8 students like only tennis and football. When, In a survey of students about favorite sports, the results include 34 who like tennis, 37 who like football, 17 who like tennis and football, 21 who like tennis and baseball, 25 who like football and baseball, 9 who like all three sports, and 7 who like none of the sports.
Define algebra.One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols. The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.
Given
Number of student who only likes tennis and football
= number of student likes only tennis and football - who like all three sports
= 17 - 9
= 8
8 students like only tennis and football. When, In a survey of students about favorite sports, the results include 34 who like tennis, 37 who like football, 17 who like tennis and football, 21 who like tennis and baseball, 25 who like football and baseball, 9 who like all three sports, and 7 who like none of the sports.
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What is the equation of the line that is parallel to the line 6x+3y=4 and has a y-intercept of −6?
Answer:
y=-2x-6
Step-by-step explanation:
Slope intercept form of a line: y=mx+b (m is the slope and b is the y-intercept)
Convert our given line 6x+3y=4 into slope-intercept form to find the slope
Subtract 6x on both sides
3y=-6x+4
Divide 3 on both sides
y=-2x+4/3
The slope of the given line is the coefficient of x, -2
Parallel lines have the same slope, so the equation we're solving for also has a slope of -2
We also know that the y-intercept is -6, so we now have all the info we need to make the equation:
y=-2x-6
Baseball Field Problem
Find the amount of fencing, dirt, and sod needed to rebuild the baseball field.
380 to the fence
Fencer
'Is'
Goss
Dit
Dirf
Cr=10¹
Grass
Grass
Fence
Dint
Note: Not drown to scale
S
15'
The baseball field's fence, soil and sod requirements will be-: Length of fencing ≈ 1410.5 feet, Area of the sod ≈ 118017.13 ft², Area of of the field covered with dirt ≈ 7,049.6 ft²
How to find the area of sector of Circle?To find the area of a sector of a circle:
The sector's central angle, expressed in degrees, can be measured or calculated.Calculate or measure the circle's radius (r).Use this equation: Sector area is equal to (θ/360) * r2 *.Insert the formula's values for r and θ.Apply the formula to the area to calculate it.Round the outcome to the required degree of precision.The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;
Circle's Area can be given by, (A)= π × r²
Circle's Circumference can be given by, (C) = 2 × π × r
Where, 'r' denotes the radius of the circle
The area of a quarter of a circle is therefore= A ÷ 4
The perimeter of a quarter of a circle = C ÷ 4
Taking reference from the image,
Fencing; (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15
Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5
The fencing ≈ 1410.5 feet
Grass; π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13
The area covered by the sod is about 118017.13 square feet
Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6
The area occupied by the dirt is about 7049.6 square feet
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Complete Question:Find the amount of fencing, dirt, and sod needed to rebuild the baseball field?(refer to image attached for dimensions of field)
Please help Asap. No links or files, i will report! Show work Please!
The value of x is 13.85.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
From the figure,
(7x + 1)° and (6x - 1)° makes a straight angle.
This means,
(7x + 1) + (6x - 1) = 180
7x + 1 + 6x - 1 = 180
13x = 180
x = 180/13
x = 13.85
Thus,
x is 13.85°
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A scale measures weight to the nearest 0. 5 lb. Which measurement shows an appropriate level of precision for the scale? A. 140lbs, B. 148. 75lbs, C. 140. 5lbs, D. 141lbs
The appropriate level of precision for the scale depends on the smallest unit of measurement it can accurately determine. In this case, the scale measures weight to the nearest 0.5 lb.
A. 140 lbs. : This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision. B. 148.75 lbs.: This measurement includes decimal places that the scale cannot accurately determine. It exceeds the precision of the scale and does not show an appropriate level of precision. C. 140.5 lbs: This measurement falls within the precision of the scale. It accounts for the nearest 0.5 lb increment and shows an appropriate level of precision. D. 141 lbs: This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision.
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A 1-point closing fee assessed on a $200,000 mortgage is equal to $2,000 O $10,000 O $20,000 $0, as it only changes the rate O $1,000 1 pts
A 1-point closing fee assessed on a $200,000 mortgage is equal to $2,000.
What are points?Points are a percentage of a mortgage loan amount. One point equals one percent of the loan amount. Points may be paid up front by a borrower to obtain a lower interest rate. Lenders can refer to this as an origination fee, a discount fee, or simply points.
So, one point of $200,000 is $2,000. Hence, a 1-point closing fee assessed on a $200,000 mortgage is equal to $2,000. Therefore, the correct option is $2,000.
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PLEASE HELP I WILL GIVE BRAINIEST? What is the mode?
Answer:
3
Step-by-step explanation:
Mode is the one that has the most so 3 has the most
What number is 75% of 300?
A. 36
B. 22.5
C. 2250
D. 225
225
What is 75 percent of 300.? = 225.
$32.98 with 25% off (SHOW WORK)
Answer:
$24.74
Step-by-step explanation:
32.98*0.75=24.735
Answer:
well for me I think
Step-by-step explanation:
25/100×32.98
also
1/4×32.98
32.98/4
8.245
Can somebody pls help me!!
Answer:
121
Step-by-step explanation:
10(3)^2-7(3)+10=121
Brillianst please!!!
The hydrogen ion concentration (h+) in a certain cleaning compound is (h+)=3.2x10^-11 use the formula ph=-log(h+) to find the pH of the clean compound the pH is approximately
Answer:
The \(pH\) of the clean compound is approximately 10.495.
Step-by-step explanation:
If the cleaning ion concentration of the cleaning compound is \([H^{+}] = 3.2\times 10^{-11}\), then the \(pH\), no unit, of the compound is:
\(pH = -\log_{10} [H^{+}]\) (1)
\(pH = -\log_{10} (3.2\times 10^{-11})\)
\(pH = -\log_{10} 3.2 - \log_{10} (10^{-11})\)
\(pH = -\log_{10} \frac{32}{10} +11\)
\(pH = -\log_{10} 32 + \log_{10} 10 + 11\)
\(pH = -\log_{10} 32 +12\)
\(pH \approx 10.495\)
The \(pH\) of the clean compound is approximately 10.495.
Curt and Melanie are mixing 70% of blue paint and 30% of yellow paint to make seafoam green paint in a 1. 5 quarts bucket. Use the percent equation to find out how much yellow paint they should use
The amount of yellow paint Curt and Melanie should use is 0.45 quarts so that they can make 1.5 quarts bucket of seafoam green paint.We can use per cent equation.
Given that to make 1.5 quarts bucket of seafoam green paint Curt and Melanie have to mix 70 parts blue paint and 30 parts yellow paint.If 100 percent represent total paint then for 1.5 quarts we have to find the proportion of yellow paint.Let it be x.
30% / 100% =30 / 100 = x / 1.5 quarts.
We can reduce the equation further,
0.3 = x / 1.5.
0.3 * 1.5 = x
x = 0.45
We can also find blue paint proportion similar by substituting 30 per cent to 70 per cent.
As a result of our calculation, we found the amount of yellow paint to be 0.45 quarts.
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solve the equation in the interval [0, 2). enter your answers as a comma-separated list. sin2(t) − 3 sin(t) − 4 = 0
To solve the equation sin2(t) − 3 sin(t) − 4 = 0 in the interval [0, 2), we can use the substitution u = sin(t). This gives us the quadratic equation u2 − 3u − 4 = 0.
Factoring this equation, we get (u − 4)(u + 1) = 0. Solving for u, we have u = 4 or u = -1. However, since the interval is [0, 2), we need to check which of these solutions fall within this range. For u = 4, there are no corresponding values of t within the interval [0, 2), so we discard this solution. For u = -1, we can solve for t using the inverse sine function, giving us t = (7π/6) or t = (11π/6). Therefore, the solutions in the interval [0, 2) are (7π/6, 11π/6).
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what operation should be used to solve x/3 = 15
Answer:
please tag brainliest
cross multiplication operation i.e
x= 45
Step-by-step explanation:
There are 30 students in Mrs. Rodriguez’s class. 20% got an A on the test. How many students got an A?
Answer
6.
Steps
30/100×30
=6
Answer:
6
Step-by-step explanation:
There are 30 students
So,
20÷100×30=6
Jodie bought a music player on sale for 50% off the original price, for $60. What was the price of the music player before the sale?
Answer:
the answer is $120
Step-by-step explanation:
60+60 is 120
At a football game, 69 out of 92 students were wearing the color red to support the home team. What percent of the students were wearing red?
A.
69%
B.
88%
C.
65%
D.
75%
Answer c
Step-by-step explanation:
Answer:
D. 75%
Step-by-step explanation:
Divide 69 by 92 and you will get 0.75, move the decimal to the right two times. and there is your answer.
you are rolling a die number 1-6. What is the theoretical probability that you roll a 6?
Answer:
16.7 percent
So to get a 6 when rolling a six-sided die, probability = 1 ÷ 6 = 0.167, or 16.7 percent chance. So to get two 6s when rolling two dice, probability = 1/6 × 1/6 = 1/36 = 1 ÷ 36 = 0.0278, or 2.78 percent.
the rule explained in your own words
the rule completed in symbols
an example that disproves of the rule in question 1.2
The multiplication rule of indices is showcased in the picture where the power of multiplied values with the same base are added.
The multiplication rule of indicesIn indices, when two or more values having the same base are multiplied, the value of it's power are added to give a singular value with the same base and the power being the sum of the power values.
\( {a }^{m } \times {a}^{n} = {a}^{m + n} \)
The multiplication rule of indices is an established rule and cannot be disproved once all conditions are met.
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If Qaundale has 7 friends that are girls and 2 guy friends, what does that make Quandale?
Answer:
Step-by-step explanation:
A person that has 9 friends
Since 7+2=9
Somebody help me with these 3.
Answer:6 ture 7 false 8 true Step-by-step explanation:
The answers you have selected i believe are correct
Step-by-step explanation:
6) True
7) False
8) True
enter the value of x that makes the equation true 12x=3
Answer:
12 x1/4 or 12x.25=3
Step-by-step explanation:
you can pick between 1/4 or 0.25 they both equal 3
The percentage of mothers who work outside the home and have children younger than 6 years old is approximated by the function \[ P(t)=33. 55(t+5)^{0. 205} \quad(0 \leq t \leq 32) \] where \( \underline
The given function allows us to estimate the percentage of working mothers with children younger than 6 years old based on the number of years since a baseline year.
The given function, \(P(t) = 33.55(t+5)^0.205\), represents the percentage of mothers who work outside the home and have children younger than 6 years old. In this function, 't' represents the number of years after a baseline year, where 't=0' corresponds to the baseline year.
The function is valid for values of 't' between 0 and 32.
To determine the percentage of working mothers for a specific year, substitute the desired value of 't' into the function. For example, to find the percentage of working mothers after 3 years from the baseline year, substitute t=3 into the function: \(P(3) = 33.55(3+5)^0.205\).
It's important to note that this function is an approximation, as it assumes a specific relationship between the number of years and the percentage of working mothers.
The function's parameters, 33.55 and 0.205, determine the shape and magnitude of the approximation.
In summary, the given function allows us to estimate the percentage of working mothers with children younger than 6 years old based on the number of years since a baseline year.
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Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary
Answer:
506π ft^2
Step-by-step explanation:
here's your solution
=> height of cylinder = 12 ft
=> radius of cylinder = 11 ft
=> surface area of cylinder = 2πr(h+r)
=> SA = 2*11(12+11)*π
=> SA = 22*23π
=> SA = 506π ft^2
hope it helps
Please help me ;-;
What's the next term?
0, 1/3
3, 2
6, 12
9, ?
(Above is supposed to be a table btw)
Answer:
72
Step-by-step explanation:
Based on the table, the left and the right side have a pattern. When 3 is added to the left side, the right side is multiplied by 6. Since 12 multiplied by 6 is 72, the missing number is 72.
The density of a certain material is such that it weighs 7 pounds for every 5.5 cups of volume. Express this density in kilograms per pint. Round your answer to the nearest hundredth.
Answer:
\(Density = 1.1546\ kg/pint\)
Step-by-step explanation:
Given
\(Mass = 7\ lb\)
\(Cups = 5.5\)
Required
Determine the density in Kg/Pint
Density is calculated as thus:
\(Density = \frac{Mass}{Volume}\)
\(Density = \frac{7\ lb}{5.5\ cups}\)
Convert pound to kg
\(Density = \frac{7/ 2.205\ kg}{5.5\ cups}\)
\(Density = \frac{3.17515\ kg}{5.5\ cups}\)
Convert cups to pint
\(Density = \frac{3.17515\ kg}{5.5/2\ pint}\)
\(Density = \frac{3.17515\ kg}{2.75\ pint}\)
\(Density = 1.1546\ kg/pint\)
3.a shoe store marks up its merchandise by 8%. what was the selling price of a pair of shoes whose wholesale price is $24.50?
Answer:
Hi there!
Your answer is:
26.46$ selling price
Step-by-step explanation:
.08 markup
Original price= 24.5
24.5+ (.08*24.5)
26.46$
what is the equation of y=x^3 with the given transformations
Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.
2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.
3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.
4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.
5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.
6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.
Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
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plz help, angles and sums
Answer: 40
Step-by-step explanation:
180-120-20=40
a straight line is 180.
Benjamin believes that \( \frac{1}{2} \)% is equivalent to 50%. is he correct? why or why not?
First, we convert 1/2% to a decimal.
\(\frac{1}{2}\%=\frac{0.5}{100}=0.005\)Similarly:
\(undefined\)Newton-Raphson iteration is to be used to solve the following system of equations:
x²= 5-y²
y+1=x3
Calculate the elements of the Jacobian matrix (to 2 decimal places) if the values of x and y in the current iteration are x = 1 and y = 1.5. Rearrange the equations to formulate the roots problems so that the constants (5 in the first equation and 1 in the second equation) are positive before taking the partial derivatives.
J_11=
J_12=
J_21 =
J_22=
The Jacobian matrix elements for the given system of equations, using the rearranged equations with positive constants, are J_11 = -0.86, J_12 = 3.00, J_21 = -1.00, and J_22 = -1.83.
To calculate the elements of the Jacobian matrix, we need to compute the partial derivatives of the equations with respect to x and y. First, let's rearrange the equations with positive constants:
1. x² + y² = 5
2. x³ - y - 1 = 0
Now, we can calculate the partial derivatives. Taking the partial derivative of equation 1 with respect to x, we get:
∂(x² + y²)/∂x = 2x
Similarly, taking the partial derivative of equation 1 with respect to y, we get:
∂(x² + y²)/∂y = 2y
For equation 2, taking the partial derivative with respect to x gives:
∂(x³ - y - 1)/∂x = 3x²
And taking the partial derivative with respect to y gives:
∂(x³ - y - 1)/∂y = -1
Now, we substitute the values x = 1 and y = 1.5 into these partial derivatives to obtain the elements of the Jacobian matrix:
J_11 = ∂(x² + y²)/∂x = 2(1) = 2
J_12 = ∂(x² + y²)/∂y = 2(1.5) = 3
J_21 = ∂(x³ - y - 1)/∂x = 3(1)² = 3
J_22 = ∂(x³ - y - 1)/∂y = -1
Thus, the Jacobian matrix elements are J_11 = 2, J_12 = 3, J_21 = 3, and J_22 = -1.
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