[tex]\dfrac{f(x)}{g(x)}=\dfrac{8x^3+16x^2-15}{2x+1}[/tex]
Use the graph showing Phillip's account balance to answer the question that follows. ^
What is the interest rate on Phillip's account?
A - 3.3%
B - 6.7%
C - 9.0%
D - 15.3%
Answer:
A - 3.3%
Step-by-step explanation:
From the graph
Where x= 0
Amount =$ 450
It shows that$450 is the capital
Then
When x= 3
Amount=$494.55
So interest generated within 3 years
= $494.55-$450
=$ 44.55
When x= 9
Amount = $583.65
So interest generated within 9 years
= $583.65-$450
=$ 133.65
PRT/10= Interest
450*x*3/100= 44.55
1350x= 4455
X= 4455/1350
X= 3.3
So the rate is =3.3%
the volume of a cube is 3375 cubic inches. what is the measure of each side of the cube
Answer:
The measure of each side of the cube is
15 inchesStep-by-step explanation:
Since it's a cube all it's sides are equal
To find the length of each side we use the formula
Volume of a cube = l³
where l is the measure of one side
From the question
Volume = 3375 cubic inches
Substitute this value into the formula and solve for l
That's
[tex] {l}^{3} = 3375[/tex]Find the cube root of both sides
That's
[tex] \sqrt[3]{ {l}^{3} } = \sqrt[3]{3375} [/tex]We have the final answer as
l = 15 inchesHope this helps you
Simplify i^38 ????????
Answer:
i is defined as the square root of -1.
i^2 = -1
i^3 = -i
i^4 = 1
Following the pattern, we see that i^40 = 1, so i^38 is two above, or equal to -1.
So, i^38 = -1.
Let me know if this helps!
someone please help me
Answer:
3 mL
Step-by-step explanation:
The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.
tan inverse 1/4 +tan inverse 2/7 = 1/2 cos inverse 3/5
Answer:
The equation is always false
Step-by-step explanation:
arctan1/4+arctan2/7=1/2arccos3/5
0.24497866+0.27829965=1/2(0.92729521)
0.52327832 =0.46364760
not equivalent and will never be.
Many countries, especially those in Europe, have significant gold holdings. But many of these countries also have massive debts. The following data show the total value of gold holdings in billions of U.S. dollars and the debt as a percentage of the gross domestic product for nine countries (WordPress and Trading Economics websites, February 24, 2012).
Gold Value ($ billions) Debt (% of GDP)
Country
China 63 17.7
France 146 81.7
Indonesia 203 83.2
Germany 33 69.2
Italy 147 119
Netherlands 36 63.7
Russia 50 9.9
Switzerland 62 55
United States 487 93.2
Using the entire data set, develop the estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings (to 4 decimals (to 4 decimals)
Answer:
X`= -0.60872 Y + 176.4085
or X`= 176.4085-0.60872 Y
Step-by-step explanation:
Country Gold Value Debt (% of GDP)
($ billions) X Y XY X² Y²
China 63 17.7 1115.1 3969 313.29
France 146 81.7 11928.2 21316 6674.89
Indonesia 203 83.2 16889.6 41209 6947.2
Germany 33 69.2 2283.6 1089 4788.64
Italy 147 119 17493 21609 14161
Netherlands 36 63.7 2293.2 1296 4057.69
Russia 50 9.9 495 2500 98.01
Switzerland 62 55 3410 3844 3025
United States 487 93.2 45,388.2 237169 8686.24
∑ 1227 592.6 101245.9 334001 48751.96
The estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings
X = a1 + bxy Y
wher e
bxy = n ∑XY -∑X∑Y/ n ∑Y²- (∑Y)²
= 9( 101245.9 )- (1227 *592.6)/ 48751.96-(592.6)²
911213.1 - 727120.2/ - 302422.8= - 0.60872
a1= X` -bxy Y`= 136.33- (-0.60872)(65.84)
= 136.33+ 40.07858= 176.4085
Hence X`= -0.60872 Y + 176.4085
or X`= 176.4085-0.60872 Y
You pay $16 to buy four pizzas, How much did each pizza cost?
Answer:
16 dollars = 4 pizzas
4 dollars = 1 pizza
Each pizza costs 4 dollars.
Let me know if this helps!
Answer: $4
Step-by-step explanation:
16 divided by 4, equals 4.
Please help!! 25 points!!
9514 1404 393
Answer:
(a) a^4/(4b^2)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
__
Your expression simplifies as follows.
[tex]\dfrac{3a^2b^{-4}}{12a^{-2}b^{-2}}=\dfrac{3}{12}\cdot\dfrac{a^{2-(-2)}}{b^{-2-(-4)}}=\boxed{\dfrac{a^4}{4b^2}}[/tex]
The population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches. A sample of 50 men and 40 women is selected. What is the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights
Answer:
The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.
Step-by-step explanation:
We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.
A sample of 50 men and 40 women is selected.
The z-score probability distribution for the two-sample normal distribution is given by;
Z = [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex] ~ N(0,1)
where, [tex]\mu_M[/tex] = population mean height of men at UMBC = 69 inches
[tex]\mu_W[/tex] = population mean height of women at UMBC = 65 inches
[tex]\sigma_M[/tex] = standard deviation of men at UMBC = 4 inches
[tex]\sigma_M[/tex] = standard deviation of women at UMBC = 3 inches
[tex]n_M[/tex] = sample of men = 50
[tex]n_W[/tex] = sample of women = 40
Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P([tex]\bar X_M-\bar X_W[/tex] > 5 inches)
P([tex]\bar X_M-\bar X_W[/tex] > 5 inches) = P( [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex] > [tex]\frac{(5)-(69-65)}{\sqrt{\frac{4^{2} }{50}+\frac{3^{2} }{40} } }[/tex] ) = P(Z > 1.35)
= 1 - P(Z [tex]\leq[/tex] 1.35) = 1 - 0.9115 = 0.0885
The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.
For each ordered pair, determine whether it is a solution to y=-9.
Is it a solution?
Yes or No
(1, -9)
(7,3)
(-9,4)
(0, -9)
Answer:
(1, -9) yes
(7,3) no
(-9,4) no
(0, -9) yes
Step-by-step explanation:
The y value must be -9
The x value can be any value to satisfy the equation y = -9
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
Find the value of x.
Answer:
6x + 6 = 32
6x = 32 - 6
6x = 26
divide both sides by 6
6x/6 = 26/6
6x + 6 = 4.35
9x - 9 = 24
9x = 24 + 9
9x = 33
divide both sides by 9
9x/9 = 24/9
9x + 9 = 2.66
9x + 9 = 2.66
Answer: x=3
Step-by-step explanation:
[tex]\frac{32}{24} =\frac{4}{3} \\\\\frac{4}{3}=\frac{6x+6}{9x-9}\\ x=3[/tex]
Which expression is equivalent to 5y^3/(5y)^-2
Answer:
5^3 y^5
125 y^5
Step-by-step explanation:
5y^3/(5y)^-2
Distribute the exponent in the denominator
5y^3/(5 ^-2 y^-2)
A negative exponent in the denominator brings it to the numerator
5y^3 5 ^2 y^2
Combine like terms
5 * 5^2 * y^3 5^2
We know that a^b * a^c = a^(b+c)
5^(1+2) * y^( 3+2)
5^3 y^5
125 y^5
[tex]Solve. Clear fraction first.6/5 + 2/5 x = 89/30 + 7/6 x + 1/6[/tex]
Step-by-step explanation:
we have denominators 5, 6 and 30.
the smallest number that is divisible by all 3 is clearly 30.
so, we have to multiply everything by 30 to eliminate the fractions.
180/5 + 60/5 x = 89 + 210/6 x + 30/6 =
36 + 12x = 89 + 35x + 5
-58 = 23x
x = -58/23
The numbers 1,2,3,4,5,6,7,8,9. How would you put them in each of a square block to create the sum on each line to make the number 15. The sum of each diagonals should also be 15.
Answer:
Here's one way:
4 9 2
3 5 7
8 1 6
Step-by-step explanation:
Okay so I need help answering another question. Can anyone who could actually understand it please help? Btw this is using Annuity formula and if anyone attempts to answer just to steal points shall be reported.
Step 1: Choose the price of the house. Then calculate 20% (which will be your down payment). Write down the price and 20% of the price.
Step 2: You don't have 20% now, so you will use an annuity to save up until you have the 20%. Choose a time in the future (2 years, 3 years, 4 years, 5, 10?) that you will purchase this house. Choose an APR that the bank will give you. Calculate how much you need to deposit every month in order to have the 20% down payment down the road. Write down the numbers of years, the interest rate, the formula with all the numbers plugged in, and the monthly deposits you will need to make.
Step 3: Now you take out a mortgage on the remaining 80%. Choose an APR that the bank will charge you (to be realistic, more than the APR in step 2) and the time you will take to pay off the loan. Write down the formula with all the numbers plugged in, and write down the minimum monthly payments.
Answer:
Step-by-step explanation:
1.)
The price of the house will be 500,000 which will make the downpayment 500,000*.2=100,000
so write down 500,000 and 100,000
2.)
For this one let's do 3 years at 3%
which would make the effective rate .03/12=.0025
let x= monthly payment
[tex]100000=x\frac{(1+.0025)^{12*3}-1}{.0025}[/tex]
which i will round to 2658.12
so write down: 3 years, 3%, [tex]100000=2658.12\frac{(1+.0025)^{12*3}-1}{.0025}[/tex], 2658.12
3.) the remaining 80% = 500,000-100000= 400,000
For this one let's do 6% for 6 years
which would make the effective rate: .06/12= .005
[tex]400000=x\frac{1-(1.005)^{-12*6}}{.005}\\x=6629.155157[/tex]
which i will round to 6629.16
so write down: [tex]400000=6629.16*\frac{1-(1+.005)^{-12*6}}{.005}[/tex], 6629.16
∠ACB is a circumscribed angle. Solve for x. 1) 46 2) 42 3) 48 4) 44
Answer:
[tex]\Huge \boxed{x=44}[/tex]
Step-by-step explanation:
The circumscribed angle and the central angle are supplementary.
∠ACB and ∠AOB add up to 180 degrees.
Create an equation to solve for x.
[tex]3x+10+38=180[/tex]
Add the numbers on the left side of the equation.
[tex]3x+48=180[/tex]
Subtract 48 from both sides of the equation.
[tex]3x=132[/tex]
Divide both sides of the equation by 3.
[tex]x=44[/tex]
Answer:
4)44
Step-by-step explanation:
Which expression is equivalent to x12 + 5x6 – 14?
Which is the graph of g(x) = (0.5)x + 3 – 4?
Answer:
Graph (A)
Step-by-step explanation:
Given question is incomplete; find the question in the attachment.
Given function is g(x) = [tex](0.5)^{x+3}-4[/tex]
Parent function of the given function is,
f(x) = [tex](0.5)^{x}[/tex]
When the function 'f' is shifted by 3 units left over the x-axis, translated function will be,
h(x) = f(x+3) = [tex](0.5)^{x+3}[/tex]
When h(x) is shifted 4 units down, translated function will be,
g(x) = h(x) - 4
g(x) = [tex](0.5)^{x+3}-4[/tex]
g(x) has a y-intercept as (-4).
From the given graphs, Graph A shows the y-intercept as (-4).
Therefore, Graph A will be the answer.
Answer:
The Answer A is correct
Step-by-step explanation:
I took the edg2020 test
What was the average speed if I drove 60 miles per hour to get to my grandmas house and 30 miles per hour to get home. Represent this in two different ways and explain your reasoning.
Answer:
40 mph.
Step-by-step explanation:
Suppose grandma's house is 30 miles away (any distance would do but 30 is convenient).
Speed = distance / time
time = distance / speed
Time to get there = 30/60 = 1/2 hour.
Time to get back = 30/30 = 1 hour
Average speed = total distance/ total time
= (30 + 30) / ( 1 + 1/2)
= 60 / 1.5
= 40 miles per hour.
You cannot take the average of the speeds directly
(60+ 30)/2 = 45 is not correct as you cannot average ratios ( speed is a ratio).
what is the absolute value of -5/9
Answer:
5/9
Step-by-step explanation:
In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:
Negative -> Positive
Positive -> Positive
Since we are working with a negative value, it will turn positive.
Best of Luck!
If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is
Answer:
The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.
Step-by-step explanation:
A coefficient of correlation of 0.8 means that dependent variable changes in 0.8 when independent variable changes in a unit. Hence, the percentage of such variation ([tex]\%R[/tex]) is:
[tex]\%R = \frac{\Delta y}{\Delta x}\times 100\,\%[/tex]
Where:
[tex]\Delta x[/tex] - Change in independent variable, dimensionless.
[tex]\Delta y[/tex] - Change in dependent variable, dimensionless.
If [tex]\Delta x = 1.0[/tex] and [tex]\Delta y = 0.8[/tex], then:
[tex]\%R = 80\,\%[/tex]
The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.
The angle between a chord and a targent is equal to the angle in the alternate segment
that's the diagram above
if <BAD =19°
find <ACB
Answer:
19
Step-by-step explanation:
The angle between a chord and a targent is equal to the angle in the alternate segment
if <BAD =19°
<ACB=19
Determine that 4/16 and 5/20 forms as proportional relationship.
Answer:
Those two are 0.25
4/16 = 1/4
5/20 = 1/4
Answer: Please Give Me Brainliest, Thank You!
4/16 = 5/20 = 1/4
Step-by-step explanation:
Because If you divide 4 and 16 by 4 you get 1/4 and if you divide 5 and 20 with 5 you get 1/4
Which of these numbers are greater than 24? Check all that apply.
O A. 12
B. 15
O C. 42
D. 41
E. 13
D F. 18
Answer:
A, B, E, F
Step-by-step explanation:
24>12, 24>15, 24>13, 24>18, 24<42, 24<41
In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?
Answer:
a
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
b
[tex]P( X >0.025 ) = 0.99379[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.10[/tex]
The sample size is [tex]n = 100[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]
=> [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]
=> [tex]SE =0.03[/tex]
The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]
Generally [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]
From the z-table
[tex]P(Z < 2.6 ) = 0.99534[/tex]
[tex]P(Z < 2.4 ) = 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as
[tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]
[tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]
From the z-table
[tex]P (Z > -2.5 ) = 0.99379[/tex]
Thus
[tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]
The weights of a sample of college textbooks has a bell-shaped distribution with a mean of 8.1 p o u n d s ( l b s ) and a standard deviation of 2.1 l b s . According to the Empirical Rule, what percent of all college textbooks will weigh between 1.8 and 14.4 l b s ?
Answer:
The interval ( 1,8 ; 14,4 ) will contains 99,7 % of all values
Step-by-step explanation:
For Normal Distribution N ( μ ; σ ) the Empirical Rule establishes that in the intervals:
( μ ± σ ) we find 68,3 % of all values
( μ ± 2σ ) we find 95,4 % of all values
( μ ± 3σ ) we find 99,7 % of all values
Then we have a normal distribution N ( 8,1 ; 2,1 )
3*σ = 3* 2,1 = 6,3
And 8,1 - 6,3 = 1,8 8,1 + 6,3 = 14,4
Then the interval ( 1,8 ; 14,4 ) will contains 99,7 % of all values
Help me with this please
Answer:
B
Step-by-step explanation:
the data value of x is 0 the the value would be .75 times that by 2 get 1.25
A region is bounded by x=y^2 and x=4 and y=0 and revolved about the line x=5. Find the volume using shell method.
If you draw the bounded region in the x,y-plane, you'll find it to be somewhat ambiguous, but since y = 0 cuts the area between the parabola x = y ² and x = 4 perfectly in half, you can use either the top or bottom half. I'll use the top one, i.e. assume y ≥ 0.
For every x taken from the interval [0, 4], we can get a shell with height √x. The distance from x to the axis of revolution, x = 5, is 5 - x, which corresponds to the radius of the shell. The area of this shell is
2π (radius) (height) = 2π (5 - x) √x
Then the volume of the solid is the sum of infinitely many such shells made at every 0 ≤ x ≤ 4, given by the integral
[tex]\displaystyle 2\pi \int_0^4 (5-x)\sqrt x\,\mathrm dx = 2\pi \int_0^4 \left(5x^{1/2}-x^{3/2}\right)\,\mathrm dx \\\\ = 2\pi \left(\frac{10}3x^{3/2}-\frac25x^{5/2}\right)\bigg|_0^4 \\\\ = \boxed{\frac{416\pi}{15}}[/tex]
3y – 6x = 3 y = 2x + 1
Answer:
infinite solutions along the line y = 2x+1
Step-by-step explanation:
3y – 6x = 3
y = 2x + 1
Replace y in the first equation with the second equation
3 ( 2x+1) -6x =3
6x +3 -6x = 3
3=3
This is always true so there are infinite solutions along the line y = 2x+1
Step-by-step explanation:
Hi, there!!!
you mean to solve it, right.
then let's begin...
3y-6x=3..........epuation 1.
y = 2x+1..........equation 2.
now, substituting the value y of equation 2 in equation 1. so, we get,
3y-6x=3
or, 3(2x+1) -6x = 3
or, 6x+3-6x=3
by simplifying it we get, 3=3
so, this equation can have infinite solution.
you may have wrote wrong question ..