Answer:
The over payment amount after 36 months is $ 0.37
Step-by-step explanation:
Given as :
The cost of the Car = $ 26,555
The number of times payment done for 36 month = 36
So, The the cost of car for 36 equal payment = [tex]\dfrac{\textrm Total cost of car}{\textrm number of times payment done }[/tex]
i.e The the cost of car for 36 equal payment = [tex]\frac{26,555}{36}[/tex]
∴ The the cost of car for 36 equal payment = $ 737.6389
Now rounding this value to nearest whole dollar = $ 738
Note - A) If after decimal , number are above 4 then round it to 1 above digit
B) If after decimal , number 4 or less then simply remove all number after decimal
So, The over payment after 36 months = $ 738 - $ 737.63 = $ 0.37
Hence The over payment amount after 36 months is $ 0.37 Answer
To rent a certain meeting room, a college charges a reservation fee of 39 and an additional fee of 5.90 per hour. The film club wants to spend less than 74.40 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.
Answer:
The answer is 6 hours
Step-by-step explanation:
The inequality
39 + 5.90 *t < 74.40 - 39
5.90 *t <35.4
t< 35.4/5.9
= 6 hours
1.) What are the zeros of the polynomial? f(x)=x^4-x^3-16x^2+4x+48.
2.) How many complex zeros does the function f(x)=x^4+3x^3+5x^2-3x-6?
3.) Factor the polynomial function. f(x)=x^4+2x^3-6x^2+4x-16.
Thanks for whoever answers
The zeros of a polynomial are the solutions to the polynomial equation. The function [tex]x^4+3x^3+5x^2-3x-6[/tex] has exactly 4 zeros due to the Fundamental Theorem of Algebra. The polynomial [tex]f(x)=x^4+2x^3-6x^2+4x-16[/tex]can be factored by grouping.
Explanation:1.) The zeros of the polynomial [tex]f(x)=x^4-x^3-16x^2+4x+48[/tex] are the solutions to the equation [tex]x^4-x^3-16x^2+4x+48=0[/tex]. Unfortunately, this equation does not have simple solutions and would require numerical techniques to solve.
2.) The function [tex]f(x)=x^4+3x^3+5x^2-3x-6[/tex] is a fourth degree polynomial, implying that it has exactly 4 zeros in the complex number system. This is a consequence of the Fundamental Theorem of Algebra, which states that every non-zero, single-variable, degree n polynomial with complex coefficients has exactly n roots in Complex Numbers.
3.) The polynomial [tex]f(x)=x^4+2x^3-6x^2+4x-16[/tex] can be factored by grouping as follows [tex]: f(x)=x^4+2x^3-6x^2+4x-16=(x^4+2x^3)-(6x^2-4x+16) = x^3(x+2)-2(x^3-2x+8)=x^3(x+2)-2(x-2)^2.[/tex]
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If 8 ounces of canned pumpkin has 82 calories ,how many calories are in one ounce? Use your answer to find how many calories are in 6 ounces of pumkin.
Number of calories in 6 ounces of pumpkin is 61.5 calories.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, 8 ounces of canned pumpkin has 82 calories
Now, number of calories in 1 ounce = Total number of calories ÷ Number of ounces
= 82/8
= 10.25 calories
Number of calories in 6 ounces of pumpkin
= 6×10.25
= 61.5 calories
Therefore, number of calories in 6 ounces of pumpkin is 61.5 calories.
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triangle ABC and triangle DEF are drawn below. If AB congruent DE, AC congruent DF and angle A congruent to angle D write a seuence of transfornation that maps tiangle ABC onto triangle DEF
Answer:
First you would translate triangle ABC to the right . next you would then translate triangle ABC up . Last you would rotate triangle ABC clockwise and matched angle A with angle D.
Step-by-step explanation:
1. In triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ. Also, AY = 7, BZ = 8, and XZ = 18. What is the perimeter of triangle ABC? (SHOW WORK)
2. What is y? (SHOW WORK) 2nd picture is the triangle.
Answer:
Part 1) The perimeter of triangle ABC is 24 units
Part 2) [tex]y=97\°[/tex]
Step-by-step explanation:
Part 1) we know that
The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side
see the attached figure to better understand the problem
so
Applying the midpoint theorem
step 1
Find the value of BC
[tex]BC=\frac{1}{2}XY[/tex]
[tex]XY=2AY[/tex] ---> because A is the midpoint
substitute the given value of AY
[tex]XY=2(7)=14\ units[/tex]
[tex]BC=\frac{1}{2}(14)=7\ units[/tex]
step 2
Find the value of AC
[tex]AC=\frac{1}{2}YZ[/tex]
[tex]YZ=2BZ[/tex] ---> because B is the midpoint
substitute the given value of BZ
[tex]YZ=2(8)=16\ units[/tex]
[tex]AC=\frac{1}{2}(16)=8\ units[/tex]
step 3
Find the value of AB
[tex]AB=\frac{1}{2}XZ[/tex]
substitute the given value of XZ
[tex]AB=\frac{1}{2}(18)=9\ units[/tex]
step 4
Find the perimeter of triangle ABC
[tex]P=AB+BC+AC[/tex]
substitute
[tex]P=9+7+8=24\ units[/tex]
Part 2) Find the measure of angle y
step 1
Find the measure of angle z
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
so
[tex]55\°+42\°+z=180\°[/tex]
solve for z
[tex]97\°+z=180\°[/tex]
[tex]z=180\°-97\°[/tex]
[tex]z=83\°[/tex]
step 2
Find the measure of angle y
we know that
[tex]z+y=180\°[/tex] ----> by supplementary angles (form a linear pair)
we have
[tex]z=83\°[/tex]
substitute
[tex]83\°+y=180\°[/tex]
solve for y
[tex]y=180\°-83\°[/tex]
[tex]y=97\°[/tex]
The number of wiring packages that can be assembled by a company's employees has a normal distribution, with a mean equal to 19.8 per hour and a standard deviation of 1.2 per hour.
(a) What are the mean and standard deviation of the number X of packages produced per worker in an 8-hour day? (Round your standard deviation to three decimal places.)
a. mean
b. standard deviation
(b) Do you expect the probability distribution for X to be mound-shaped and approximately normal? Explain.
Choose
A. Yes, since the standard deviation is less than 3, the sampling distribution of the sum will be approximately normal.
B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.
C. No, since the original population is not normal, the sampling distribution of the sum will not be approximately normal.
D. No, since the original population is normal, the sampling distribution of the sum cannot be normal.
E. No, since the standard deviation is more than 3, the sampling distribution of the sum will not be approximately normal.
(c) What is the probability that a worker will produce at least 160 packages per 8-hour day? (Round your answer to four decimal places.)
Answer:
a) mean= 158.4 , standard deviation = 3.394
b) Best option : B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.
c) P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188
Step-by-step explanation:
1) Notation
n = sample size = 8
[tex] \mu [/tex] = population mean = 19.8
[tex] \sigma [/tex] = population standard deviation = 1.2
2) Definition of the variable of interest
Part a
The variable that we are interested is [tex] \sum x_i [/tex] and the mean and the deviation for this variable are given by :
E([tex] \sum x_i [/tex]) = [tex] \sum E(x_i) [/tex] = n [tex] \mu [/tex] = 8x19.8 = 158.4
Var([tex] \sum x_i [/tex]) = [tex] \sum Var(x_i) [/tex] = n [tex] \sigma^2 [/tex]
Sd([tex] \sum x_i [/tex]) = [tex] \sqrt{n \sigma^2} [/tex] = [tex] \sqrt(8) [/tex] x 1.2 = 3.394
Part b
For this case the populations are normal, then the distribution for the sample ([tex] \sum x_i [/tex]) is normal too.
Based on this the distribution for the variable X would be normal, so the best option should be:
B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.
Part c
From part a we know that the mean = 158.4 and the deviation = 3.394
The z score is defined as
Z = (X -mean)/ deviation = (160-158.4)/ 3.394 = 0.471
Then we can find the probability P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188
Students were surveyed about their favorite colors 1/4 of the students preferred read 1/8 of the students preferred blue and 3/5 of the remaining students were for green if 15 students prefer green how many students were surveyed
Answer: the number of students that were surveyed is 40
Step-by-step explanation:
Let x = total number of students that were surveyed about their favorite colors
1/4 of the students preferred red.
This means that the number of students that preferred red is 1/4 × x = x/4
1/8 of the students preferred blue.
This means that the number of students that preferred blue is 1/8 × x = x/8
The remaining number of students will be the total number of students - the sum of the number of students that preferred red and the number of students that preferred blue. It becomes
x - (x/4 + x/8) = x - 3x/8 = 5x/8
3/5 of the remaining students were for green. This means that the number of students that preferred green is 3/5 × 5x/8 = 3x/8
if 15 students prefer green, then
3x/8 = 15
3x = 120
x = 120/3 = 40 students
Simplify 15x^2-18/6
A. 15x+3
B. X+3
C. 5x^2-18/2
D. 5x^2-6/2
Answer:
D. 5x^2-6/2
Step-by-step explanation:
5x^2-18/6 , 18/6 is 6/2
5x^2-6/2 ,
After simplification, the equation obtained is 5x² - 6/2. Hence, option D is correct.
What is Simplification?A phrase must be simplified and made shorter using a variety of methods. The steps required to decrease something are carried out according to a specified order known as BOD MAS.
Make a fraction simpler by reducing it to the base form. If both the numerator and denominator of a fraction only include the integer, the fraction is considered to be in its basic form.
As per the given information in the question,
The given equation in the question is,
15x² - 18/6
Divide the equation by 3,
= 5x² - 6/2.
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Ben paid 45 dollers for an old giutar than resold it after marking up the price 15 persent he used 36 persent of the money he got fornthe giutar tpo buy books how much money did ben spend on books
Answer:
18.63
Step-by-step explanation:
45*115%= 45*1.15 = 51.75
51.75*0.36 = 18.63
Answer:
18.63 dollars.
Step-by-step explanation:
The selling price was 45 + 15% or 45
= 45 + 0.15*45
= 51.75 dollars.
36% of 51.75
= 0.36 * 51.75
= 18.63 dollars which he had to spend on books.
Mrs. Martin directs two courses one chorus has 28 students the other chorus has 36 students for rehearsals she wants to divide each chorus into the largest possible equal groups with no students left over how many students will be in each group
Answer:4 students will be in each group.
Step-by-step explanation:
28 and 36. The 2 numbers are divisible by 4 without remainder
Answer:
4 students will be in each group.
Step-by-step explanation:
28 and 36. The 2 numbers are divisible by 4 without remainder
brainilest pl.z? i've never got brainilest.
Simplify.
7/8+(−2/3) divided by 5/6
Enter your answer, in simplest form, in the boxes.
Answer:
your answer is 1/4
Step-by-step explanation:
part 1
7/8 + -2/3 = 5/24
part 2
5/24÷5/6 = 1/4
Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y)
(B) y/(x+y)
(C) xy/(x+y)
(D) xy/(x-y)
(E) xy/(y-x)
Answer:
(E) xy/(y-x)
Step-by-step explanation:
The sum of the individual rates is the total rate. Each machine's rate is nails per hour is the inverse of its rate in hours per nail.
total rate = (800 nails)/(x hours) = 800/x nails/hour
A rate = (800 nails)/(y hours) = 800/y nails/hour
We want to find the time "b" such that ...
B rate = (800 nails)/(b hours) = 800/b nails/hour
__
As we said, the total rate is the sum of the individual rates:
800/x = 800/y + 800/b
Multiplying by xyb/800, we get
yb = xb + xy
Solving for b, we have ...
yb -xb = xy
b(y -x) = xy
b = xy/(y-x) . . . . . matches choice E
It takes Machine B xy/(y-x) hours to produce 800 nails.
You have a $30 gift card from Amazon that you use to purchase two T-shirts for a total of $25. The sales tax is 8%. Will your gift card cover the cost? Write an expressions and solve. Explain your answer.
Answer:
Step-by-step explanation:
Total cost of the two T-shirts that you purchased is $25. The sales tax on the T-shirts is 8%. This means that the additional amount that you will pay on the T shirt is
25/100 × 25 = 0.25 × 25 = $6.25
The new cost of the T shirt would be the sum of the original cost and the value of the sales tax. Therefore,
New cost = 25 + 6.25 = $31.25
You have a $30 gift card from Amazon. The new cost of the shirts is higher than that value of the gift card. So the gift card will not cover the cost of the T shirts
To determine if the gift card will cover the cost of the two T-shirts, calculate the sales tax and subtract it from the total cost. The gift card will cover the cost if the remaining balance is positive.
Explanation:To determine if your gift card will cover the cost of the two T-shirts, you need to calculate the cost of the sales tax and subtract it from the total cost of the T-shirts. First, convert the sales tax percentage to decimal form by dividing it by 100 (8% becomes 0.08). Then, multiply the total cost of the T-shirts (which is $25) by the sales tax rate to find the amount of sales tax. Multiply $25 by 0.08 to get $2. Next, subtract the sales tax amount from the total cost of the T-shirts: $25 - $2 = $23. Finally, determine if the gift card covers the cost by comparing it to the final cost: $30 - $23 = $7.
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A 500-turn circular coil with an area of 0.050 m^2 is mounted on a rotating frame, which turns at a rate of 20.0 rad/s in the presence of a 0.050-T uniform magnetic field that is perpendicular to the axis of rotation. What is the instantaneous emf in the coil at the moment that the normal to its plane is at a 30.0 degree angle to the field?
a) zero
b) 12.5 V
c) 21.6 V
d) 25.0 V
Answer:
option (b) 12.5 V
Step-by-step explanation:
Given:
Number of turns, N = 500
Area of the coil, A = 0.050 m²
Angular speed, ω = 20 rad/s
Magnetic field, B = 0.050 T
Angle to the field, θ = 30°
Now,
EMF induced, ε = NBAωsinθ
on substituting the values, we get
ε = 500 × 0.050 × 0.050 × 20 × sin30°
or
ε = 25 × 0.5
or
ε = 12.5 V
Hence,
option (b) 12.5 V
Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks. Write an equation that represents the relationship between the dollar amount in her bank account and the number of weeks of saving
The equation d=50+20w represents the relationship between dollar amount in her bank account and the number of weeks of savings.
Step-by-step explanation:
Amount in bank account = $50
Amount deposited by Priya = $20
Time period = 12
Let,
d be the dollar and w be the weeks
Therefore, we will multiply the number of week,w, with 20 to find total savings and add the amount that she has initially in her account.
Therefore,
[tex]d=50+20w[/tex]
The equation d=50+20w represents the relationship between dollar amount in her bank account and the number of weeks of savings.
Keywords: linear equation, addition
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The equation that represents Priya's savings over time is y = 50 + 20x. In this equation, y is the total amount in the bank account and x is the number of weeks.
Explanation:The relationship described in the problem can be represented by a linear equation. Here, the initial $50 in Priya's bank account is the starting value (or y-intercept). The $20 she deposits each week represents the constant rate of change (or slope), and the number of weeks is the variable.
Therefore, the relationship can be represented by the equation y = 50 + 20x, where y represents the total dollar amount in the bank account and x is the number of weeks Priya has been saving.
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The total operating total cost of the truck is $400000 per year the percentage break down $40% fixed cost $30 fuel $20 fianiance $10 maintance Increace 1.5 to 1.6
Answer:
$8,000.00 /yr
Step-by-step explanation:
The original fuel cost was 30% of 400,000 or $120,000.
If the previous cost was 1.50/L, then 120,000/1.5 = 80,000L/yr
The extra $0.10/L thus adds .1(80,000) = $8,000.00 /yr
the length of a rectangular piece of land is 5ft more than two times it’s width. the perimeter is 34ft. find it’s dimensions
Answer: Length = 11 feet
Width = 6 feet
Step-by-step explanation:
A rectangle is a four sided shape that has 2 equal lengths,L and 2 equal widths,W
The perimeter of the rectangular piece of land is the total distance around it. It is expressed as
Perimeter = 2L + 2W = 2(L+W)
The perimeter is given as 34ft. It means that
34 = 2(L+W) - - - - - - - -1
The length of the rectangular piece of land is 5ft more than two times its width. It means that
L = W + 5
Substituting L = W + 5 into equation 1, it becomes
34 = 2(W + 5 +W) = 2(2W + 5)
2W + 5 = 34/2 = 17
2W = 17 - 5 = 12
W = 12/2 = 6 feet
L = W + 5 = 6+5
L = 11 feet
What value of x is in the solution set of 3(x-4) > 5x + 2?
Answer:
x < -7
Step-by-step explanation:
Eliminate parentheses:
3x -12 > 5x +2
-14 > 2x . . . . . . . . . add -2-3x
-7 > x . . . . . . . . . . . divide by 2
Any value of x less than -7 is in the solution set.
A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are 17.5 degrees and 18.5 degrees.
(a) Draw a diagram that visually represents the problem
(b) Find the air distance the plane must travel until touching down on the near end of the runway.
(c) Find the ground distance the plane must travel until touching down
(d) Find the altitude of the plane when the pilot begins the descent
Answer:
a. See attachments
B. 163630.2ft
C. 147056.70ft
D. 49205.4ft
Step-by-step explanation:
Check attachments for details
Angle a.. Angle of dep to beginning of runway
Angle b... Angle of del to end of runway
AD... Altitude of plane
DB..... Ground distance before touch down
AC... Air distance travelled until touch down on the near end of runway
Ian is a phycologist interested in determining the proportion of algae samples from a local rivulet that belonged to a particular phylum. A random sample of 50 alga were obtained and each was categorized as either being cyanobacteria or not. It was found that 38 were, in fact, cyanobacteria.Without relying on any previous knowledge Ian wanted to estimate the proportion that were cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval. How large a sample size would be required?
To estimate the proportion of cyanobacteria in algae samples with a 99% confidence level and a margin of error ≤ 0.01, Ian would need a sample size of at least 12111.
To determine the required sample size (n) for estimating the proportion of cyanobacteria in the algae samples with a margin of error of at most (0.01) and a (99%) confidence level, you can use the formula for the margin of error in estimating a population proportion:
[tex]\[ E = Z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \][/tex]
Given:
- Margin of error (E) = 0.01
- Confidence level = (99%), which corresponds to a Z-score of approximately 2.576
- Estimated proportion [tex](\(\hat{p}\)) = \(\frac{38}{50} = 0.76\)[/tex] (from the given sample)
Now, the formula can be rearranged to solve for (n):
[tex]\[ n = \frac{\hat{p}(1-\hat{p})}{\left(\frac{E}{Z}\right)^2} \][/tex]
Substitute the given values:
[tex]\[ n = \frac{0.76 \times (1 - 0.76)}{\left(\frac{0.01}{2.576}\right)^2} \][/tex]
Now calculate:
[tex]\[ n \approx \frac{0.76 \times 0.24}{\left(\frac{0.01}{2.576}\right)^2} \][/tex]
n ≈ 12111
Therefore, Ian would need a sample size of at least 12111 algae samples to estimate the proportion of cyanobacteria with a margin of error of at most (0.01) in a (99%) confidence interval.
Ian would require a sample size of approximately 12,102 algae to estimate the proportion of cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval.
To determine the required sample size for estimating the proportion of algae samples that are cyanobacteria with a margin of error of at most 0.01 and a 99% confidence level, we can use the formula for the confidence interval for a proportion:
[tex]\[ n = \left(\frac{z_{\alpha/2} \cdot \sqrt{p(1-p)}}{E}\right)^2 \][/tex]
where:
- n is the sample size,
- [tex]\( z_{\alpha/2} \)[/tex] is the z-score corresponding to the desired confidence level (for 99%, [tex]\( z_{\alpha/2} = 2.576 \),[/tex]
- p is the estimated proportion of the population that has the characteristic of interest (in this case, being cyanobacteria),
- E is the margin of error.
The estimated proportion p can be taken from the initial sample of 50 algae, where 38 were cyanobacteria. Thus, pis estimated as:
[tex]\[ p = \frac{\text{Number of cyanobacteria}}{\text{Total sample size}} = \frac{38}{50} = 0.76 \][/tex]
Now, we plug in the values into the formula:
[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.76(1-0.76)}}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.76 \cdot 0.24}}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.1824}}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{2.576 \cdot 0.427}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{1.101}{0.01}\right)^2 \][/tex]
[tex]\[ n = (110.1)^2 \][/tex]
[tex]\[ n \ = 12101.01 \][/tex]
Since we cannot have a fraction of an algae sample, we round up to the nearest whole number:
[tex]\[ n \ = 12102 \][/tex]
Omar picks 7 pounds of cherries . He divides them into containers that holds one whole 1/4 pounds of blue berries each. How many containers can he fill?
Answer:
Omar can fill 28 containers
Step-by-step explanation:
Omar have 7 pounds of cherries, each pound need 4 containers because each one only hold of [tex]\frac{1}{4}\\[/tex] pound, now we multiplicate 7 pounds with 4 container for each one and we get 28 containers.
[tex]Number containers = \frac{7 pounds}{\frac{1}{4}pounds } = 28[/tex]
The p-value for a two-sided test of the null hypothesis H0: μ = 10 is 0.06.(a) Would a 95% confidence interval for μ include the value 10? Why?(b) Would a 90% confidence interval for μ include the value 10? Why?
Answer:
a) Yes b) No
Step-by-step explanation:
Given that the p value for a two-sided test of the null hypothesis H0: μ = 10
is 0.06
a) [tex]p value = 0.06.\\Confidence level = 95%\\Significance level = 100-95 = 5%\\Alpha = 0.05\\\\p \geq \alpha is true[/tex]
Hence we accept null hypothesis
This implies that 10 will be within the confidence interval of 95%
b) If confidence level = 90%
[tex]\alpha = 0.10\\p value = 0.06\\p \leq 0.10[/tex]
So we have to reject null hypothesis.
So we do not have 10 in the confidence interval
The reason is the lower the confidence level, the narrower the confidence interval. In this case, 10 has gone outside the narrower interval hence we get this.
The school system is trying to help their students be more successful. They are going to hire tutors to help. They must have more teachers than tutors. The maximum number of teachers and tutors to be hired is 50. How many tutors and how many teachers can they hire? Let x = number of teachers hired. Let y = number of tutors hired. a. Write an inequality that represents the statement that the number of teachers hired must exceed the number of tutors hired. (2 points) b. Write an inequality that represents the statement that the maximum number of teachers and tutors is 50. (2 points) c. Choose a point that satisfies the situation, and explain why you chose that number of tutors and teachers. (1 point)
Answer:
a. [tex]x-y > 0[/tex]
b. [tex]x+y \leq 50[/tex]
c. x=26; y=24 or (24,26)
Step-by-step explanation:
Let x = number of teachers hired.
Let y = number of tutors hired.
Now solving for part a we get
a. Write an inequality that represents the statement that the number of teachers hired must exceed the number of tutors hired.
[tex]x-y > 0[/tex]
solving for part b we get;
b. Write an inequality that represents the statement that the maximum number of teachers and tutors is 50.
[tex]x+y \leq 50[/tex]
solving for part c we get;
c. Choose a point that satisfies the situation, and explain why you chose that number of tutors and teachers.
Now we know that [tex]x-y > 0[/tex] also [tex]x+y \leq 50[/tex]
x=26; y=24
(24,26)
Explanation: To make number of teacher more than number of tutors this is the maximum value we can achieve for the requirement.
a. The inequality x > y represents the statement that the number of teachers hired must exceed the number of tutors hired. b. The inequality x + y ≤ 50 represents the statement that the maximum number of teachers and tutors is 50. c. The point (25, 10) satisfies both inequalities and represents hiring 25 teachers and 10 tutors.
Explanation:a. To represent the statement that the number of teachers hired must exceed the number of tutors hired, you can write the inequality x > y. This means that the number of teachers, represented by x, must be greater than the number of tutors, represented by y.
b. To represent the statement that the maximum number of teachers and tutors is 50, you can write the inequality x + y ≤ 50. This means that the total number of teachers and tutors hired, represented by x + y, cannot exceed 50.
c. Let's choose the point (25, 10) which represents hiring 25 teachers and 10 tutors. This point satisfies both inequalities: 25 > 10 and 25 + 10 ≤ 50.
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Ella can complete the cheep cheep beatch course in 1 minute and 25 seconds. If the course is 3 laps long. How long would it take her to race 2 laps? ( proportion)
Answer: it will take her 56.67 seconds or 0.945 minutes to race 2 laps
Step-by-step explanation:
It takes Ella 1 minute and 25 seconds to complete the cheep beach course.
We can express this time in seconds or minutes. Expressing it in seconds,
1 minute = 60 seconds
Therefore,
1 minute and 25 seconds = 60 +25 = 85 seconds
If the course is 3 laps long, that means she completed 3 laps in 85 seconds. The time it will take her to race 2 laps would be
(2 × 85)/3
= 56.67 seconds
Converting to minutes, it will be
56.7/60 = 0.945 minutes
The area of a triangle is 72 cm2. The height of the triangle is 8 cm. What is the measure of the base of the triangle? A. 18 cm B. 36 cm C. 27 cm D. 32 cm
Answer:
A. 18x8 is 144 then divided by 2 is 72
Answer:
Step-by-step explanation:
Abscissa is:
a. the first number (or x value) of an ordered pair coordinate plane
b. a way of locating points in a plane that consists of a horizontal and a vertical number line intersecting at the zeros coordinates
c. an ordered pair, (x, y), that describes the location of a point in the coordinate plane ordinate
d. the second number (or y-value) of an ordered pair origin
e. the point of intersection, (0, 0), of the axes in the coordinate plane quadrant
f. region in the coordinate plane x-axis
g. the horizontal axis in the coordinate plane y-axis
h. the vertical axis in the coordinate plane
Answer:
The first number (or x value) of an ordered pair.
Step-by-step explanation:
Abscissa is the first number (or x value) of an ordered pair.
A coordinate plane is a way of locating points in a plane that consists of a horizontal and a vertical number line intersecting at the zeros.
Coordinates are an ordered pair, (x, y), that describes the location of a point in the coordinate plane.
Ordinate is the second number (or y value) of an ordered pair.
Origin is the point of intersection, (0, 0), of the axes in the coordinate plane.
A quadrant is a region in the coordinate plane.
X axis is the horizontal axis in the coordinate plane.
Y axis is the vertical axis in the coordinate plane.
Line A is the
✔ y-axis .
Region B is
✔ a quadrant .
Point C is the
✔ origin .
Line D is the
✔ x-axis .
hope this helps :)
The brand name of a certain chain of coffee shops has a 54% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 10 Coffleton residents. Find the probability that exactly 7 of the 10 Coffleton residents recognize the brand name.
0.0824
0.156
0.000806
0.0850
Answer:
0.156
Step-by-step explanation:
Using binomial probability formula, we have :
P( a out of n ) =ⁿCₐ x pᵃ x qⁿ⁻ᵃ ------------------------------------------------- (1)
Where n = total number of sample
a = number of success
p = probability of success
q = probability of failure
n-a = number of failures
From the question:
n =10 , a = 7, p=0.54, q = 1-p = 0.46
Substituting into equation (1) we have:
P (7 out of 10) = ¹⁰C₇ x (0.54)⁷x (0.46)¹⁰⁻⁷
= 0.1563
≈ 0.156
determine the intervals on which the function is increasing, decreasing, and constant
Answer:
increasing: (-1, ∞)decreasing: (-∞, -1)constant: nowhereStep-by-step explanation:
A function is increasing when it is rising to the right. Here, that is everywhere right of x=-1.
A function is decreasing when it is falling to the right. Here, that is everywhere left of x=-1.
A function is constant when its graph is horizontal. There are no places on this graph like that.
Nina earns $60 for 5 hours of shoveling snow. Complete each statement if Nina keeps earning her money at this same rate.
Answer:
she keeps her earnings the same
Given that lines a and b are parallel, what angles formed on line b when cut by the transversal are congruent with ∠2?
Answer:
The angles formed on line b when cut by the transversal are congruent with ∠2 are [tex]\angle{6}\text{ and }\angle{7}[/tex]
Step-by-step explanation:
Consider the provided information.
If transversal line crossed by two parallel lines, then, the corresponding angles and alternate angles are equal .
The angles on the same corners are called corresponding angle.
Alternate Angles: Angles that are in opposite positions relative to a transversal intersecting two lines.
∠2 and ∠6 are corresponding angles
Therefore, ∠2 = ∠6
∠2 and ∠7 are alternate exterior angles
Therefore, ∠2 = ∠7
Hence, the angles formed on line b when cut by the transversal are congruent with ∠2 are [tex]\angle{6}\text{ and }\angle{7}[/tex]