Answer:
787.50
Step-by-step explanation:
interest=3500*7.5*3/100
interest=35*7.5*3
interest=787.50
find the inverse function of F(x) = 1/2x-6
Answer:
[tex]F^{-1} (x) = 2x + 12[/tex]
Step-by-step explanation:
Let's assume F(x) = y, then
[tex]y = \frac{1}{2} x - 6[/tex]
Let us solve the equation for x.
[tex]y + 6 = \frac{1}{2} x[/tex]
[tex]2y + 12 = x[/tex]
Next, replace y with x and also replace x with F⁻¹(x)
Answer: [tex]F^{-1} (x) = 2x + 12[/tex]
subtract
a2-b2 from a2 +b2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
plus a square and minus a square gets cancel
b^2 + b^2
since they are like terms they can be added
2b^2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
= b^2 + b^2
like terms can be added
+2b^2
Which of the following best describes the use of the formula S = (n - 2)180°,
where n is the number of sides?
A. It is used to find the number of interior angles in a regular polygon.
B. It is used to find the sum of the interior angles in a regular
polygon.
O c. It is used to find the sum of the exterior angles in a regular
polygon
O D. It is used to find the number of exterior angles in a regular
polygon
SUBMIT
Given the set of vectors , decide which of the following statements is true:
A: Set is linearly independent and spans ℛ 3. Set is a basis for ℛ 3.
B: Set is linearly independent but does not span ℛ 3. Set is not a basis for ℛ 3.
C: Set spans ℛ 3 but is not linearly independent. Set is not a basis for ℛ 3.
D: Set is not linearly independent and does not span ℛ 3. Set is not a basis for ℛ 3.
(1,0,0),(0,1,2)
A professor wants to estimate the average time it takes his students to finish a computer project. Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours. He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.
Answer:
A sample size of 3 is required.
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 - 0.96}{2} = 0.02[/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 - 0.02 = 0.98[/tex], so Z = 2.054.
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.
Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.
This means that [tex]\sigma = 3.6[/tex]
He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.
The sample size needed is of n, and n is found when M = 5. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 2.054\frac{3.6}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 2.054*3.6[/tex]
[tex]\sqrt{n} = \frac{2.054*3.6}{5}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2[/tex]
[tex]n = 2.19[/tex]
Rounding up:
A sample size of 3 is required.
|-5| >3 true or false plssssss answer it’s important
Answer:
TRUE
Step-by-step explanation:
Those lines around the -5 mean the absolute value of the number, basically the value of the number without any negative signs. SO the absolute value of -5 is just 5.
5 IS GREATER than 3, so this is true
ur welcome :)
I need help resolving this please
27x^6 = 387420489
You want something similar but cubed.
[tex]\sqrt[3]{387420489}[/tex] = 729
YOUR ANSWER: 729x^3 = 387420489
Step-by-step explanation:
There are four points on a line: A, B, C and D, so that AB=1,BC=2,CD=4. Find the length of segment AD. Consider all possibilities and draw a picture for each one of them.
All possible answers for the length of AD are, _, _, _, _, _.
Answer:
7
Step-by-step explanation:
Since it's on a line, we add up all of the numbers. So 1 + 2 + 4 = 7.
Answer:
7, 1, 5, and 3
Step-by-step explanation:
Because you have to consider all possibilities, you will have multiple different-looking number lines. Using the ratios given in the problem, just by playing around with the letters' placements on the number line you can easily find the length of AD.
Help help help help help
I need help I’ll give u brainlest
Answer:
1000
Step-by-step explanation:
Volume = 10 * 10 * 10 = 1000
Answer:
[tex]Volume = 1000[/tex]
Step-by-step explanation:
Formula to find volume of cube:
[tex]Volume=a^{3}[/tex]
[tex]Volume = 10^{3}[/tex]
[tex]Volume = 10*10*10[/tex]
[tex]Volume = 1,000[/tex]
hope this helps.....
A box of golf balls contains 10 balls. Each golf ball has a diameter of 3.6 centimeters. What is the total
volume of golf balls in 3 boxes?
about 1465.74 cm
c. about 1221.45 cm
b. about 732.87 cm
d. about 81.43 cm
Answer:
C
Step-by-step explanation:
please help! (listing BRAINLIST and giving points) :)
Answer:
Tan B = 12/5
Sin B = 12/13
Cos B = 5/13
Step-by-step explanation:
sine B = opposite (12)/hypotenuse (13)
= 12/13
Cosine B = adjacent/hypotenuse
= 5/13
Tangent B = opposite/adjacent
= 12/5
Here is a picture that can always help you with the three trig ratios.
tracy has 63 colors pens and jacob has 46 colors pens how many more colors pens does tracy have than jacob
Given:
Number of color pens Tracy have = 63
Number of color pens Jacob have = 46
To find:
How many more colors pens does Tracy have than Jacob?
Solution:
We need to find the difference between the number of color pens Tracy have and the number of color pens Jacob have.
[tex]Difference=63-46[/tex]
[tex]Difference=17[/tex]
Therefore, Tracy have 17 more color pens than Jacob.
!PLS HELP I WILL GIVE BRAINLEST!
The net of a rectangular prism is shown
What is the surface area of this prism?
The answer would be 18 square units
Step-by-step explanation:
When talking about surface area, just add up all the units that is listed in the question. - just a tip ;)
Anyways, Hope this helps!! If it's wrong, feel free to curse me out.. haha...
Two triangles have the same area. One triangle has a base of 4 cm and a height of 7 cm. If the height of the other triangle is 14 cm, then what is its base length?
3 cm
2 cm
4 cm
5 cm
Answer:
x = 2
Step-by-step explanation:
→ Work out the area of the first triangle
0.5 × 4 × 7 = 14
→ Set up an equation for the second base
0.5 × x × 14 = 14
→ Simplify
7x = 14
→ Divide both sides by 7
x = 2
Answer:
option B = 2cm
Step-by-step explanation:
[tex]Area \ of \ first \ triangle = \frac{1}{2} \times base_1 \times height_1 \ [ \where base_1 = 4\cm \ height_1 \ = 7cm \ ][/tex]
[tex]=\frac{1}{2} \times 4 \times 7 \\\\= 14 \ cm^2[/tex]
Given area of second triangle is same as first.
[tex]Area \ of \ second \ triangle = \frac{1}{2} \times base_2 \times height_2 \ [ \ where \ height _ 2 = 14cm \ ][/tex]
[tex]14 = \frac{1}{2} \times base_2 \times 14\\\\14 = 7 \times base_2\\\\base_2 = 2 \ cm[/tex]
Which recursive sequence would produce the sequence 6, 20, 62, …
Step-by-step explanation:
Using an online calculator, I was able to find that one pattern is
[tex]a_{n} = a_{n-1} + 14 * 3^{n-1}[/tex] . Finding a recursive sequence is generally based on guess and check, so there isn't much explanation to obtaining one
5/8 + 3/4 / -2/3- 5/6.
Answer:
-5/16 or -0.3125
Step-by-step explanation:
Answer:
-11/12
Step-by-step explanation:
Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
For each of the following properties write down a matrix that has this property or explain why there is no such matrix (Hint: Check first whether the dimensions add up)
(a) The column space contains (1,0,0)T, (0,0,1)T while the row space contains (1,1)T and (1, 2)T.
(b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
(c) The column space is R4 and the row space is R3.
Answer:
a) A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
b) attached below ( Matrix dose not exist )
c) attached below ( Matrix does not exist )
Step-by-step explanation:
a) Matrix
A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
From the matrix ; Column 1 and Column 2 Belong to COL(A)
while : (1,1)^T = ( 1,0 )^T + ( 0,1 )^T i.e. (1,1)^T ∈ Row( A )
and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T i.e. (1, 2)^T ∈ Row( A )
Hence ; all requirements are fulfilled in Matrix A
b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
Matrix is Non-existent because condition is not met
attached below
c) Rank | A |
dimension of column space= 4 , dimension of Row space = 3
Given that ; column space ≠ Row space
Hence Matrix does not exist
Which angle is coterminal to a 185° angle?
Answer:
the answer is -175. I hope that helped
the temperature of a cup of coffee obeys newton's law of cooling. The initial temperature of the coffee is 150F and 1 minute later it is 135F. The temperature of the room is 70F. If T(t) represents the temperature of the coffee at time T the correct differential equation for the temperature for this condition is
Answer:
Newton's law of cooling says that:
T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)
or:
[tex]\frac{dT}{dt} = -k*(T - T_a)[/tex]
in the differential form.
where:
T is the temperature as a function of time
Tₐ is the ambient temperature, in this case, 70F
T₀ is the initial temperature of the object, in this case, 150F
k is a constant, and we want to find the value of k.
Then our equation is:
T = 70F + (150F - 70F)*e^(k*t)
Now we also know that after a minute, or 60 seconds, the temperature was 135F
then:
135F = 70F + (150F - 70F)*e^(k*60s)
We can solve this for k:
135F = 70F + 80F*e^(k*60s)
135F - 70F = 80F*e^(k*60s)
65F = 80F*e^(k*60s)
(65/80) = e^(k*60s)
Now we can apply the Ln(x) function to both sides to get:
Ln(65/80) = Ln(e^(k*60s))
Ln(65/80) = k*60s
Ln(65/80)/60s = k = -0.0035 s^-1
Then the differential equation is:
[tex]\frac{dT}{dt} = -0.0035 s^-1*(T - 70F)[/tex]
The dean of the UTC Engineering School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Engineering School graduates are selected at random, and data on GPA and starting salary ( in $thousands) for each graduate were used to fit the model The dependent variable is____________________________.
Answer:
grade-point average (GPA).
Step-by-step explanation:
The Independent variable may be explained as the variable which is used to manipulate the variable to be predicted. The Independent variable also called the predictor variable takes up several input values in other to observe how the predicted variable changes due to this independent variable. In the scenario described above, the independent variable is the Grade - point average, as it is used to make prediction or manipulate the value of the starting salary earned by a graduate. The starting salary earned is the predicted variable or dependent variable in this scenario.
2. Kayli swam 0.7 kilometers at the school swimming pool. How many meters did she swim?
Kayli swam
meters in the swimming pool.
Answer:
To convert kilometres to metres, divide the value by 1000.
0.7 ÷ 1000 = 700 metres
Kayli swam 700 meters in the swimming pool
Hope this helps!
Mr. Arju wishs to purchase a house . to buy the house he needs to make a down payment of nu.300000 and also pay nu.15000 every quarter for the next 8 years. the interest charge is 9% per year compounded quarterly. what is the price of the house?
Answer:
The price of the house is $ 853,735.05.
Step-by-step explanation:
Since Mr. Arju wishes to purchase a house, and to buy the house he needs to make a down payment of $ 300,000 and also pay $ 15,000 every quarter for the next 8 years, if the interest charge is 9% per year compounded quarterly, to determine what is the price of the house, the following calculation must be performed:
300,000 + (15,000 x 12 x 8) = X
300,000 + (180,000 x 8) = X
300,000 + 1,440,000 = X
1,740,000 = X
X x (1 + 0.09 / 4) ^ 8x4 = 1,740,000
X x (1 + 0.0225) ^ 32 = 1,740,000
X x 1.0225 ^ 32 = 1,740,000
X x 2.0381030257737 = 1,740,000
X = 1,740,000 / 2.03810
X = 853,735.05
Therefore, the price of the house is $ 853,735.05.
55
3. Patrick paid $20 for 5 peaches. How much did he pay per peach? Show
your work!
Answer:
Step-by-step explanation:
LA EDUCACION ES IMPIRTANTE YA QUE PROMUEVE UN MEJOR DESARROLLO DE LOS NIÑOS,NIÑAS Y ADOLESCENTES QUE LOS HACE FOMENTAR UN VINCULO MUY ESPECIAL CON SUS MAESTROS,COMPAÑEROS QUE LOS HACE SENTIR QUE SON PARTE DE SU FAMILIA ADEMAS ELLOS PASAN LA MAYORIA DE TIEMPO EN LA ESCUELA QUE LOS HACE SENTIRSE MÁS CÓMODOS COMO SI FUERA SU PROPIO HOGAR
Answer:
4 peaches
Step-by-step explanation:
$20/5 = 4 peaches
Y=x^3/2(x^2+1) I need the steps.
Answer:
0
Step-by-step explanation:
If you are looking for the x- intercept image is below
if you are looking for the y- intercept its the same as the x. Image is below
Select the correct answer.
The function g(x) = x is transformed to obtain function :
Rx) = g(x) + 1.
Which statement describes how the graph of his different from the graph of g?
ОА
The graph of his the graph of gvertically shifted up 1 unit.
OB.
The graph of his the graph of g horizontally shifted right 1 unit.
OC. The graph of his the graph of g horizontally shifted left 1 unit
D. The graph of his the graph of g vertically shifted down 1 unit.
Answer: A
Step-by-step explanation:
Find the inverse of \(\Large h(x) = \frac {3}{2}x + 1 \)
Answer:
[tex]h(x) = \frac {3}{2}x + 1 \\ { \tt{let \: the \: inverse \: be \: { \bold{m}}}} \\ { \tt{m = \frac{1}{ \frac{3}{2}x + 1 } }} \\ \\ { \tt{m = \frac{2}{3x + 2} }} \\ \\ { \tt{m(3x + 2) = 2}} \\ \\ { \tt{3x + 2 = \frac{2}{m} }} \\ \\ { \tt{x = \frac{2 - 2m}{3m} }} \\ \\ { \tt{x = \frac{2}{3m}(1 - m) }} \\ \\ { \bf{h {}^{ - 1} (x) = \frac{2}{3x}(1 - x) }}[/tex]
The following data represent the weights in pounds of a sample of 25 police officers:
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
Required:
a. Determine the location and value of the lower quartile of the weights
b. Determine the location and value of the upper quartile of the weights.
c. Find the interquartile range of the weights.
Given:
The data values are:
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
To find;
a. Lower quartile.
b. Upper quartile.
c. Interquartile range.
Solution:
We have,
164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, 171.
Arrange the data values in ascending order.
134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157, 162, 163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177.
Divide the data values in two equal parts.
(134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177)
Divide each parentheses in two equal parts.
(134, 137, 140, 145, 146, 148), (151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169), (171, 172, 173, 174, 174, 177)
a. Location of lower quartile is:
[tex]Q_1=\dfrac{1}{4}(n+1)\text{th term}[/tex]
[tex]Q_1=\dfrac{1}{4}(25+1)\text{th term}[/tex]
[tex]Q_1=\dfrac{26}{4}\text{th term}[/tex]
[tex]Q_1=6.5\text{th term}[/tex]
The lower quartile of the weights is:
[tex]Q_1=\dfrac{148+151}{2}[/tex]
[tex]Q_1=\dfrac{299}{2}[/tex]
[tex]Q_1=149.5[/tex]
Therefore, the location of the lower quartile of the weights is between 6th term and the 7th term. The value of the lower quartile is 149.5.
b. Location of upper quartile is:
[tex]Q_3=\dfrac{3}{4}(n+1)\text{th term}[/tex]
[tex]Q_3=\dfrac{3}{4}(25+1)\text{th term}[/tex]
[tex]Q_3=\dfrac{3\cdot 26}{4}\text{th term}[/tex]
[tex]Q_3=19.5\text{th term}[/tex]
The upper quartile of the weights is:
[tex]Q_3=\dfrac{169+171}{2}[/tex]
[tex]Q_3=\dfrac{340}{2}[/tex]
[tex]Q_3=170[/tex]
Therefore, the location of the upper quartile of the weights is between 19th term and the 20th term. The value of the upper quartile is 170.
c. The interquartile range of the given data set is:
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=170-149.5[/tex]
[tex]IQR=20.5[/tex]
Therefore, the interquartile range of the weights is 20.5.
Score on last try: 0 of 8 pts. See Details for more.
Get a similar question
You can retry this question below
Five cards are drawn randomly from a standard deck of 52 cards
Determine the probability that exactly 3 of these cards are Aces. Write your answer in decimal form, rounded to 5 decimal
places
Answer
Answer:
there are 4 aces in the deck of 52 cards
so the probability to draw one ace is 4/52
if we draw an ace, there are 3 left in 51 cards.
so the next probability will be 3/51
we need to multiply probabilities to know how likely it is that this happens in a row.
for three in a row that's
[tex] \frac{4}{52} \times \frac{3}{51} \times \frac{2}{50} [/tex]
rewritten its:
[tex] \frac{4 \times 3 \times 2}{52 \times 51 \times 50} [/tex]
we'll see soon why this is easier to write.
we also have to account for the two cards that are no aces. it doesn't matter if the first two cards are no aces, the last two, or any rodney. just the ammount of non-aces is important.
there are 48 non-aces in the deck.
so the probability to draw one of them in the first step is 48/52.
wich each draw the number of cards left in the deck decreases by 1. and depending what we draw, that ammount also decreases.
we draw 5 cards, so we know what the denominators will be. the numerator will be the rest-ammounts of each event, like shown in the complicated fraction above.
let's write it most easily as this:
[tex] \frac{4 \times 3 \times 2 \times 48 \times 47}{52 \times 51 \times 50 \times 49 \times 48} [/tex]
this scenario looks like it only describes 3 aces, then two non-aces, but the order of multiplication isn't important. you could put the 48 and 47 to the left, same solution. so this expression represents all permutations of "3 aces when drawing 5 cards", including the two cards that are not aces.
that's why writing it as one convoluted fraction is indeed better and simpler than many fraction multiplied in row.
time to grap a calculator.
our probability for the event is
54144 possible valid outcomes out of
311875200 possible combinations.
luckily the calculator can reduce that to a simpler form of
[tex] \frac{47}{270725} [/tex]
(reduced with 2^6*3^, big number, but tried it out by hand stacking up prime factors until hittinga prime in the numerator)
written as a readable kind of number you probably know and like it's
0.0001736079047
in decimal form. now rounded as asked for:
0.00017
(as percentage: 0.017%)
hope the way how we got here is somewhat clear. feel free to ask any questions.
kind regards
Alex
Elysia has 2 apples she gives 1 to her friend so how many does she have?
Answer:
One Apple.
Step-by-step explanation:
This is a basic subtraction and addition problem. She began with one apple and gave one to her friend. How many apples is Elysia holding now? 2-1= 1
One apple.
Elysia will have one apple, as one apple is being subtracted because she gave it to her friend.
What is subtraction?In math, to subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.
Given that, Elysia has 2 apples she gives 1 to her friend,
To find the number of apples Elysia left with, we will subtract the number of apples she gave to her friend to the number of apples she had,
Number of apples Elysia left with = 2-1 = 1
Hence, Elysia will have one apple.
Learn more about subtraction, click;
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