,
2
)
,
(
3
,
5
)
,
(
7
,
10
)
}
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
{
(
−
8
,
−
3
)
,
(
−
6
,
−
5
)
,
(
−
4
,
−
2
)
,
(
−
2
,
−
7
)
,
(
−
1
,
−
4
)
}
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
Answer:
B
Step-by-step explanation:
you cannot have to same x
Hence , Option B set is not a function
What is a function?A function is an equation which states relation between x and y variable.
How to solve?a-{(5,2),(4,2),(3,2),(2,2),(1,2)}
Here, x: x>1 ,x∈N, hence function is possible.
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
here ,x can't be established as same x has different values.
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
Here, every x has it's unique value hence function can be established.
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
Here, every x has it's unique value , hence function can be established.
∴option B - {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)} is one from which we can't establish function.
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In △ABC,c=12, m∠B=27°, and a=9. Find b.
A. 11.5
B. 13.2
C. 6.8
D. 5.7
Answer:
Option D is correct.
Step-by-step explanation:
We are given c = 12
m∠B = 27°
a = 9
We need to find b
We would use Law of Cosines
[tex]b = a^2 + c^2 -2ac\,cosB[/tex]
Putting values and solving
[tex]b^2 = (9)^2 + (12)^2 -2(9)(12)\,cos(27°)\\b^2 = 81 + 144 - 216(0.891)\\b^2 = 81 + 144 - 192.456\\b^2 = 32.54\\taking\,\,square\,\,roots\,\,on\,\,both\,\,sides\\\\\sqrt{b^2} = \sqrt{32.54}\\ b = 5.7[/tex]
So, Option D is correct.
Answer:
D. 5.7
Step-by-step explanation:
We have been given that in △ABC,c=12, m∠B=27°, and a=9. We are asked to find the value of b.
We will use law of cosines to solve for b.
[tex]b^2=a^2+c^2-2ac\cdot \tect{cos}(B)[/tex]
Upon substituting our given values in law of cosines, we will get:
[tex]b^2=9^2+12^2-2\cdot 9\cdot 12\cdot {cos}(27^{\circ})[/tex]
[tex]b^2=81+144-216\cdot 0.891006524188[/tex]
[tex]b^2=225-192.457409224608[/tex]
[tex]b^2=32.542590775392[/tex]
Now, we will take square root of both sides of our equation.
[tex]b=\sqrt{32.542590775392}[/tex]
[tex]b=5.70461136059[/tex]
[tex]b\approx 5.7[/tex]
Therefore, the value of b is 5.7 and option D is the correct choice.
Convert the radian measure to degrees. (Round to the nearest hundredth when necessary): π/4
A. 45
B. 45π
C. π4
D. 90
Answer:
the degree measure of pie/4 is 45
Step-by-step explanation:
=pie/4
=180/4
=45
The basic formula that need to be recalled is:
Circular Area = π x R²
Circle Circumference = 2 x π x R
where:
R = radius of circle
The area of sector:
[tex]\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}[/tex]
The length of arc:
[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]
Let us now tackle the problem!
This problem is about conversion unit of angles
Remember that :
[tex]\large {\boxed {1 \pi ~ \text{radians} = 180^o} }[/tex]
[tex]\frac{\pi}{4} = \frac{1}{4} \times 180^o = \boxed {45^o}[/tex]
Another Example:
[tex]\frac{\pi}{6} = \frac{1}{6} \times 180^o = \boxed {30^o}[/tex]
[tex]\frac{\pi}{3} = \frac{1}{3} \times 180^o = \boxed {60^o}[/tex]
[tex]\frac{\pi}{2} = \frac{1}{2} \times 180^o = \boxed {90^o}[/tex]
[tex]\frac{3\pi}{2} = \frac{3}{2} \times 180^o = \boxed {270^o}[/tex]
[tex]\frac{3\pi}{4} = \frac{3}{4} \times 180^o = \boxed {135^o}[/tex]
[tex]\frac{4\pi}{3} = \frac{4}{3} \times 180^o = \boxed {240^o}[/tex]
Learn moreCalculate Angle in Triangle : https://brainly.com/question/12438587Periodic Functions and Trigonometry : https://brainly.com/question/9718382Trigonometry Formula : https://brainly.com/question/12668178Answer detailsGrade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area , Radian , Degree , Unit , Conversion
Convert r = 8cos θ to rectangular form.
A. x^2 + y^2 = 8y
B. x^2 + y^2 = 64x
C. x^2 + y^2 = 16x
D. x^2 + y^2 = 8x
Answer:
D
Step-by-step explanation:
To convert from polar to rectangular form
• x = rcosΘ , y = rsinΘ
• r = [tex]\sqrt{x^2+y^2}[/tex] ⇒ r² = x² + y²
Given
r = 8cosΘ
r = 8 × [tex]\frac{x}{r}[/tex] ( multiply both sides by r )
r² = 8x, hence
x² + y² = 8x ⇒ D
Answer:
The correct answer is D
Step-by-step explanation:
Plato
Complete the solution of the equation. Find the
value of y when x equals -8.
-5x - 5y = 50
Answer: -2 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Subbing 8 for x
-5(-8)-5y=50
Simplifying
40 + -5y = 50
Solving
40 + -5y = 50
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-40' to each side of the equation.
40 + -40 + -5y = 50 + -40
Combine like terms: 40 + -40 = 0
0 + -5y = 50 + -40
-5y = 50 + -40
Combine like terms: 50 + -40 = 10
-5y = 10
Divide each side by '-5'.
y = -2
Simplifying
y = -2
An Aluminum bar is 2 m long at a temperature of 20 degrees Celsius. What will it be at 100 degrees Celsius?
Answer:
5
Step-by-step explanation:
20*5=100
Answer:
10 meters
Step-by-step explanation:
Let at 100 degrees Celsius, the aluminum bar is x m long.
We have been given that aluminum bar is 2 m long at a temperature of 20 degrees Celsius.
Thus, we have the equation
[tex]\frac{2}{20}=\frac{x}{100}[/tex]
Solve the equation for x
[tex]x=\frac{2\times100}{20}\\\\x=10[/tex]
Thus, at 100 degree Celsius, the aluminium bar is 10 meters long.
The solution to a system of linear equations is (-3, -3) Which system of linear equations has this point as its solution?
A. x-5y = -12 and 3x+2y = -15
B. x-5y = -12 and 3x+2y = 15
C. x-5y = 12 and 3x+2y = -15
D. x-5y = 12 and 3x+2y = 15
Answer:
C. x-5y = 12 and 3x+2y = -15
Step-by-step explanation:
We need to substitute the solution into the equations
A. x-5y = -12 and 3x+2y = -15
-3 -5(-3) = -12
-3 +15 = -12
False
B. x-5y = -12 and 3x+2y = 15
-3 -5(-3) = -12
-3 +15 = -12
False
C. x-5y = 12 and 3x+2y = -15
-3 -5(3) = 12 3(-3) +2(-3) = -15
-3 -15 = 12 -9 -6 = -15
True True
D. x-5y = 12 and 3x+2y = 15
-3 -5(3) = 12 3(-3) +2(-3) = 15
-3 -15 = 12 -9 -6 = 15
True False
Find the length of the base of a square pyramid if the volume is 256 cubic inches and the height is 12 inches.
Answer: The base of the square is 52.67
Step-by-step explanation:
256=1/2bh
b=base
h=height
256=1/2(12)b
256=6b
52.67=b
Which inequalities have the solution set graphed on the number line? Check all that apply.
Answer:
x ≥ -2; -2 ≤ x
Step-by-step explanation:
Your number line shows a closed diamond -2.
That shows that 2 is a member of the solution set.
One interpretation of the inequality is
x ≥ -2
Another inequality with the same solution set is
-2 ≤ x
Answer:
x≥ -2
-2≤x
Step-by-step explanation:
In the given number line, the arrow is towards right. We know that if the arrow is towards right then the sign of the inequality is greater than >
Now, at the end point, which is 2, there is a solid circle. Hence, we must include 2 in our solution set.
Thus, there must be ≥ sign.
Hence, the inequality is x≥ -2
We can rewrite this as -2≤x
Sixth and seventh options are correct.
Which statement is true of the function f(x) = -3x? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of
The function f(x) = -3x is always decreasing, has a domain of all real numbers, and also has a range of all real numbers. The statement about the function always increasing is false.
Explanation:When considering the function f(x) = -3x, we can evaluate its properties to determine which statements are true. First, since the coefficient in front of x is negative, the function has a negative slope, indicating that it is always decreasing, not increasing. This rules out the first statement.
Second, the domain of this function is indeed all real numbers because there are no restrictions on the values that x can take in the equation. So, the second statement is true.
Third, because x can take on any real number value and there's a constant multiplier of -3, the output can also take on any real number value, but will always be the opposite sign of x or zero. This means the range of the function is also all real numbers. Therefore, the statement about the range is incomplete as provided, but it is true that the range of f(x) is all real numbers.
Suppose medical records indicate that the length of newborn babies(in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6 find the probability that a given infant is between 14.8 and 25.2 inches long
Answer:
P=0.954 or 95.4%
Step-by-step explanation:
Using the formula for the standardized normal distribution to find Z:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Where μ is the mean (μ=20) and σ is the standard deviation (σ=2.6).
[tex]Z_{1} =\frac{14.8-20}{2.6}=-2.0[/tex]
[tex]Z_{1} =\frac{25.2-20}{2.6}=2.0[/tex]
In the table of the normal distribution, we can look for positive values z, and these values are going to represent the area under the curve between z=0 and the values searched. the negatives values are found by symmetry (with the corresponding positive value but remember this area is under the left side of the curve). To find a value in the table, find the units in the first column and the follow over the same row till you find the decimals required.
[tex]P_1=0.4772[/tex]
[tex]P_2=0.4772[/tex]
[tex]P_1[/tex] represents the probability of length being between 14.8 and 20 (the mean) and [tex]P_2[/tex] represents the probability of length being between 20 and 25.2, The requested probability is the sum of these two.
[tex]P=P_1+P_2=0.954[/tex]
Answer:
95%
Step-by-step explanation:
write an equation in point-slope form from the line through the given point with the given slope . (10,-9); m= -2
[tex]\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{-9})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=-2(x-10)\implies y+9=-2(x-10)[/tex]
The diagram shows EFG. Which term describes point H?
Answer:
D
Step-by-step explanation:
The line segments drawn from each vertex of the triangle and intersecting at H are the Altitudes of the triangle.
The point H is called the Orthocenter
Answer:
D. Ortho-center.
Step-by-step explanation:
We have been given an image of a triangle. We are asked to find the term that describes point H.
We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.
We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option D is the correct choice.
x2 + 12x =
– 20
what are the roots of the following quadratic equation
Answer:
x = -2
x = -10
Step-by-step explanation:
Step 1 : Rearrange
x² + 12x + 20 = 0
Step 2: Factorise
(x + 2)(x + 10)
Step 3: Find the roots / values of x
Make each bracket equal zero.
(x + 2) = x = -2
(x + 10) = x = -10
Hope this helps!
Find the LCM of 30 and 22
Which is the graph of y = cos4(x - 2)?
Answer:
undefined
Step-by-step explanation:
Answer:
It's the image that is more compressed. This is because the period is decreased.
Step-by-step explanation:
What is the present value of $992 to be received in 13.5 years from today if our discount rate is 3.5 percent?
Answer: $1578
Step-by-step explanation:
1) Take your discount rate of 3.5% and convert it to decimal form (0.035)
2) Then, 0.035 * 13.5 = 1.59109
3) 1.59109 * 992 = $1578
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each situation to its corresponding expression. There are 7 trout fish in a pond, and the population doubles every year. Find the population after t years. arrowBoth A company buys a machine for $3,000. The value of the machine depreciates by 7% every year. Find the value of the machine after t years. arrowBoth The initial population of a colony of ants is 300. The number of ants increases at a rate of 1.5% every month. Find the population of ants after t months. arrowBoth A research laboratory is testing a new vaccine on 300 infected cells. The decay rate is 1.5% per minute. Find the number of infected cells after t minutes. arrowBoth
Answer:
Step-by-step explanation:
We will use the pattern f(x)= a(b)^t where a is the initial value, b is the base of the exponent. All these questions are about exponent function
A) Number of trout fish in the pound = 7 , it means a =7
population increases double every year. It means b=2
f(x)= a(b)^t
f(x)=7(2)^t
B) Cost of machine = $3000
The value depreciated every year = 7%
It means 100%-7%= 93% which is equal to 0.93
Therefore,
a = 3000
b = 0.93
f(x)= a(b)^t
f(x)=3000(0.93)^t
C) Initial population of a colony of ants = 300
The number of ants increase at a rate of 1.5%
It means 100%+1.5%=101.5%
101.5% = 1.015
Therefore,
a= 300
b = 1.015
f(x)= a(b)^t
f(x)=300(1.015)^t
D) A research laboratory is testing a new vaccine on 300 infected cells
The decay rate is 1.5% per minute
It means 100%-1.5% =98.5%
98.5% = 0.985
Therefore,
a = 300
b = 0.985
f(x)= a(b)^t
f(x)= 300(0.985)^t ....
Which point is on the graph of f(x) = 2.5^x
А. (1, 10)
в. (0, 0)
с. (0, 10)
D. (10, 1)
Answer:
A. (1, 10).
Step-by-step explanation:
I'm going to assume that it is 2*5^x, then
2 * 5^1
= 2 * 5 = 10.
So a point on the grapg is (1, 10).
(0, 1) is on the graph of [tex]f(x)=2.5^{x}[/tex].
What is a graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given function
[tex]f(x)=2.5^{x}[/tex]
Drawing this function in a graph we can see that (0, 1) is on the graph.
Hence,
(0, 1) is on the graph of [tex]f(x)=2.5^{x}[/tex].
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Which value of x that makes this equation true: 2/3x=10/3
Answer:
5
Step-by-step explanation:
If x=5...
2/3(5)=10/3
That would be true.
Answer:
x=5
Step-by-step explanation:
2/3 x = 10/3
Multiply each side by 3
3 *2/3 x = 10/3*3
2x = 10
Divide each side by 2
2x/2 = 10/2
x = 5
Need help on number 1, 5 and 7
Answer:
1) y = (x + 8)² + 7; 5) y = (x - 6)² + 10; 7) y = (x - 3)² - 4
Step-by-step explanation:
Complete the square in order to figure these out. To complete the square, use the formula [½B]². Each time you do this, you get a perfect trinomial in the form of a product of two monomials [h], then you have to figure out how much more to deduct from or add on to your C they gave you in each exercise [k].
If you are still in need of assistance, do not hesitate to let me know and subscribe to my channel [username: MATHEMATICS WIZARD].
I am joyous to assist you anytime.
12x=76-20y
8x=84-20y
Answer:
x = -2, y = 5 → (-2, 5)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}12x=76-20y&\text{change the signs}\\8x=84-20y\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x=-76+20y\\8x=84-20y\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-4x=8\qquad\text{divide both sides by (-4)}\\.\qquad x=-2\\\\\text{put the value of x to the second equation}\\\\8(-2)=84-20y\\-16=84-20y\qquad\text{subtract 84 from both sides}\\-100=-20y\qquad\text{divide both sides by (-20)}\\5=y\to y=5[/tex]
find tan of 45 degrees
Answer:
tan(45°) = 1
Step-by-step explanation:
We know that sin (45°) = √2/2, and cos(45°) = √2/2.
Given that tan(x) = sen(x) / cos(x), we get:
tan(45°) = (√2/2) / (√2/2) = 1
Therefore, tan(45°) = 1
Attached you will find the important angles summary
Question 2
A circular picture is 8 inches in diameter.
Part A
What is the area of the picture in square inch
OA. 4TT square inches
OB. 8 square inches
OC. 16Tf square inches
OD. 32 square inches
Part B
A frame that is 2 inches wide surrounds the picture. What is the total area of the
picture and the frame in square inches?
OA. 4TT square inches
OB. 12 TT square inches
OC. 36TT square inches
OD. 401 square inches
Save
Answer:
Part A: OC. 16π square inches
Part B: OC. 36π square inches
Step-by-step explanation:
Part A:
Given
Diameter of circular picture = d = 8 inches
We need to find the radius first to find the area
So,
Rdius = r = d/2 = 8/2 = 4 inches
[tex]Area = \pi r^2\\= \pi *(4)^2\\= 16\pi\ square\ inches[/tex]
Therefore, option C is the correct answer..
Part B:
As two inches frame is added around the picture, the diameter will become 8+4 =12 inches
The new radius will be:
r = 12/2 = 6
So,
[tex]Area\ with\ frame = \pi r^2\\=\pi *(6)^2\\=36\pi\ square inches[/tex]
Therefore, option C is correct ..
Dave receives a salary of $200 a week plus a commission of 10% of his weekly sales. An equation y = mx + b represents
Dave's weekly earnings. The y-intercept is Dave's base salary. The slope of the line is his commission.
Write an equation representing Dave's weekly earnings.
a. y=-0.1x-200
b. y = 0.1% - 200
C. y=-0.1x+ 200
d. y = 0.1x+ 200
Please select the best answer from the choices provided
Answer:
d. y = 0.1x+ 200
Step-by-step explanation:
His weekly salary is 200, that is the y intercept
He makes 10% (.10 in decimal form) of his weekly sales, that is the slope
y= mx+b
y = .1x+200
The function f(x) = x^2 - 12x + 5 written in vertex form is f(x)=(x-6)^2 - 31. What are the coordinates of the vertex?
(6,31)
(-6,31)
(6,-31)
(-6, -31)
Answer:
(6, - 31)
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x - 6)² - 31 ← is in vertex form
with vertex = (6, - 31 )
A triangle has sides of the square root of 2 and 3. Which could not be the length of the third side if it is a right triangle?
Answer:
the third side is √11
Step-by-step explanation:
By Pythagoras theorem, we can find the third side
c^2 = a^2 + b^2
if a = √2
b = 3
then,
c^2 = a^2 + b^2
c^2 =(√2)^2 + (3)^2
c^2 = 2+9
c^2 = 11
Taking square root on both sides:
√c^2 = √11
c = √11
So, the third side is √11
Bulan rows on a crew team. Her team rows their boat at a split (rate) of 2 min/500 m.
What is Bulan’s team’s rowing rate in m/min ?
Answer:
250
Step-by-step explanation:
If Bulan's team rows their boat at a rate of
2
minutes per
500
meters, they row at a rate of
1
minute per
250
meters. We know this because
1
minute is
1
2
of
2
minutes, and in this time, they will have to have rowed
1
2
the distance they would row in
2
minutes (
500
m).
1
2
of
500
is
250
.
So, we now have the rate in min/m.
If, every
1
minute, Bulan's team rows
250
meters, this means that every
250
meters, they have rowed for
1
minute.
Bulan's team's rowing rate in m/min is
250
m/
1
min.
Answer with explanation:
Speed of rowing boat by Bulan is given as:
→ 2 Minute = 500 meter
→ 1 Minute = 250 Meter
So, Bulan Rowing rate is equal to
[tex]250 \frac{\text{meter}}{\text{minute}}[/tex]