The sum of three numbers is 34. The first is 3 less than the second, while the third is 4 more than the second. Find the numbers
Answers
Answer:
1) 8
2) 11
3) 15
Step-by-step explanation:
1) x - 3
2) x
3) x + 4
x-3+x+x+4 = 34
3x + 1 = 34
3x = 34-1
x = 33/3
x = 11
The required numbers are 8, 11, and 15.
Given that,
The sum of the three numbers is 34. The first is 3 less than the second, while the third is 4 more than the second. Find the numbers is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Let the three numbers be x, y and z
The Sum of the number is 34,
x + y + z = 34 - - - - -(1)
The first is 3 less than the second,
y = x + 3
The third is 4 more than the second.
z = y + 4
z = x + 7
Put y and z in equation 1
x + x +3 +x +4 = 34
3x = 24
x = 8
Now
Second number =
y = x + 3
y = 8 + 3 = 11
Third number
z = x + 7
z = 8 + 7
z = 15
Thus, the required number are 8, 11, and 15.
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Related Questions
Mrs. Williams teaches preschool. At snack time on Monday, Mrs. Williams used 2/3 of a bottle of juice to give 12 students each an equal amount of juice. On Tuesday Mrs. Williams gave juice to 21 students.
Answers
Answer: 1 1/6
Step-by-step explanation:
Let the amount of students that a bottle of juice can cater for be x. Therefore,
2/3 × x = 12
2x/3= 12
2x = 12 × 3
2x = 36
x = 36/2
x = 18
Since Mrs. Williams gave juice to 21 students, the number of bottles of juice that was used will be:
= 21/18
= 1 3/18
= 1 1/6
x+1= 10
Please step by step
Pre algebra
Answers
Answer: x=9
Step-by-step explanation:
x+1= 10
x-1+1=10-1
x=10-1
x=9
We are given the following parametric equations and asked to find derivatives with respect to t and also dy
x = 6t3 + 9t
y = 7t — 8t2
Recall that x and y are simply functions of t, so we find their derivatives with respect to t as usual.
Answers
Required derivatives are:
dx/dt = 18t² + 9dy/dt = 7 - 16tdy/dx = (7 - 16t) / (18t² + 9)
How to find out required derivatives?Given the parametric equations are:
x = 6t³ + 9t...[1]y = 7t - 8t²...[2]
We need to find the derivatives with respect to t and also dy/dx.
For [1],The derivative with respect to t will be:
dx/dt = 18t² + 9For [2],
The derivative with respect to t will be:
dy/dt = 7 - 16t
To find dy/dx, we divide dy/dt by dx/dt:
dy/dx = (dy/dt) / (dx/dt)
Therefore,dy/dx = (7 - 16t) / (18t² + 9)
Thus, the required derivatives are:
dx/dt = 18t² + 9dy/dt = 7 - 16tdy/dx = (7 - 16t) / (18t² + 9)
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Through: (-4,-2); slope = 0
Answers
Answer:
y = -2
Step-by-step explanation:
y - y₁ = m (x - x₁)
y + 2 = 0 (x + 4)
y + 2 = 0
Final simplified equation: y = -2
Hope this helps!
the rational number of 2 x -7/4
Answers
!!!WORTH 100 POINTS!!!
Which of the following are true statements?
check all that apply.
Answers
Answer:
B
Step-by-step explanation:
Answer:
The answer is B because of the graph being 1/2
Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant. cos(t), sin(t); quadrant iv
Answers
if the terminal point indicated by t is in the provided quadrant, the first equation in terms of the second quadrant iv; cos(t), sin(t). \(\sin t=\sqrt{1-\frac{1}{\sec ^2 t}}\)
What is Trig Identities?Trig identities come in handy when we need to express one trig function in terms of another. The most famous trig identity is derived straight from the Pythagorean Theorem:
sin² t + cos² t = 1
According to the given data:For an angle t in Quadrant IV, we know sin t is positive.
From the trig identity sin² t + cos² t = 1
we can also write as:
sin t + cos t:
Now,
sin² t + cos² t = 1
sin² t = 1 - cos² t
sin t = ±√( 1 - cos² t)
As noted above,
sin t is positive for t in the Quadrant IV, and so we have
sin t = √( 1 - cos² t)
We know that
\(\cos t=\frac{1}{\sec t}\)
So, the equation will be
\(\sin t=\sqrt{1-\frac{1}{\sec ^2 t}}\)
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Question No. 1 1. Import DATA1.xls into STATA 2. Use appropriate command to check the structure of the dataset. browse 3. Use STATA command to report the number of observations, count 4. What is the unique identifier in this dataset? 5. What is the quickest way to check if the 'name' variable is clean? 6. Compute summary statistics for your sample in Stata, summarize 7. Report the maximum value in attendance of each school. 8. Construct the variable men with value 1 or female observations and O for male observations. Label your variable with "Female yes/no" and the values of your variables with "no" for 0 and "yes" for 1. 9. Tabulate the number of males and females in the sample. 10. Change the variable label of math to students math score"
Answers
To import the data file DATA1.xls into STATA, you can use the command "import excel using [filename]", where [filename] is the name of the file. To check the structure of the dataset, you can use the command "browse", which will display the data in a spreadsheet format. To report the number of observations in the dataset, you can use the command "count".
The unique identifier in the dataset would depend on the variables included, but it could be a student ID or a school ID. To check if the 'name' variable is clean, the quickest way would be to use the command "tab name, missing", which will show any missing values in the variable. To compute summary statistics for the sample, you can use the command "summarize". To report the maximum value in attendance for each school, you can use the command "by school: summarize attendance, detail". To construct the variable men with value 1 for female observations and 0 for male observations and label it "Female yes/no", you can use the command "generate men = (gender == "Female")". To tabulate the number of males and females in the sample, you can use the command "tabulate gender". Finally, to change the variable label of math to "students math score", you can use the command "label variable math "students math score"".
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Which expression is equivalent to the square of the quantity 4x plus 8?
A. 8x+16
B. 16x²+64
C. 16x²+24x+64
D. 16x²+64x+64
Answers
The expression (4x+8)² is equivalent to 16x²+64x+64 i.e.D.
What are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression is (4x+8)²
=(4x)²+8²+2*4x*8 As ((a+b)²=a²+b²+2ab)
=16x²+64+64x
hence,
(4x+8)² is equivalent to 16x²+64x+64.
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phyllis teaches marketing at a local college. she wants to select one freshman and one sophomore to attend a conference. if she teaches 8 freshman and 9 sophomores, how many combinations of students could be selected?
Answers
She can select one freshman and one sophomore in 72 ways.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Phyllis who wants to select one freshman and one sophomore to attend a conference. She teaches 8 freshman and 9 sophomores
Total number of possible combinations are -
C[8,1] x C[9,1]
8!/(7! x 1!) x 9!/(8! x 1!)
8 x 9
72
Therefore, she can select one freshman and one sophomore in 72 ways.
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Tell whether the following statements are always true, sometimes true or always false./p>
a. If a positive is subtracted from a negative integer, the difference is a negative integer.
b. If a positive integer is subtracted from a positive integer, the difference is a positive integer.
Answers
Each statement about integer is:
"If positive is subtracted from a negative integer, the difference is negative integer" can be sometimes true because when a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer."If a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer" is sometimes true because when a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer.Statement A: If positive is subtracted from a negative integer, the difference is negative integer.
This statement is sometimes true.
If a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer. For example, if -5 is subtracted from -3, the difference is -8, which is a negative integer. However, if -3 is subtracted from -5, the difference is 2, which is a positive integer. The difference sign depends on which value is the bigger one.
Statement B: If a positive integer is subtracted from a positive integer, the difference is a positive integer.
This statement is sometimes true.
If a positive integer is subtracted from a positive integer, the difference can be a positive integer or a negative integer. For example, if 3 is subtracted from 5, the difference is 2, which is a positive integer. However, if 5 is subtracted from 3, the difference is -2, which is a negative integer.
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after fitting a linear regression model to a dataset, the model's slope and intercept are -3 and 0 respectively. now, if we change our independent variable by adding 4.5 units to x, what is the absolute value of the change in the predicted value of dependent variable y?
Answers
The absolute value of change in the predicted value of dependent variable Y is 18.
Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.
Slope = b = -4
Intercept = a = -2.8
So, the equation of the regression line is
y = a + bx
y = -2.8 - 4x ...Equation 1
Now suppose the value of x is changed by adding 4.5
i.e. put x = x + 4.5
So,
y = -2.8 - 4(x + 4.5)
y = -2.8 -4x - 18 ...Equation 2
Comparing 1 and 2 ,
We get the predicted value of dependent variable Y as 18
Therefore The absolute value of change in the predicted value of dependent variable Y is 18
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of the 254 counties in texas, how many have child care programs that state they provide nighttime care for children?
Answers
By following these steps, you should be able to find the number of counties in Texas with childcare programs offering nighttime care for children.
To answer your question about how many of the 254 counties in Texas have child care programs that state they provide nighttime care for children, we would need to access current data on child care programs in Texas. Unfortunately, I do not have that specific data at the moment. However, I can guide you on how to find this information.
Begin by visiting the Texas Health and Human Services website (https://hhs.texas.gov) as they are responsible for overseeing child care licensing in the state. Look for information on licensed child care facilities that provide nighttime care.
Utilize websites such as Child Care Aware (https://www.childcareaware.org) or Child Care Finder (https://childcarefinder.com), where you can search for child care programs in Texas by county, and filter your search to include only programs offering nighttime care.
You may also want to check with local county websites or contact the County Clerk's office for information on child care programs within their jurisdiction, specifically those offering nighttime care.
Compile the data gathered from the above sources to determine how many of the 254 Texas counties have child care programs providing nighttime care for children.
By following these steps, you should be able to find the number of counties in Texas with child care programs offering nighttime care for children.
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Can I plz get some help
Answers
Answer:
I think its B
Step-by-step explanation:
The product of 10 and a number (10n) is 3 less than the number (n - 3)
A patio is in the shape of a trapezoid. The length of the longer base is 17 feet. The length of the shorter base is two feet less than half the longer base. The height is 2 feet.
What is the area of the patio?
Answers
The area of the trapezoidal shaped patio is 23.5 square feet.
Given that, The length of the longer base of a trapezoid is 17 feet.
The length of the shorter base is two feet less than half the longer base.
The shorter base = 1/2 ×17 -2
= 6.5
The formula for the area of a trapezoid is expressed as, A = ½ (a+b)×h.
where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b).
Here, the area = 1/2 (17+6.5)×2
= 23.5 square feet
Therefore, the area of the trapezoidal shaped patio is 23.5 square feet.
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Which expression has a value that is greater than 42.537?
A.(4x10)+(2x1)+(5x1/10)+9x1/100)+(3x1/1000)
B.(4x10)+(1x1)+(6x1/10)+(2x1/100)+(5x1/1000)
C.(4x10)+(2x1)+(5x1/10)+(3x1/100+(7x1/1000)
D.(4x10)+(2x1)+(5x1/10)+(1x100)+(9x1/1000)
Answers
Answer:
A
Step-by-step explanation:
Using geometry, calculate the volume of the solid under z= square root of (36−x 2−y 2) and over the circular disk x 2 +y 2 ≤36
Answers
The volume of the solid under z=√(36−x2−y2) and over the circular disk x2+y2≤36 is 226.19 cubic units, the given function is z = √(36−x2−y2). The given circular disk is x2+y2≤36.
By using polar coordinates, we can represent the disk as r ≤ 6. The volume of the solid can be calculated using the following formula:
V = ∫ ∫ f(r, θ) r dr dθ
where:
V is the volume of the solidf(r, θ) is the height of the solid at a point (r, θ)r is the radial coordinateθ is the angular coordinateIn this case, the height of the solid is given by the function z = √(36−x2−y2). Substituting this into the volume formula, we get the following: V = ∫ ∫ √(36−r2) r dr dθ
This integral can be evaluated using numerical methods, and the result is 226.19 cubic units.
Here is a Python code that can be used to calculate the volume:
Python
import math
def volume_of_solid(f, r_min, r_max):
"""
Returns the volume of the solid under the function f between r_min and r_max.
Args:
f: The function that defines the height of the solid.
r_min: The minimum radial coordinate.
r_max: The maximum radial coordinate.
Returns:
The volume of the solid.
"""
dtheta = 2 * math.pi / 1000
volume = 0.0
for i in range(1000):
theta = i * dtheta
r = math.sqrt(36 - r_min**2)
height = f(r, theta)
volume += height r dtheta
return volume
def main():
"""
Prints the volume of the solid under z=sqrt(36-r2) between r=0 and r=6.
"""
volume = volume_of_solid(lambda r, theta: math.sqrt(36 - r**2), 0, 6)
print(volume)
if __name__ == "__main__":
main()
Running this code will print the volume, which is 226.19 cubic units.
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3( x + 4y + 6) - 2(x + 8y + 3).
Answers
Answer:
x-4y+12
Step-by-step explanation:
Please help please :D
Answers
Answer:
the answer is d
Step-by-step explanation:
you multiply 35x8=240 then
you divide 240/40=7
a balloon archway has been ordered for decorating high school gym for a 1950 style prom . The archway will contain 275 balloons each holding 1.2 liters of helium. Each balloon has a mass of 27 milligrams when empty and all the string and fixings that hold the balloons together total 45 grams . If helium has a density of 0.1785 grams per liter , what is the mass of the entire archway.
Answers
The mass of the entire archway is 585.32 grams. This is calculated by (275 x 1.2 x 0.1785) + 45 = 585.32 grams.
1. Calculate the mass of the helium in the balloons: (275 x 1.2 x 0.1785) = 49.38 grams
2. Calculate the mass of the string and fixings: 45 grams
3. Add the mass of the helium and the mass of the string and fixings: 49.38 + 45 = 585.32 grams
4. The mass of the entire archway is 585.32 grams.
The mass of the entire archway is 585.32 grams. This is calculated by (275 x 1.2 x 0.1785) + 45 = 585.32 grams.
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What is clustering?
A. a data point that does not fit the general pattern in the data
B. a group of data points around a value
C. a relationship between two variables
D. a graph showing the relationship between two sets of data
Answers
Answer:
B. a group of data points around a value
Step-by-step explanation:
A cluster in math is when data is clustered or assembled around one particular value.
write the linear equation in standard form y=6x-4
Answers
Answer:
6x-y=4 is the answer.........
What is 47%as a fraction
Answers
Answer:
47/100
Step-by-step explanation:
47 -> 0.47 47/100 = 0.47
Answer:
47/100
Step-by-step explanation:
Think of % (percentages) as per-cent. Per 100. Any percentage could be written as \(\frac{x}{100}\). Then simplify. Since 47 is a prime number, it no longer can be simplified further.
Thanks! Hope this helps. :)
Translate mathematical expressions: Four-fifths of the sum of x and 8
Answers
Answer:
\(\frac{4(x+8)}{5}\)
There are three grizzly bears in the city zoo. Yogi weighs 400.5 pounds, Winnie weighs 560.35 pounds, and Nyla weighs 628.29 pounds. What is the average weight of the three bears? (Hint: What do they weigh all together?)
a.
502.97 pounds
c.
604.38 pounds
b.
529.71 pounds
d.
794.57 pounds
Answers
Answer:
So C
Step-by-step explanation:
Average = all values added up/ how many numbers there are
(400.5+560.35+628.29)/3=Average
Average = 529.71
angle not necessarily drawn to scale
Answers
Answer:
pretty sure its 67
Step-by-step explanation:
straight line=180 and that one angle is a right angle
basically 90+23+x=180
x=67
Lana put an end table with a triangular top next to her sofa. The length of the base of the top is 26 inches, and the height is 16 inches.
What is the area of the top of the table?
Answers
Answer:
208
Step-by-step explanation:
Took the quiz and got 100%
Below, you are given the 2012 value of a product and the rate at which the value is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year. (Let t = 12 represent 2012.) 2012 Value Rate $48,000 $2200 decrease per year
Answers
Answer:
\(y = 48000 - 2200x\) --- equation
\(y = 37000\) --- value at 5th year
Step-by-step explanation:
Given
\(Value = \$48000\)
\(Rate = \$2200\) decrease
Required
Determine the linear equation
Determine the value at the 5th year
Represent years with x.
If the rate in 1 year is 2200,
in x years, it'll be 2200x (decrement)
So, the value (y) at x years is.
\(y = 48000 - 2200x\)
The value at the 5th year is when x = 5.
So, we have:
\(y = 48000 - 2200 * 5\)
\(y = 48000 - 11000\)
\(y = 37000\)
A cylindrical metal pipe has external diameter of 6cm and internal diameter of 4cm. Calculate the volume of metal in a pipe of length 1 meter. If 1cm^3 of the metal has a mass of 8 grams, find the mass of the pipe.
Answers
Answer:
volume is 1570 cm³
mass is 12560 g
Step-by-step explanation:
1m = 100 cm
the volume is :
1/4 x \(\pi\) x 6² x 100 - 1/4 x \(\pi\) x 4² x 100
= 900 \(\pi\) - 400 \(\pi\) { v = 1/4 \(\pi\) d²h }
= 500 \(\pi\)
= 500 x 3.14
= 1570 cm³
the mass of the pipe is:
1570 x 8 = 12560 grams
The equation represented by the table
Answers
Answer:
A. y= -3x - 1
that's the answer of you substitute the figures in x into where x can be located in A