Answer:
47
Step-by-step explanation:
substitute the value of 5 in for c and 7 in for d;
(5) + 6(7)
5 + 42
47
A cube has sides that measure 12 inches each.
(a) Write an expression using an exponent that
represents the volume, V, of the cube.
12=V
12.
12
12
b) Evaluate the expression from (a) to fund the
cube's volume. Use the correct units.
12 in
12 in
w many cubes that measure 2 inches by 2 inches by 2 inches would fit inside a cube
asures 10 inches by 10 inches by 10 inches? Justify
This calculation yields a volume of a cube equal to 1728 cube inches. In order to calculate the volume, the length must be multiplied by itself three times.
How do you write the volume of a cube?Volume =[tex]a^{3}[/tex], where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.
A.) 12 × 3 cubic inches
B.) Volume of a cube equals length × breadth × height, which is 12× 12 × 12 = 123 = 144 × 12 = 1728 cube inches. V=[tex]a^{3}[/tex]=123=1728 [tex]cm^{3}[/tex]is the result, giving the cube's volume.
1,728 times twelve cubed. The term "x cubed," or cubing a number, is identical to: x cubed equals x 3. A real number with a cube equal to 12 is the cube root of 12. It is about equal to 2.289 to take the cube root of 12. Volume per volume, or % v/v, is the way volume concentrations in solutions are stated. This is employed when a solution contains liquid versions of both compounds.
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Reasoning with linear equations
Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)
f(x) = √5x + 4
X = ?
Answer:
-4/√5
Step-by-step explanation:
when f(x) = 0.
we can set the function equal to 0 and solve for x:
√5x + 4 = 0
√5x = -4
x = -4/√5
So the zero of the function is x = -4/√5
If you are surveying students about whether or not they own a bicycle, where are you more likely to get a random sample?
A) at a bicycle parking area
B) at a bicycle repair shop
C) inside the school cafeteria
Answer: C. Inside the school cafeteria.
Step-by-step explanation:
Which situation could be represented by the equation
18x=19+12x
A situation which could be represented by the equation 18x = 19 + 12x include the following: J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?
What is an algebraic expression?In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.
Assuming the variable x represents the number of hours spent tutoring, an algebraic expression which relates the number of hours which these two tutors must spent during tutorial to earn the same amount of money is given by:
18x = 19 + 12x
18x - 12x = 19
6x = 19
x = 19/6 hours.
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Complete Question:
Which situation can be represented by this equation?
18x = 19 + 12x
F Krystal reads 12 pages per hour. Jondo reads 18 pages per hour.
How many hours, x, would it take for Krystal and Jondo to read
the same number of pages?
G Krystal paid a deposit of $19 plus $18 per hour to rent a dining
room at a restaurant. Jondo paid $12 per hour to rent a dining
room at a restaurant. How many hours, x, would it take for
Krystal and Jondo to pay the same amount of money?
H Krystal installs 12 tiles per hour. Jondo installs 19 tiles per hour
and started with 18 tiles already installed. How many hours, x,
would it take for Krystal and Jondo to install the same number
of tiles?
J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?
The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?
answer choices
0.03
±
2.326
(
0.03
)
(
0.97
)
500
0.03±2.326 500
(0.03)(0.97)
0.15
±
2.326
(
0.15
)
(
0.85
)
500
0.15±2.326 500
(0.15)(0.85)
0.03
±
2.576
(
0.03
)
(
0.97
)
500
0.03±2.576 500
(0.03)(0.97)
0.15
±
2.576
(
0.15
)
(
0.85
)
500
0.15±2.576 500
(0.15)(0.85)
The confidence interval is (0.0104, 0.0496) (can include those endpoints too)
You can find the standard mean error and then use that to find the confidence interval limits.
The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by
Lower limit = 0.0104
Upper limit = 0.0496
The confidence interval is (0.0104, 0.0496) (can include those endpoints too)
To find the confidence interval for proportions
Let the sample size be n
Let the interested quantities in the sample be present x times
Let the confidence level be of p%.
Then the level of significance is given by
The standard mean error is calculated by:
Then the confidence interval limits can be found by
Using the above formula for finding the confidence interval
We have n = 500, x = 15 and
Finding the standard mean error:
From the z tables, we get z = 2.5758
Thus, the confidence interval is obtained by
Lower limit = 0.0104
Upper limit = 0.0496
Thus,
The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by
Lower limit = 0.0104
Upper limit = 0.0496
Therefore, The confidence interval is (0.0104, 0.0496) (can include those endpoints too)
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Dave is 4 years older than Colin. Ruth is three times as old as Dave. The total of their three ages is 56 Work out Ruth's age.
Answer:
Ruth is 36 years old
Step-by-step explanation:
let Colin's age be x , then
Dave's age is x + 4
Ruth's age is 3(x + 4) = 3x + 12
sum their ages and equate to 56
x + x + 4 + 3x + 12 = 56
5x + 16 = 56 ( subtract 16 from both sides )
5x = 40 ( divide both sides by 5 )
x = 8
Then
Ruth's age = 3x + 12 = 3(8) + 12 = 24 + 12 = 36
The age of Ruth is 36 years while Dave is 12 years old and Colin is 8 years old.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Using variables to represent the ages of Colin and Dave:
C = Colin's age
D = Dave's age
From the given statement,
D = C + 4 (Dave is 4 years older than Colin)
We know that Ruth's age is three times Dave's age:
R = 3D (Ruth is three times as old as Dave)
Now, the sum of their ages is 56:
C + D + R = 56
Substituting the expressions for D and R in terms of C, we get:
C + (C + 4) + 3(C + 4) = 56
Simplifying and solving for C:
5C + 16 = 56
5C = 40
C = 8
So Colin is 8 years old. Using the expression for Dave's age in terms of C, we get:
D = C + 4 = 8 + 4 = 12
So, Dave is 12 years old.
Ruth's age in terms of D:
R = 3D = 3(12) = 36
Therefore, Ruth is 36 years old.
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The center of a circle is at (-2,-7) and its radius is 6. What is the equation of the circle?
(X+2)^2 +(Y+7)^2 =36
Since the centre of the circle is (-2;-7), we equate the variable to its coordinate:
X=-2
Y=-7
now we bring the coordinate over to the left side which changes its sign.
X+2=0
Y+7=0
That explains the :
(X+2)^2 +(Y+7)^2
Now for the R.
its given that the radius is 6 and since the standard form for the equation of a circle requires r^2.
we simply square 6.
6^2=36.
Answer: (x+2)^2+(y+7)^2=36
Step-by-step explanation:
To write an equation for a circle when you know
the radius is R
the center is at (A, B), remember that the standard form of the equation of the circle is:
Just plug those values into this equation:
(x-A)^2+(y-B)^2=R^2
You will end up with this equation
(x+2)^2+(y+7)^2=36
Convert each rate using dimensional analysis 44yds/s=?mi/h
Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.
What is dimensional analysis?Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.
Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.
As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.
We know that 1 yards/sec = 2.04545 miles/hour
Here given that 44yds/s = ? miles/hour
Lets solve
1 yards/sec = 2.04545 miles/hour
44 yards/sec = 44 × 2.04545 miles/hour
44 yards/sec = 89.9998 miles/hour
44 yards/sec = 90 miles/hour
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1. Antonio sets his remote-controlled car at the start of the racetrack and starts its run on the track. His car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance and then stops for good. It is 38m from the starting line. How long is the racetrack? (a) Let x = the length of the racetrack. Write an equation that fits the story (b) Solve the equation from Part a. (How long is the racetrack?) Show your work. (c) How much farther did Antonio’s car have to go to the finish line? Show your work.
The total length of the race track that Antonio remote controlled car runs on is 70 m.
What is an equation?An equation is an expression that shows how numbers and variables relate with each other.
Equations can either be linear, quadratic and so on depending on the degree of the polynomial
Let x represent the length of the racetrack.
Antonio car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance. It can be represented by the equation:
(2/5)x + 10 = 38
(2/5)x = 28
x = (28 * 5)/2
x = 70
The length of the race track is 70 m.
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Write an exponential
function y = ab∧x
whose
graph passes through the
points
(2, –50), (4, –1250)
The exponential function will be y= -2(3)^x.
What are exponential functions?
An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Now,
Given points for exponential function are (2, –50), (4, –1250).
and exponential function is y=ab^x
To find a and b put points in the function
-50=ab^2 -->1
-1250=ab^4 --->2
From equation 1
a=-50/b^2
Put value of a into 2
-1250=-50/b^2*b^4
b^2=25
b=5
For b=5, a=-50/5^2=-2
Hence, a=-2
Therefore,
The exponential function will be y= -2*5^x.
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What is the value of log0.5^16
Answer:
Step-by-step explanation:
log(0.5)^16=log(1/2)^16
=log(2^(-1))^16
=-16log(2)=-4.81647
-5(2x+14)=-2(x+63) x=6
The value of the variable, x is 7
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.
These mathematical operations are also made up of arithmetic operations. These operations includes;
AdditionSubtractionMultiplicationFloor divisionBracketParenthesesDivisionFrom the information given, we have;
-5(2x+14)=-2(x+63)
expand the bracket
-10x -70 = -2x - 126
Now, collect like terms
-10x + 2x = -126 + 70
Add or subtract the terms
-8x = -56
Make 'x'' the subject
x = 7
Hence, the value is 7
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How many different ways can you rearrange the letters in the word RECEIVER
a. 40320
b. 1120
C. 70
d. 3360
e. 20160
f. 6720
Answer:
don’t care 9
Step-by-step explanation:lol
ella has 0.5 lb of sugar how much water should she add to make the following concentrations? tell ella how much syrup she will have in each case. 75% syrup ella should add _ lb water and she will have to add _lb syrup
Answer: The answer provided is based on the following calculation:
To make a 75% syrup, Ella should add enough water to the sugar to create a solution that is 25% sugar and 75% water.
To calculate how much water to add, you can use the formula: (desired % of sugar) / (100 - desired % of sugar) * (amount of sugar).
In this case, it would be: (0.75) / (100 - 0.75) * (0.5 lb) = 0.67 lb of water.
To calculate the total amount of syrup, you add the amount of sugar and the amount of water: 0.5 lb + 0.67 lb = 1.17 lb.
So Ella should add 0.67 lb of water to make a 75% syrup and will have a total of 1.17 lb syrup.
Step-by-step explanation:
Answer:
for the 75% syrup: 0.167lbs
For the 1.5% syrup: 32.83 lbs
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A drink stand is selling small drinks for $2 each and large drinks for $4 each. One day, a total of 150 drinks were sold for $552. How many large drinks were sold?
Answer:
Step-by-step explanation:
please help me with this
Answer: B
Step-by-step explanation: 85.10 is total. 46 per minutes. $85/$/Min.46. The $ cancels and you get minutes.
Find all the missing side and angles < p
Therefore , the solution of the given problem of triangle comes out to be ∠P = 30° , PQ = 4√3 and PN = 2.
A triangle is what exactly?An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.
Here,
Given : A right triangle,
=> ∠P + 60° + 90° = 180°
=> ∠P = 180° - 150°
=> ∠P = 30°
For PQ
=> Tan 60° = √3
=> PQ /4 = √3
=> PQ = 4√3
For PN ,
=> Sin 60° = √3/2
=> 4√3 / PN = √3/2
=> PN = 2
Therefore , the solution of the given problem of triangle comes out to be
∠P = 30° , PQ = 4√3 and PN = 2.
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The cross-section of the reflector in a flashlight is a parabola. Suppose the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.
Assume the vertex is at the origin and that the parabola is concave left (it opens left as depicted in the picture). What is the equation for the cross-section of the reflector?
The equation of the cross-section of the reflector which is in the form of a parabola is y² = -10x
What is a parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Given that, The cross-section of the reflector in a flashlight is a parabola, the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.
We know that, the equation of the parabola turned to the left i.e. to the negative side of the coordinate system is:
y² = -2px
where p is the parameter of the parabola
The relationship between the parameter and the focus is.
p = 2 f
p = 2×2.5 = 5 cm
Since, the equation of the parabola is:
y² = -2p
Therefore, put p = 5
y² = - 2×5x = -10x
y² = -10x
Hence, the equation is y² = -10x
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Solve for y, x+10i=y-yi
The value of y in the equation that we have here is given as , y = x + (10 + y)i
How to solve for yTo solve for y, we can start by isolating y on one side of the equation. We can do this by adding yi to both sides:
x+10i+yi = y-yi+yi
This simplifies to:
x+10i+yi = y
We can then rearrange the equation to get:
y = x+10i+yi
So, y = x + (10 + y)i
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IXL Question‼️
Write the answer in the form mx + b
The equation in slope intercept form is y=-9x-8
What is slope?Slope is defined the rate of change of y with respect to x. the slope is also denoted by increase in y over increase in x.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
The equation of the slope intercept form is in the form y= mx +c
The given equation y= -9x +9
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is either x = 6 or x = 4 a solution to 33 - x = 27?
A: x = 6 is a solution, but x = 4 is not.
B: x = 4 is a solution, but x = 6 is not.
C: Neither are solutions
D: they are both solutions
Answer: A: x=6
Step-by-step explanation: If we plug in 6 for X in the equation we get
33 - 6. 33 - 6 does equal 27.
Now to make sure X = 4 is not an answer, we plug that in too. 33 - 4.
33 - 4 = 29, so this is not the answer.
Answer:
A: x = 6 is a solution, but x = 4 is not.
Step-by-step explanation:
33-x=27
-33 -33
-x=-6
-x/ -x/
x=6
A coin with a head on one side and a tail on the other is tossed, followed by a six-sided die with faces marked 1 through 6 being rolled. If each outcome is equally likely, what is the probability of each outcome?
The probability of each outcome is given as follows:
1/12.
How to obtain the probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
For this problem, we have that the total number of outcomes is of twelve, as:
The coin has two outcomes.The die has six outcomes.Hence:
6 x 2 = 12.
(applying the Fundamental Counting Theorem).
Meaning that the probability of each outcome is given as follows:
1/12.
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What is the domain of the function y=3^√x?
-∞AX<∞
O 0
O 0
0 1
Answer: The domain of a function is the set of all input values (x-values) for which the function produces a valid output value (y-value).
For the function y = 3^√x, the input value x can't be negative because the value under the square root should be non-negative and 3^√x is defined for all x in the domain of real numbers. This means that the domain of the function y = 3^√x is (-∞,∞).
Step-by-step explanation:
The domain of the function is [0, ∞).
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The function y = 3^√x has a base of 3, which means that the output of the function is always a positive number.
For the function to be defined, the input x must also be a positive number or zero, as the square root of a negative number is not a real number.
Therefore,
The domain of the function is all non-negative real numbers, or [0, ∞).
In interval notation, the domain can be written as [0, ∞).
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Find three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.
Answer:
2, 4, 6
Step-by-step explanation:
You want three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.
SetupLet x represent the middle integer. Then the first is (x-2) and the third is (x+2). The given relation is ...
2(x -2) + 3x = 2(x +2) +4
SolutionSimplifying the equation gives ...
2x -4 +3x = 2x +4 +4
5x -4 = 2x +8 . . . . . . . collect terms
3x = 12 . . . . . . . . . . . add 4-2x
x = 4 . . . . . . the middle integer
The integers are 2, 4, 6.
__
Additional comment
It often simplifies the equation if the variable is used to represent the middle of the consecutive integers in problems like this. In this particular problem, there is not a great advantage.
<95141404393>
Unit price of 3 scarves totaling 26.25
Answer:
Step-by-step explanation:
26.25 divided by three = 8.75
Kellen is having a party at a restaurant that charges $350 to rent a room and $12.50 per person for the meal. His maximum budget is $1500 . He will have x people at the party. Which of the following must be satisfied by x if Kellen does not exceed his budget?
Answer:
Step-by-step explanation:
350 + x people = 1500
x = 1500 - 350
x = 1150 / 12.50
x = 92 people
Write the slope-intercept form of the equation of each line: 1) x − y = −3, 2) 2x + y = −6, 3) 4x + y = −7
The slope - intercept form of the equations of each of the given lines is:
y = x + 3y = - 2x - 6 y = - 4x - 7How to find the slope - intercept form?The slope - intercept form is:
y = mx + b
Where
m = slope
b = y - intercept
Basically, given the equations of each line, you are to move y such that it goes to the left of the equation and remains there alone, while the other figures stay on the right side.
Equation 1:
x − y = −3
x + 3 = y
y = x + 3
Equation 2:
2x + y = −6
y = - 6 - 2 x
y = - 2x - 6
Equation 3 :
4x + y = −7
y = - 4x - 7
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What are the solutions of 2 - 5x+7=0?
○ A. x = 5+3² or x =
OB. x =
5+1v2 or 2 = 5-√2
OC. x =
- 5+₁v²
5+√2
2
or x =
○ D. x = 5+√³ or x =
5-i√2
The solution to the equation x^2-5x+7=0 are x=5/2+3/2i and x=5/2-3/2i
What are the equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
According to the given question, we see
by solving the inequality we get
x=5/2+3/2i and x=5/2-3/2i
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HELP ME OUT PLEASE I NEED HELP
The equation x / y = 4 is an example of direct variation formula. (Correct choice: A)
How to find a case of direct variation formula
Herein we find four types of equations, of which we must determine what choice represents a direct variation formula, whose definition is shown below:
y ∝ x
y = k · x
Where k is the constant of proportionality.
This form is equivalent to the following expressions:
y / x = k, x / y = 1 / k
Then, by direct inspection, we see that equation x / y = 4 represents a direct variation formula.
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