The mortgage on your new house is $180,000. Your monthly mortgage payment is $839 for 30 years. How much interest will be paid if the house is kept for the full 30 years?
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Answer:
$122,040
Step-by-step explanation:
The interest is the difference between the mortgage value and the total amount paid.
($839/mo)×(12 mo/yr)×(30 yr) -180,000 = $302,400 -180,000 = $122,040
$122,040 will be paid in interest.
Miller's Steakhouse offers 8 side dishes, 5 types of steak, and 4 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 3 different toppings and 3 different side dishes?
Answer:
1120
Step-by-step explanation:
To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.
a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by
Complete Question:
A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.
a. What is his maximum profit per day?
b. How many cans must be sold in order to obtain the maximum profit?
Answer:
a. $450
b. 1500 cans
Step-by-step explanation:
Given the following quadratic function;
P(x) = -0.001x² + 3x - 1800 ......equation 1
a. To find his maximum profit per day;
Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]
Note : the standard form of a quadratic equation is ax² + bx + c = 0 ......equation 2
Comparing eqn 1 and eqn 2, we have;
a = -0.001, b = 3 and c = -1800
Now, we determine the maximum profit;
[tex] x = \frac {-b}{2a} [/tex]
Substituting the values, we have;
[tex] x = \frac {-3}{2*(-0.001)} [/tex]
Cancelling out the negative signs, we have;
[tex] x = \frac {3}{2*0.001} [/tex]
[tex] x = \frac {3}{0.002} [/tex]
x at maximum = 1500
Substituting the value of "x" into equation 1;
P(1500) = -0.001 * 1500² + 3(1500) - 1800
P(1500) = -0.001 * 2250000 + 4500 - 1800
P(1500) = -2250 + 2700
P(1500) = $450
b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.
Зу = -2 - 6
3y = 2z - 6
Answer:
y = -8/3, z = -1
solve each question please thank you
Answer:
SURE
Step-by-step explanation:
Josue leans a 26-foot ladder against a wall so that it forms an
angle of 80° with the ground. How high up the wall does the
ladder reach? Round your answer to the nearest hundredth of a
foot if necessary.
Answer:
25.61 feet
Step-by-step explanation:
First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.
Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.
One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have
sin(80°) = opposite / 26 feet
multiply both sides by 26 feet
sin(80°) * 26 feet = opposite
= 25.61 feet as the height of the wall the ladder reaches
The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.
The condition is shown in the diagram.
Then the height of the wall will be
[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]
More about the right-angle triangle link is given below.
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What is the least common denominator that will allow you to combine the constant terms? 10 21 35 or 42
Answer:
[tex]LCM = 21[/tex]
Step-by-step explanation:
Given
[tex]-\frac{3}{5}y + \frac{1}{7}= \frac{1}{3}y -\frac{2}{3}[/tex]
Required
LCM of the constant terms
Collect like terms
[tex]\frac{1}{3}y+\frac{3}{5}y = \frac{1}{7}+\frac{2}{3}[/tex]
The constant terms are on the right-hand side
To combine them, we simply take the LCM of the denominator, i.e. 7 and 3
The prime factorization of 3 and 7 are:
[tex]3 = 3[/tex]
[tex]7 = 7[/tex]
So:
[tex]LCM = 3 * 7[/tex]
[tex]LCM = 21[/tex]
In the picture the exponent says 5/3
Answer:
the answer is B
Step-by-step explanation:
[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]
write -8 form of 2 on up and complete other steps
moses is inviting 10 friends to a party each friend wants 4 cookies and each box has 10 cookies how many boxes should moses get?
Answer:
4
Step-by-step explanation:
Since each friend wants 4 cookies, and there are 10 friends, there are 10 x 4 = 40 cookies total Moses should buy. Since each cookie box has 10 cookies in it, he should buy 40/10 = 4 total cookie boxes.
Find the number that comes after 144five
Answer:
The number that comes after 144five is:
= 200five.
Step-by-step explanation:
Adding 1 to 144 base 5 will result in:
144
+ 1
= 200
b) To obtain the next number that comes after 144five, add 1five to 144five. Since the numbers are in base 5, 1five added to 4five will result in 0 with 1 carried backward. When 1 is added to the next 4, the result will be 0 with 1 carried backward. 1 added to 1 = 2, all in base 5. Figures in base 5 cannot exceed 4. The usual numbers for a base 5 operation are 0, 1, 2, 3, and 4.
The credit department of Lion's Department Store in Anaheim, California, reported that 30% of their sales are cash, 30% are paid with a credit card, and 40% with a debit card. Twenty percent of the cash purchases, 90% of the credit card purchases, and 60% of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability that she paid cash?
Answer:
Hence the probability that she paid cash is 0.105
Step-by-step explanation:
P(cash) = 0.3
P(credit card ) = 0.3
P(debit card ) = 0.4
P ( more than $50 | cash ) = 0.2
P (more than $50 | credit card ) =0.9
P (more than $ 50 |debit card ) = 0.6
P ( more than $50) = P ( more than $50 | cash )* P (cash) + P (more than $50 credit card ) * P(credit card ) + P (more than $ 50 |debit card )* P(debit card )
= 0.2 * 0.3 + 0.9 * 0.3 + 0.6* 0.4
= 0.57
P ( more than $50) = P ( more than $50 | cash )* P (cash) / P ( more than $50)
= 0.2* 0.3 / 0.57
= 0.105
PLEASE HELP QUICKLY
Determine whether the given sequence could be arithmetic. If so, identify the first difference and the next term.
-6, -11, -16, -21, -26.....
Answer:
The first difference is -5. The next term is -31.
Step-by-step explanation:
If you find the difference between -6 and -11, then you get -5.
And, all the other ones also have differences of -5, so basically, the next term is -31.
Thanks! Please mark me Brainliest!
Answer:
It could be arithmeticIf so, then the first difference is -5 and the next term is -31===================================================
Explanation:
Pick any term and subtract off the previous term
term2 - term1 = -11 - (-6) = -11 + 6 = -5term3 - term2 = -16 - (-11) = -16 + 11 = -5term4 - term3 = -21 - (-16) = -21 + 16 = -5term5 - term4 = -26 - (-21) = -26 + 21 = -5No matter what we picked, we end up with the same result which is -5. This is the common difference aka first difference.
If this pattern keeps up forever, then the sequence is arithmetic.
And if the pattern keeps up, then the next term would be
term6 = term5 + (common difference)
term6 = -26 + (-5)
term6 = -31
Note: Adding -5 is the same as subtracting 5.
the measures of three angles of a triangle are given by (8x-10), (2x), and (3x-5). What is the measure of the larges tangle
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Answer:
110°
Step-by-step explanation:
The sum of angles of a triangle is 180°.
(8x -10) +(2x) +(3x -5) = 180
13x -15 = 180
13x = 195
x = 15
The largest angle is ...
8x -10 = 8(15) -10 = 110 . . . . degrees
The sum of two integers is 90 and their difference is 30. Find the larger number
Answer:
60 is the larger number
Step-by-step explanation:
Let the two numbers be a and y
x+y = 90
x-y = 30
Add the two equations together
x+y = 90
x-y = 30
-----------------
2x = 120
Divide by 2
2x/2 =120/2
x = 60
x+y =90
60+y = 90
y = 90-60
y = 30
The numbers are 60 and 30
A sofa regularly sells for $760. The sale price is $676.40. Find the percent decrease of the sale price from the regular price.
Answer: (760 - 676. 40) × 100 ÷ 760 = 11%
Step-by-step explanation:
Answer:
11% decrease
Step-by-step explanation:
Concepts:
Percent change is the change between an old value and its new value represented as a %. If a percent change is a decrease, it means that the new value is less than the old value. If a percent change is a increase, it means that the old value is less than the new value. The formula for percent change is: (NV - OV)/OV · 100 = C, where NV = New Value, OV = Old Value, and C = Percent Change.The sale price is the price at which something sells or sold after the price has been reduced by sales, discounts, etc.Solving:
Let's find the percent change by using the formula.
1. Formula for Percent Change
(NV - OV)/OV · 100 = C2. Plug in the values of NV and OV
(676.40 - 760)/760 · 100 = C3. Simplify
-83.6/760 · 100 = C-0.11 · 100 = C-11 = CTherefore, our percent decrease is 11% decrease.
The width of a rectangle measures (7k-2m)(7k−2m) centimeters, and its length measures (5k-m)(5k−m) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
[tex]P = 24k-6m[/tex]
Step-by-step explanation:
The correct expressions are:
[tex]W = 7k - 2m[/tex]
[tex]L = 5k - m[/tex]
Required
The perimeter (P)
This is calculated as:
[tex]P = 2 *(L + W)[/tex]
So, we have:
[tex]P = 2 *(5k - m + 7k -2m)[/tex]
Collect like terms
[tex]P = 2 *(5k + 7k- m -2m)[/tex]
[tex]P = 2 *(12k-3m)[/tex]
Open bracket
[tex]P = 24k-6m[/tex]
If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *
Given:
There is a 65% chance you will make a free throw.
To find:
The percent of the time you will miss.
Solution:
If p is the percent of success and q is the percent of failure, then
[tex]p+q=100\%[/tex]
[tex]q=100\%-p[/tex] ...(i)
It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss. It means we have to find the percent of failure.
Substituting p=65% in (i), we get
[tex]q=100\%-65\%[/tex]
[tex]q=35\%[/tex]
Therefore, there is a 35% chance you will miss the free throw.
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
To learn more about an equation visit:
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Find x on this triangle
Answer:
3 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = x/6
6 cos 30 = x
6 ( sqrt(3)/2) = x
3 sqrt(3) =x
A jar contains 11red marbles, 12 blue marbles and 6 white marbles. Four marbles from the jar are selected. With each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?
Answer:
Red on the 5th draw = 0.0907
Step-by-step explanation:
The first to fourth selections are all the same.
Blue + white = 12 + 6 = 18
The total number of marbles is 11 + 12 + 6 = 29
P(~ red) for the first four times = (18/29)^4 = 0,1484
Now on the 5th time, the first red is 11/18
So the Probability is 0.1484 * 11/18 = 0.0907
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,450. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 570 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)
Answer:
The manufacturer should advertise 11720 pages.
Step-by-step explanation:
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.
Mean of 12450, standard deviation of 570:
This means that [tex]\mu = 12450, \sigma = 570[/tex]
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time?
They should advertise the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 12450}{570}[/tex]
[tex]X - 12450 = -1.28*570[/tex]
[tex]X = 11720[/tex]
The manufacturer should advertise 11720 pages.
f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).
Answer:
4x-5=4x-5
(f+g) (x)=6x³+3Step-by-step explanation:
please help me its timed -H.M
Answer:
f(3) = g(3)
General Formulas and Concepts:
Algebra I
Functions
Function NotationGraphingStep-by-step explanation:
We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.
Rewriting this in terms of function notation:
f(3) = 6, g(3) = 6
∴ f(3) = g(3)
Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by
The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is
[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]
In this case, we have
x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )
y(t) = 5 - 2t ==> dy/dt = -2
and [a, b] = [0, 2]. The length of the curve is then
[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]
[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]
The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.
[tex]e^2 -\dfrac{1}{e^2 }[/tex]
What is integration?It is the reverse of differentiation.
The parametric equations are given below.
[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]
Then the arc length of the curve will be given as
[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]
Then
[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]
More about the integration link is given below.
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the length of a rectangle is twice its width the perimeter is 48 cm what are the dimensions of the rectangle
Answer:
The length=16cm and the width=8cm.
Step-by-step explanation:
Given that the length is twice the breadth or width of the rectangle
Let's assume that the breadth of the rectangle is x.
Thus the length is 2x.
Given perimeter=48cm
The formula for the perimeter of a rectangle is 2(l+b) where l is length and b is breadth.
2(x+2x)=48
(3x)=48/2
3x=24
x=8cm
2x=16cm
Step-by-step explanation:
length=2x
width=x
2x+x+2x+x=48
6x=48
6x÷6=48÷6
x=8
length=16
width=8
What is the value of x in the equation
-%y = 30, when y = 15?
Answer:
x not given
therefore no answer for x
Julio has a net pay of $ 537.00 each paycheck. He pays $ 142.00 in pre-tax deductions and taxes each paycheck. What is Julio's gross income before the tax deductions?
Answer:
Julio's gross income before the tax deductions is $ 405.
Step-by-step explanation:
Given that Julio has a net pay of $ 537.00 each paycheck, and he pays $ 142.00 in pre-tax deductions and taxes each paycheck, to determine what is Julio's gross income before the tax deductions the following calculation must be performed:
547 - 142 = X
405 = X
Therefore, Julio's gross income before the tax deductions is $ 405.
can someone help me out with this question???
Answer:
a
Step-by-step explanation:
Not sure how to do this
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within with % confidence if (a) she uses a previous estimate of ? (b) she does not use any prior estimates?
Answer:
732 samples ;
752 samples
Step-by-step explanation:
Given :
α = 90% ; M.E = 0.03 ; p = 0.58 ; 1 - p = 1 - 0.58 = 0.42
Using the relation :
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.58 * 0.42) / 0.03²
n = 0.65918769 / 0.0009
n = 732.43076
n = 732 samples
B.)
If no prior estimate is given, then p = 0.5 ; 1 - p = 1 - 0.5 = 0.5
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.5 * 0.5) / 0.03²
n = 0.67650625 / 0.0009
n = 751.67361
n = 752 samples
