Ms. Diaz wants to divide her class of 30 students into 10 groups, not necessarily of equal size. What are some of her choices?
Evaluate the following expression using the values given.
Find 5x - 3y - z if x = -2, y = 2, and z = -3
Answer
A.19
B.-19
C.-13
D.13
Answer:
-3 ----- C
Step-by-step explanation:
how do you plot y-5= 3/2 (x-2)
a childrens book has dimensions 20cm by 24cm what scale factor should be used to make a enlarged version that has dimensions 25cm by 30cm
Final answer:
To find the scale factor for enlarging a children's book from 20 cm by 24 cm to 25 cm by 30 cm, divide the enlarged dimension by the original corresponding dimension, resulting in a scale factor of 1.25.
Explanation:
We are asked to find the scale factor used to enlarge a children's book from dimensions of 20 cm by 24 cm to a larger version with dimensions of 25 cm by 30 cm. To find the scale factor, we need to divide one dimension of the enlarged book by the corresponding dimension of the original book. We can take either the length or the width to find the scale factor.
Let's use the width for this example:
Original width = 20 cm
Enlarged width = 25 cm
Scale factor = Enlarged width / Original width
Scale factor = 25 cm / 20 cm
Scale factor = 1.25
Therefore, a scale factor of 1.25 should be used to enlarge the book from the original dimensions to the new dimensions.
If a right circular cone intersects a plane that passes through one of its nappes but the plane is not parallel to an edge of the cone the resulting curve will be:
parabola
circle
ellipse
hyperbola
Answer:
D) Hyperbola.
Step-by-step explanation:
If a right circular cone intersects a plane that passes through one of its nappes, but the plane is not parallel to an edge of the cone, the resulting curve will be one arc of a hyperbola.
Therefore, the answer is Hyperpola.
Hope this will helpful.
Thank you.
If F(x) = x² + 5x and G(x) = 2x + 1, find F(5) + G(6).
What two ratios are equivalent to 8/6?
A landscaper earns $30 for each lawn her company mows, but she pays $210 per day in salary to her employees. if her company made more than $150 profit from mowing lawns in a 7-day week, what are the possible numbers of lawns the company could have mowed?
The company could have mowed more than 54 lawns.
How to Solve linear inequality?Let the number of lawns mowed be x.
Then the total earning of landscaper is 30x.
The total amount given to the employees in a week is 210*7=$1470.
Then the profit of landscaper would be 30x-1470 which is greater than $150.
30x-1470 > 150
30x > 1620
x > 54
Therefore, possible numbers of lawns the company could have mowed are greater than 54 lawns.
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Between 61 and 80 lawns could have been mowed by the business in a week in order to turn a profit of more than $150. So options (d) and (e) are correct.
To determine the possible numbers of lawns the company could have mowed, we need to calculate the profit for a 7-day week and compare it with the given condition that the profit exceeds $150.
Step 1: Determine daily and weekly expenses
The daily salary expense is $210.
For 7 days, the total salary expense is:
[tex]\[ 210 \times 7 = 1470 \text{ dollars} \][/tex]
Step 2: Calculate profit per lawn
The company earns $30 for each lawn mowed.
Let ( n ) be the number of lawns mowed in a week.
Step 3: Calculate total earnings from mowing lawns
Total earnings for ( n ) lawns is:
[tex]\[ 30n \text{ dollars} \][/tex]
Step 4: Determine the profit
Profit is total earnings minus total expenses:
[tex]\[ \text{Profit} = 30n - 1470 \][/tex]
Step 5: Apply the condition that profit is more than $150
The inequality to solve is:
[tex]\[ 30n - 1470 > 150 \][/tex]
Step 6: Solve the inequality
Add 1470 to both sides:
[tex]\[ 30n > 1620 \][/tex]
Divide both sides by 30:
[tex]\[ n > 54 \][/tex]
Step 7: Identify the possible number of lawns mowed
The number of lawns must be greater than 54.
From the given options (12, 37, 54, 61, 80), the possible numbers are:
[tex]\[ 61 \text{ and } 80 \][/tex]
Thus, the two possible numbers of lawns the company could have mowed to make a profit of more than $150 in a week are 61 and 80.
Complete Question:
A landscaper earns $30 for each lawn her company mows, but she pays $210 per day in salary to her employees. If her company made more than $150 profit from mowing lawns in a 7-day week, what are the possible numbers of lawns the company could have mowed? Select two options. 12
37
54
61
80
rx+9/5=h, Solve for the value of x
rx+(9/5)=h
rx=h-(9/5)
x=(h-(9/5))/r
a golf ball travels a distance of 600 feet as measured along the ground and reaches an altitude of 200 feet. If the origin represents the tee and the ball travels along a parabolic path that opens downward, find an equation for the path of the golf ball.
...?
Answer:
y=1.32x-0.0022[tex]x^{2}[/tex]
Step-by-step explanation:
Let the standard equation of parabola be y=a[tex]x^{2}[/tex]+bx+c ....... (1)
Let y be the altitude of the ball and x be the distance traveled by the ball.
Now by putting the points one by one, we get the required equation.
first point = (0,0)
golf ball travels a distance of 600 feet along the ground. Therefore point = (600,0)
At altitude of 200, it travels the distance of 300 feet(mid point) = (300,200)
By putting y=0 and x=0 in (1),
we get c=0,
By putting y=0 and x=600 we get
0 = 360000a+600b ..............(2)
By putting y=200 and x=300, we get
200=90000a+300b ................(3)
Solving (2) and(3) we get, a=-0.0022 and b = 1.32
So the required equation is :
y= =0.0022[tex]x^{2}[/tex]+1.32x
what is The _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ of equality allows you to divide both sides of an equation by the same number.
A laptop computer is purchased for 2300 . After each year, the resale value decreases by 35% . What will the resale value be after 4 years?
round your answer to the nearest dollar ...?
help please !!!!! asap
Sure Fire Auto Supplies marked down its entire stock of imported tires 30% on Wednesday only. The sale price of all tires was $79. What will be the price to the nearest cent, of each tire on Thursday when the tires are marked back to their original price?
The answer is $112.86
A = a+b+c / 3
Solve for b.
A.) 3A - a - c = b
B.) -c / 3 = b
C.) A - c / 3 = b
C.) -3 - c = b ...?
To solve for b in the equation A = (a + b + c) / 3, multiply both sides by 3 and then subtract a and c from both sides. The correct answer is A) 3A - a - c = b.
Explanation:To solve for b in the equation A = (a + b + c) / 3, you need to isolate the variable b.
First, multiply both sides of the equation by 3 to eliminate the denominator:
3A = a + b + c
Then, subtract a and c from both sides to get b by itself:
3A - a - c = b
So, the correct answer is:
A) 3A - a - c = b
What is the solution to the inequality below?
x2  144
What is 20% of 300 EXPLAIN ...?
This scatter plot shows a__ .
Factor 9x3 + 18x2 – x – 2
...?
To factor the polynomial 9x^3 + 18x^2 − x − 2, group terms to factor out common factors and then factor further if possible. The factored form is (x + 2)(3x + 1)(3x - 1).
Explanation:To factor the polynomial 9x3 + 18x2 − x − 2, we look for common factors and use techniques such as grouping. First, we can try to group the terms in pairs and factor out the greatest common factor from each pair.
Let's group the first two terms and the last two terms separately:
(9x3 + 18x2) − (x + 2)From the first group, we can factor out 9x2 and from the second group, we can factor out -1:
9x2(x + 2) - 1(x + 2)We now have a common factor of (x + 2) that we can factor out:
(x + 2)(9x2 - 1)The expression 9x2 - 1 is a difference of squares, which can be factored further:
(x + 2)(3x + 1)(3x - 1)So, the fully factored form of the given polynomial is (x + 2)(3x + 1)(3x - 1).
The polynomial 9x^3 + 18x^2 - x - 2 can be factored by grouping and by recognizing the difference of squares, resulting in the factors (x + 2)(3x + 1)(3x - 1).
Explanation:The student has asked to factor the polynomial 9x3 + 18x2 - x - 2. Factoring polynomials is a process of expressing a polynomial as a product of its factors, which can involve numbers, variables, or both. This can make the expression simpler or more useful for further mathematical operations such as solving equations.
To begin factoring 9x3 + 18x2 - x - 2, we look for a common factor in each term. Here, there is no common factor, so we attempt to factor by grouping. We group terms that can potentially have common factors or that can be factored further.
Let's separate the polynomial into two groups:
First group: 9x3 + 18x2Our two groups now look like this:
First group: 9x2(x + 2)Second group: -1(x + 2)Because the (x + 2) is a common factor in both groups, we can factor it out:
(x + 2)(9x2 - 1)
The second term, 9x2 - 1, is a difference of squares which can be factored as (3x + 1)(3x - 1).
Finally, the completely factored form of the given polynomial is:
(x + 2)(3x + 1)(3x - 1)
The axis of symmetry for a quadratic equation can be found using the formula x = -b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.
When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?
2x
–2x
1/2x
–1/2x
The denominator of the fraction is -2x.
The correct answer is option (b)
What is equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
What is numerator?"In a fraction, the value placed above the horizontal line."
What is denominator?"In a fraction, the value placed below the horizontal line."
For given question,
The axis of symmetry for a quadratic equation can be found using the formula [tex]x=-\frac{b}{2a}[/tex]
where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.
[tex]\Rightarrow x=\frac{-b}{2a}\\\\ \Rightarrow \frac{a}{x} \times x=\frac{-b}{2a}\times \frac{a}{x}\\\\\Rightarrow a=\frac{b}{-2x}[/tex]
For the fraction [tex]\frac{b}{-2x}[/tex] the numerator is b and denominator is -2x.
Therefore, the denominator of the fraction is -2x.
The correct answer is option (b)
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Mass is the ________(1)________, where as depth is the ________(2)________.
357 miles in 5 hours ____miles per hour find until rate rounded to he nearest hundredth
is 30y^2 a polynomial?
write the explicit formula for the sequence 3,5,7,9,11
Which of the following has a graph that is a straight line?
Equation 1: y = 4x^3 + 6
Equation 2: y = 5x − 4.5
Equation 3: y^2 = x − 1
Equation 4: y = 2x^2 + 6
Answer:
y=5x - 4.5
Step-by-step explanation:
I took the test
Help, please!
he table shows the population of a school for the years 1992-2008.
Year: 1992, 1994 1996, 1998, 2000, 2002, 2004, 2006, 2008
Population: 628, 656, 692,751, 793, 840 ,868, 902, 940
Which is the best prediction for the population in 2012?
1000
1100
1150
2010
Answer with explanation:
Year Population
1992 628
1994 656→(628+28)
1996 692→(656+36)
1998 751→(692+59)
2000 793→(751+42)
2002 840→(793+47)
2004 868→(840+28)
2006 902→(868+34)
2008 940→(902+38)
There is no fixed pattern the rate at which population is increasing.But if you will look at the way the population is increasing , the range of the number is from [28,59].
⇒Most appropriate prediction for the population in 2012 will be
Option A : 1000
if a rubik's cube has a volume of 384 cubic centimeters, how long is one side of the cube? (recall that the volume of a cube is calculated by L3, where L is the length of one side.
To determine the side length of a Rubik's cube with a volume of 384 cubic centimeters, take the cube root of 384 to find that each side is approximately 7.24 centimeters long.
To find the length of one side of a cube when given the volume, you can use the formula for the volume of a cube, which is V = L³, where V is the volume and L is the length of a side of the cube.
In this case, the volume is 384 cubic centimeters, so we need to find the cube root of 384 to find the length of one side.
The calculation is as follows:
L³ = 384 cm³L = ∛384 cm³L ≈ 7.24 cmTherefore, each side of the Rubik's cube is approximately 7.24 centimeters long.
Trent is 25 years old and works for a company that matches his 401(k) contribution up to 5%. The interest rate for his 401(k) is 7.3%. If he puts away 10% of his $32,000 salary every year, how much would he have saved in 10 years? Round your answer to the nearest cent.
Answer:
The answer is : $67,266.16
Step-by-step explanation:
This question is a future value question.
As given, Trent puts away 10% of his $32,000 every year and the company will put half amount of $1,600. So, total amount becomes =[tex]3200+1600=4800[/tex] each year.
Formula for future value or FV is Fv = Pmt (1 + r/n)^(nt) – 1 / (r/n)
Where, Fv = Future Value , Pmt = repeated payments , R = interest rate ,N = total number of payment periods
Putting the values in the formula,
Fv = 4800 (1 + 0.073/1)^(1x10) – 1 (0.073/1)
Fv = $67266.16
Hence, the answer is $67266.16
The amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
Further Explanation:
Annuity is a series of payment that is made after equal interval of time.
Future value of annuity of payment P for n year if the return is i can be expressed as,
[tex]\boxed{{\text{Future Value}} = {\text{P}} \times \frac{{{{\left( {1 + \frac{i}{n}} \right)}^{nt}}}}{{\frac{i}{n}}}}[/tex]
Given:
Total salary is [tex]\$ 32000.[/tex]
The interest rate is [tex]7.3\%.[/tex]
Trent save [tex]10\%[/tex] of his salary every year.
Company puts [tex]5\%[/tex] of salary every year.
Calculation:
The [tex]10\%[/tex] of [tex]\$32000[/tex] can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}}&= \frac{{10}}{{100}} \times 32000\\&= \$ 3200\\\end{aligned}[/tex]
The amount that company put can be obtained as follows,
[tex]\begin{aligned}{\text{Company Amount}} &= \frac{5}{{100}} \times 32000\\&= \$ 1600\\\end{aligned}[/tex]
The total amount can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}} &= 3200 + 1600\\&= \$ 4800\\\end{aligned}[/tex]
The future value can be obtained as follows,
[tex]\begin{aligned}{\text{FV}} &= 4800 \times \frac{{{{\left( {1 + 0.073} \right)}^{10}} - 1}}{{0.073}} \\ &= 4800 \times 14.014\\&= \$ 67266.20\\\end{aligned}[/tex]
Hence, the amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Investment and return
Keywords: Trent, 25 years old, works, company, matches, 401(k), 7.3%, 10%. $32000, salary, every year, 10 years, amount, 5%, nearest cent.
A side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches. What is the area of a cross-section of the prism? What is the volume of the prism?
A) 12 in2; 216 in3 B) 24 in2; 432 in3 C) 60 in2; 1080 in3
D) 120 in2; 2160 in3
Answer:
Area and volume of pentagonal prism is 660 inches² and 1080 inches³
Step-by-step explanation:
Given : A pentagonal prism having side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches.
We have to calculate
1) area of a cross-section of the prism
2) the volume of the prism
1) Area of cross section of pentagonal prism =5ab +5bh
Where a = apothem
b - base length
h = height.
For the given pentagon
apothem = 4 inches
base = 6 inches
Height = 18 inches
Area of cross section of pentagonal prism =5 ×4 × 6 + 5× 6 × 18
Area of cross section of pentagonal prism = 120 + 540
Area of cross section of pentagonal prism = 660 inches²
2) Volume of pentagonal prism = [tex]\frac{AP}{2} \times H[/tex]
Where, A = apothem
P is perimeter of base
H= height
Perimeter of pentagon is 5b = 30 inches
Volume of pentagonal prism = [tex]\frac{4\times 30}{2} \times 18[/tex]
Volume of pentagonal prism = 1080 inches³
Thus, Area and volume of pentagonal prism is 660 inches² and 1080 inches³.
The table below shows the distance d(t) in feet that an object travels in t seconds.
t d(t)
(second) (feet)
1 15
2 60
3 135
4 240
What is the average rate of change of d(t) between 2 seconds and 4 seconds and what does it represent?
A) 50 m/s; it represents the average speed of the object between 2 seconds and 4 seconds
B) 90 m/s; it represents the average speed of the object between 2 seconds and 4 seconds
C) 90 m/s; it represents the average distance traveled by the object between 2 seconds and 4 seconds
D) 50 m/s; it represents the average distance traveled by the object between 2 seconds
Answer:
Option B is correct
The average rate of change of d(t) between 2 second and 4 second is; 90 ft/s
and it represents the average speed of the object between 2 seconds and 4 seconds.
Step-by-step explanation:
Average rate of change of function is defined as the ratio of the difference in the function f(x) as it changes from a to b to the difference between a and b. Then, the average rate of change is denoted as A(x).
[tex]A(x) =\frac{f(b)-f(a)}{b-a}[/tex]
As per the given statement, the distance d(t) is in feet and t is the time in second.
To find the average rate of change of d(t) between 2 seconds and 4 seconds.
From the table we have;
at t = 2 , d(2) = 60
and
at t =4 , d(4) = 240.
Then, by the definition of average rate of change ;
[tex]A(t) = \frac{d(4)-d(2)}{4-2}[/tex] = [tex]\frac{240-60}{4-2} =\frac{180}{2}[/tex]
Simplify:
[tex]A(t) = 90 ft/s[/tex]
therefore, the average rate of change of d(t) between 2 second and 4 second is; 90 ft/s and it represents the average speed of the object between 2 seconds and 4 seconds.