Answer:
129469.3194
342000
212530.6806
Step-by-step explanation:
Going to assume that the 8% is a nominal, montly rate
which means the effective monthly rate is .08/12= .006667
using the annuity immediate formula...
a.)
[tex]950(\frac{1-(1+.006667)^{-30*12}}{.006667})=129469.3194[/tex]
b.) we would pay 950*30*12= 342000
c.) the amount in interest would be 342000-129469.3194=212530.6806
a) The loan one can afford is $1,29,460.2
b) The total amount of money paid to the loan company over the life of the loan is $342,000.
c) $212539.8 of the total amount paid is interest.
To determine the answers to these questions, we'll need to use the formula for calculating a fixed monthly mortgage payment:
[tex]M = \frac{P \times r \times (1 + r)^n}{((1 + r)^n - 1)}[/tex]
where:
M is the monthly payment,
P is the principal loan amount,
r is the monthly interest rate (annual interest rate divided by 12),
and n is the total number of payments (number of years multiplied by 12).
Given:
Monthly payment (M) = $950
Loan term = 30 years
Interest rate = 8% per year
a) How big of a loan can you afford?
Let's calculate the principal loan amount (P):
First, we need to convert the annual interest rate to a monthly interest rate:
r = 0.08 / 12
= 0.00667
n = 30 years × 12 months
n= 360
Using the formula and plugging in the values we have:
[tex]950 = \frac{P \times 0.00667 \times (1 + 0.00667)^{360}}{((1 + 0.00667)^{360} - 1)}[/tex]
[tex]950 = \frac{P \times 0.00667 \times 10.948}{10.948 - 1}[/tex]
[tex]950=\frac{P \times 0.07302316}{9.948}[/tex]
[tex]950\times9.948 = 0.0730P[/tex]
Divide by 0.073:
Now we can solve for P:
[tex]P=\frac{9450.6}{0.0730}[/tex]
[tex]P = 1,29,460.2[/tex]
Therefore, you can afford a loan amount of $1,29,460.2
b) The total amount paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:
Total amount = Monthly payment × Total number of payments
Total amount =[tex]$950 \times 360[/tex]
Total amount = [tex]342,000[/tex]
Therefore, the total amount of money paid to the loan company over the life of the loan is $342,000.
c) To find out how much of the total amount paid is interest, we can subtract the principal loan amount from the total amount:
Interest = Total amount - Principal loan amount
Interest = [tex]342,000 - 129460.2[/tex]
=$212539.8
Therefore, $212539.8 of the total amount paid is interest.
To learn more on Simple Interest click:
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The distribution of the number of children for families in the United States has mean 0.9 and standard deviation 1.1. Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.
Required:
a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.
b. What average numbers of children are reasonably likely in the sample?
c. What is the probability that the average number of children per family in the sample will be 0.8 or less?
d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?
Answer:
a) By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.
b) Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.
c) 0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less
d) 0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 0.9 and standard deviation 1.1.
This means that [tex]\mu = 0.9, \sigma = 1.1[/tex]
Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.
This means that [tex]n = 1000, s = \frac{1.1}{\sqrt{1000}} = 0.035[/tex]
a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.
By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.
b. What average numbers of children are reasonably likely in the sample?
By the Empirical Rule, 95% of the sample is within 2 standard deviations of the mean, so:
0.9 - 2*0.035 = 0.83
0.9 + 2*0.035 = 0.97
Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.
c. What is the probability that the average number of children per family in the sample will be 0.8 or less?
This is the p-value of Z when X = 0.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]
[tex]Z = -2.86[/tex]
[tex]Z = -2.86[/tex] has a p-value of 0.0021
0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less.
d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?
p-value of Z when X = 1 subtracted by the p-value of Z when X = 0.8.
X = 1
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1 - 0.9}{0.035}[/tex]
[tex]Z = 2.86[/tex]
[tex]Z = 2.86[/tex] has a p-value of 0.9979
X = 0.8
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]
[tex]Z = -2.86[/tex]
[tex]Z = -2.86[/tex] has a p-value of 0.0021
0.9979 - 0.0021 = 0.9958
0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0
2.
The height of a kicked football can be represented by the polynomial - 16+ + 22t+
3, where tis the time in seconds. Find the factored form of the polynomial.
-
5
A) (8t + 3)(-2t + 1)
OB) (-8t+ 3)(2t+ 1)
8
OC) (8t+ 1)(-2t + 3)
OD) (-8t + 1)(2t+ 3)
Lisa, an experienced shipping clerk, can fill a certain order in 9 hours. Felipe, a new clerk, needs 10 hours to do the same job. Working together, how long will it take them to fill the order?
Answer:
9.5hrs
Step-by-step explanation:
since they are working together you have to take the average time since is the same order
What is the point estimate for the number of cars sold per week for a sample consisting of the following weeks: 1, 3, 5, 7, 10, 13, 14, 17, 19, 21?
A.
4.8
B.
5.22
C.
6.38
D.
6.1
Answer: A.
Step-by-step explanation:
Hope this helps!
What is the sum?
CO
3 5
x2-gx+3
+
8
x2+x-6
O
5x-12
X-3
-5x
(x+3)(x-3)
O
5x-12
(x+3)(x-3)
a. Consider the situation where you have three game chips, each labeled with one of the the numbers 3, 5, and 10 in a hat a. If you draw out 2 chips without replacement between each chip draw, list the entire sample space of po ssible results that can occur in the draw Use the three events are defined as follows, to answer parts b through n below:
Event A: the sum of the 2 drawn numbers is even.
Event B: the sum of the 2 drawn numbers is odd.
Event C: the sum of the 2 drawn numbers is a prime number
Now, using your answer to part a find the following probability values
b. P (A)=
c. P (B)=
d. P (C)=
e. P (A and C)-=
f. P(A or B)=
g. P (B andC)=
h. P(A or C)- =
i. P (C given B)=
j. P(C given A)=
k. P (not B)=
l. P (not C)=
Are events A and B mutually exclusive?Why or why not?
Are events B and C mutually exclusive? Why or why not?
Answer:
a) {3,5}{3,10}{5,10}
b) [tex]P(A)=\frac{1}{3}[/tex]
c) [tex]P(B)=\frac{2}{3}[/tex]
d) [tex]P(C)=\frac{1}{3}[/tex]
e) [tex]P(A and C)=0[/tex]
f) [tex]P(A or B)=1[/tex]
g) [tex]P(B and C)=\frac{1}{3}[/tex]
h) [tex]P(A or C)=\frac{2}{3}[/tex]
i) [tex]P(C given B)=\frac{1}{2}[/tex]
j) [tex]P(C given A)=0[/tex]
k) [tex]P(not B)=\frac{1}{3}[/tex]
l) [tex]P(not C)=\frac{2}{3}[/tex]
Yes, events A and B are mutually exclusive. Because the results can either be even or odd, not both. No, events B and C are not mutually exclusive because the result can be both, odd and prime.
Step-by-step explanation:
a)
In order to solve part a of the problem, we need to find the possible outcomes, in this case, the possible outcomes are:
{3,5}{3,10} and {5,10}
We could think of the oppsite order, for example {5,3}{10,3}{10,5} but these are basically the same as the previous outcomes, so we will just take three outcomes in our sample space. We can think of it as drawing the two chips at the same time.
b)
Now the probability of the sum of the chips to be even. There is only one outcome where the sum of the chips is even, {3,5} since 3+5=8 the other outcomes will give us an odd number, so:
[tex]P=\frac{#desired}{#possible}[/tex]
[tex]P(A)=\frac{1}{3}[/tex]
c) For the probability of the sum of the chips to be odd, there are two outcomes where the sum of the chips is odd, {3,10} since 3+10=13 and {5,10} since 5+10=15 the other outcomes will give us an even number, so:
[tex]P(B)=\frac{2}{3}[/tex]
d) The probability of the sum of the chips is prime. There is only one outcome where the sum of the chips is prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:
[tex]P(C)=\frac{1}{3}[/tex]
e) The probability of the sum of the chips to be even and prime. There are no results where we can get an even and prime number, since the only even and prime number there is is number 2 and no outcome will give us that number, so:
P(A and C)=0
f) The probability of the sum of the chips is even or odd. We can either get even or odd results, so no matter what outcome we get, we will get an odd or even result so:
[tex]P(A or B)=1[/tex]
g) The probability of the sum of the chips is odd and prime. There is only one outcome where the sum of the chips is odd and prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:
[tex]P(B and C)=\frac{1}{3}[/tex]
h) The probability of the sum of the chips is even or prime. There are two outcomes where the sum of the chips is even or prime, {3,10} since 3+10=13 and {3,5} since 3+5=8 so:
[tex]P(A or C)=\frac{2}{3}[/tex]
i) The probability of the sum of the chips is prime given that the sum of the chips is odd. There are two possible results where the sum of the chips is odd {3,10} and {5,10} and only one of those results is even, {3,10}, so
[tex]P(C given B)=\frac{1}{2}[/tex]
j) The probability of the sum of the chips is prime given that the sum of the chips is even. There is only one possible even result: {3,5} but that result isn't prime, so
[tex]P(C given A)=0[/tex]
k) The probability of the sum of the chips is not odd. There is only one outcome where the sum of the chips is not odd (even), {3,5} so:
[tex]P(not B)=\frac{1}{3}[/tex]
l) The probability of the sum of the chips is not prime. There are two outcomes where the sum of the chips is not prime, {3,5} and {5,10} so:
[tex]P(not C)=\frac{2}{3}[/tex]
Are events A and B mutually exclusive?
Yes, events A and B are mutually exclusive.
Why or why not?
Because the results can either be even or odd, not both.
Are events B and C mutually exclusive?
No, events B and C are not mutually exclusive.
Why or Why not?
Because the result can be both, odd and prime.
The linear equation Y = a + bX is often used to express cost formulas. In this equation:_________
a) the b term represents variable cost per unit of activity.
b) the a term represents variable cost in total.
c) the X term represents total cost.
d) the Y term represents total fixed cost.
Eight more than one-half of a number is twenty-two. Find the number.
Answer:
Below.
Step-by-step explanation:
22-8 = 14x2 = 28.
Suppose that you are headed toward a plateau 37 meters high. If the angle of elevation to the top of the plateau is , how far are you from the base of the plateau?
Answer:
21.36 meters
Step-by-step explanation:
Given
[tex]h = 37m[/tex]
[tex]\theta = 60^o[/tex]
Required
The distance from the base (b)
The question illustrates right-angled triangle (see attachment)
To solve for (b), we make use of tangent formula
[tex]\tan(60)=\frac{h}{b}[/tex]
Make b the subject
[tex]b =\frac{h}{\tan(60)}[/tex]
So:
[tex]b =\frac{37}{\tan(60)}[/tex]
[tex]b =\frac{37}{1.7321}[/tex]
[tex]b =21.36[/tex]
(c) Construct a 99% confidence interval for u if the sample
size, n, is 35.
Answer:
The confidence interval is [tex](\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})[/tex], in which [tex]\overline{x}[/tex] is the sample mean and [tex]\sigma[/tex] is the standard deviation for the population.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]M = 1.99\frac{\sigma}{\sqrt{35}}[/tex]
The lower end of the interval is the sample mean subtracted by M, while upper end of the interval is the sample mean added to M. Thus, the confidence interval is [tex](\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})[/tex], in which [tex]\overline{x}[/tex] is the sample mean and [tex]\sigma[/tex] is the standard deviation for the population.
Triangle A'B'C' is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between AABC
and A'B'C'?
Answer:
[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]k = 2[/tex] --- scale factor
Required
Relationship between ABC and A"B"C"
[tex]k = 2[/tex] implies that the sides of A"B"C" are bigger than ABC
i.e.
[tex]A"B" = 2AB[/tex]
[tex]A"C" = 2AC[/tex]
[tex]B"C" = 2BC[/tex]
In [tex]A"B" = 2AB[/tex]
Divide both sides by A"B"
[tex]1 = \frac{2AB}{A"B"}[/tex]
Divide both sides by 2
[tex]\frac{1}{2} = \frac{AB}{A"B"}[/tex]
Rewrite as:
[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]
(a) is correct
Pls help me someone this is annoying me
Answer:
They are both 42 cm
Step-by-step explanation:
Write the equations for a line parallel to the line:
y=-4/3x-4
That goes through the point (-7,-6)
Write your equation in slope intercept form, using reduced fractions for the slope and intercept if necessary.
Answer:
y = -4/3x -46/3
Step-by-step explanation:
The question tells us to write an equation that is:
- parallel to the given line
- goes through the point (-7, -6)
Parallel lines will have the same slope, because if the slope was different, they would eventually intersect and not be parallel lines anymore.
We are going to use the point-slope form to find the other line.
Point-slope form uses a point that the graph will cross through and the slope of the graph to find the graph in y = mx + b form (also called slope-intercept form).
(I attached the point-slope form as an image below)
m = slope
x1 = x coordinate of the point
y1 = y coordinate of the point
We are going to substitute our slope into the form first:
y - y1 = (-4/3)(x - x1)
Next let's put in our point (-7, -6):
(Remember! -7 is our x coordinate & -6 is our y coordinate :-) )
y - (-6) = -4/3(x - (-7))
(cancel out the negatives to make them positive)
y + 6 = -4/3 (x +7)
Now solve for x using basic algebra:
y + 6 = -4/3 (x +7)
(distribue the -4/3)
y + 6 = -4/3x - 28/3
(subtract 6 from both sides)
y = -4/3x -46/3
That's your answer!
Hope it helps (●'◡'●)
Answer:
Step-by-step explanation:
y + 6 = -4/3(x + 7)
y + 6 = -4/3x - 28/3
y + 18/3 = -4/3x - 28/3
y = -4/3x - 46/3
2) There are 40 boys and 16 girls in a class of students. What is the ratio of girls to students?
Add boys and girls together for total students:
40 + 16 = 56 total students
Girls to total students is 16/56
Divide both numbers by 8 to get 2/7
The ratio is 2/7
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
There are 40 boys and 16 girls in a class of students. ⠀⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀What is the ratio of girls to students?⠀⠀⠀[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
In a class,
boys=40
girls =16
So,
The students of the class =
boys+girls 40+1656According to the question,
we have to find the ratio of girls to the total students
ratio=[tex]\sf{\dfrac{girls}{students} }[/tex] ratio=[tex]\sf{\dfrac{16}{56} }[/tex] ratio=[tex]\sf{\dfrac{\cancel{16}}{\cancel{56}} }[/tex]ratio=[tex]\sf{\dfrac{2}{7} }[/tex] ratio=[tex]\sf{2:7 }[/tex]⠀⠀⠀⠀
[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
⠀⠀⠀⠀
Hence,the ratio of girls to students is 2:7
⠀⠀⠀⠀
Tiham is the only striker of his team. He can catch one of the four passes delivered to him and when he get a pass he takes the shot. One of his four shots go towards the net but the goal keeper of the opposite team stop one of every two shots. What is the minimum number of passes have to be delivered to Tiham to score minimum one goal?
Answer:
1/4 *1/4*1/2 =0.03125
which as a fraction is 1/32
so the minimuim number of passes that will get him a goal is 1 since he could get it on the first try
Hope This Helps!!!
Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.
f(x)=6x^2+12x
Answer:
(-1, -6)
Step-by-step explanation:
This a term in this function is not negative, which would make it be flipped over the x-axis. Therefore this function takes the typical parabola shape, and it will have a minimum point.
To find the x-value of the minimum use the formula -b / 2a.
-12 / 2(6) = -1
Then plug in the x-value and find the y-value for this function
f(-1) = 6(-1)^2 + 12(-1) = -6
1. S = 10 mm
V= S×S×S
=___×___×___
=____ mm3
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]V=1000\text{mm}^3[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
I am assuming by the infomation given that the figure is a cube.
⸻⸻⸻⸻
[tex]\boxed{\text{Finding the volume of the cube...}}\\\\S = 10mm; V= s^3\\--------------\\\rightarrow V = 10^3\\\\\rightarrow V = 10 * 10 * 10\\\\\rightarrow \boxed{V=1000\text{mm}^3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
The radius of a circle is 5 yd.
Answer the parts below. Make sure that you use the correct units in your answers.
If necessary, refer to the list of geometry formulas.
Answer:
Circumference =10 pi yard
Area =25 pi yard squared
Step-by-step explanation:
C=2*pi*r
Circumfrance =10 pi
A=pi r^2
Area =25 pi
For the estimate just sub in pi on the calculator for pi, then round to the hundreth.
Circumfrence= just the unit
Area= squared
4,3,5,9,12,17,...what is the next number?
Answer:
The next number is going to be 21
Answer:
19
Step-by-step explanation:
4 even number
3,5,7 odd numbers
14 even
17, 19, 21 even
5t/4y=3b/4c (solve for y)
I also need to know the steps.
thanks.
Answer:
[tex]y = \frac{5ct}{3b}[/tex]
Step-by-step explanation:
[tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex]
1. start by multiplying y to both sides:
y × [tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex] × y
[tex]\frac{5t}{4} =\frac{3b}{4c}y[/tex]
2. divide both sides by [tex]\frac{3b}{4c}[/tex]
[tex]\frac{5t}{4}/\frac{3b}{4c} =\frac{3b}{4c}y/\frac{3b}{4c}[/tex]
[tex]y = \frac{5ct}{3b}[/tex]
(3b-4)(b+2) in standard form
Answer:
3b^2 + 2b -8
Step-by-step explanation:
* means multiply
^ means exponent
3b * b = 3b^2
3b * 2 = 6b
-4 * b = -4b
-4 * 2 = -8
3b^2 + 6b -4b -8
3b^2 + 2b -8
Bateman Corporation sold an office building that it used in its business for $800,800. Bateman bought the building 10 years ago for $599,600 and has claimed $201,200 of depreciation expense. What is the amount and character of Bateman's gain or loss?
Answer:
$402.700 capital gain
Step-by-step explanation:
A sphere has radius 7cm then find its volume
Answer:
1437.3 cm^3 is the volume of sphere whose radius is 7cm
Work out m and c for the line:
y – 37 = 5
Answer:
first thing is y - 35 = 5
then y = 35 + 5 because when = come here - will be + and
then we should do+ y=40 answer
A binomial experiment consists of 11 trials. The probability of success on trial 4 is 0.41. What is the probability of success on trial 8?A. 0.71B. 0.41C. 0.39D. 0.84E. 0.14
Answer:
B. 0.41
Step-by-step explanation:
Binomial experiment:
In a binomial experiment, the probability of the success on each trial is always the same.
The probability of success on trial 4 is 0.41.
This means that the probability of success on trial 8, and all the other 10 trials, is of 0.41, and thus the correct answer is given by option B.
Find m angle JRQ if m angle SRQ=166^ and m angle SRJ=110^
Answer:
[tex] \large{ \tt{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]
[tex] \large{ \tt{❉ \: m \: \angle \:SRQ = m \: \angle \: SRJ\: + \: m \: \angle \:JRQ}}[/tex]
[tex] \large{ \tt{⟼ \: 166 \degree = 110 \degree + m \: \angle \: JRQ}}[/tex]
[tex] \large{ \tt{⟼ \: 166 \degree - 110 \degree = m \: \angle \: JRQ}}[/tex]
[tex] \boxed{ \large{ \tt{⟼ \: 56 \degree = m \: \angle \: JRQ}}}[/tex]
Our final answer is 56° . Hope I helped! Let me know if you have any questions regarding my answer! :)what is the answer some one help me please so i can do this
Answer:
They can buy up to 240 drinks.
Step-by-step explanation:
Let x = number of drinks
The price of 1 drink is 75¢ = $0.75
The price of x drinks is 0.75x
The store gives a discount of $100.
The rice of x drinks is
0.75x - 100
The total price of the drinks must be less than or equal to $80.
0.75x - 100 ≤ 80
Add 100 to both sides.
0.75x ≤ 180
Divide both sides by 0.75
x ≤ 240
Answer: They can buy up to 240 drinks.
Trapezoid A B C D is shown. A diagonal is drawn from point B to point D. Sides B C and A D are parallel. Sides B A and C D are congruent. Angle C B D is 24 degrees and angle B A D is 116 degrees.
What is the measure of angle ABD in trapezoid ABCD?
24°
40°
64°
92°
Answer:
40 degrees un edge
Step-by-step explanation:
Answer:
The person above me got this correct, so the answer to this is 40! I just did the Unit Test and got a 100%!
Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
Answer:
Step-by-step explanation:
-4 is a root for 3 times and 1 is root for once
so (x+4)^3 * (x-1) is part of f(x)
the constant term there is 4^3*(-1)=-64
so there is a multiplier of 320/-64=-5
f(x) = -5 * (x+4)^3 * (x-1)
At a store sales tax is charged at a rate of 2% on the cost price of an item . the sales tax on a dress which cost $180 is
Answer:
$3.60
Step-by-step explanation:
100% = 180
1% = 180/100 = $1.80
2% = 1%×2 = 1.8×2 = $3.60
