Numerical Reasoning
Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...
... 2×$20 +45 = $85
To have revenue of at least $510, the studio must sell ...
... $510/$85 = 6
sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.
_____
With an equation
Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...
... 20·2x +45·x ≥ 510
... 85x ≥ 510
... x ≥ 510/85
... x ≥ 6
The studio needs to sell at least 6 large prints and 12 small prints.
The logistic growth function Upper P left parenthesis x right parenthesis equals StartFraction 90 Over 1 plus 271 e Superscript negative 0.122 x EndFraction P(x)= 90 1+271e−0.122x models the percentage, P(x), of Americans who are x years old and have some coronary heart disease. Use this function to find the the percentage of 66 66-year olds who have some coronary heart disease.
about 83%
Step-by-step explanation:Put the given value in the formula and do the arithmetic.
... P(66) = 90/(1 +271·e^(-0.122·66))
... = 90/(1 +271·e^-8.052)
... = 90/(1 +271·0.00031846)
... = 90/(1 +0.0863)
... = 90/1.0863
... = 82.8 . . . . percentage with some coronary heart disease
(X+5) to the power 6 use binomial theorem to expand the power of a binomial
Answer:
x⁶ +30x⁵ +375x⁴ +2500x³ +9375x² +18750x +15625
Step-by-step explanation:
The expansion is the sum of C(6, k)·x^(6-k)·5^k for k=0–6, where ...
... C(6, k) = 6!/(k!(6-k)!)
For k = 0–6, C(6, k) = {1, 6, 15, 20, 15, 6, 1}
Then the expansion is ...
... x⁶ +6·5¹·x⁵ +15·5²·x⁴ +20·5³·x³ +15·5⁴·x² +6·5⁵·x +5⁶
Using binomial theorem to expand the power of a binomial (X+5) to the power 6 and the result is [tex]X^6 + 30 \times X^5 + 300 \times X^4 + 1500 \times X^3 + 3750 \times X^2 + 4500 \times X + 3125[/tex].
To expand the expression (X+5) to the power 6 using the binomial theorem, we can use the formula [tex](a + b)^n = nC_0 \times a^n + nC_1 \times a^{(n-1)} \times b^1 + nC_2 \times a^{(n-2)} \times b^2 + ... + nC_n * b^n[/tex].
In this case, a = X, b = 5, and n = 6.
Using the binomial coefficients, the expanded expression becomes:
[tex]X^6 + 6 \times X^5 \times 5 + 15 \timesX^4 \times 5^2 + 20 \times X^3 \times 5^3 + 15 \times X^2 \times 5^4 + 6 \times X \times 5^5 + 5^6[/tex]
Simplifying this expression gives
[tex]X^6 + 30 \times X^5 + 300 \times X^4 + 1500 \times X^3 + 3750 \times X^2 + 4500 \times X + 3125[/tex].
PLEASE HELP
A laptop computer is purchased for $2500. After each year, the resale value decreases by 25%. What will the resale value be after 5 years?
Use the calculator provided and round your answer to the nearest dollar.
After 5 years, the resale value of the laptop will be approximately $592.
The resale value of the laptop after each year can be calculated by multiplying the previous year's value by 0.75. Starting with the initial value of $2500, the resale value after 5 years can be found by multiplying $2500 by 0.75 five times. Let's calculate:
Year 1: $2500 x 0.75 = $1875Year 2: $1875 x 0.75 = $1406.25Year 3: $1406.25 x 0.75 = $1054.69Year 4: $1054.69 x 0.75 = $790.02Year 5: $790.02 x 0.75 ≈ $592.52Therefore, the resale value of the laptop after 5 years will be approximately $592.
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someone pls me out with this problem. Divide m2n2/p3 by mp/n2
Answer:
[tex]\dfrac{mn^5}{p^4}[/tex]
Step-by-step explanation:
As with dividing any fractions, invert the denominator and multiply. Use the rules of exponents to combine factors.
[tex]\dfrac{\dfrac{m^2n^3}{p^3}}{\dfrac{mp}{n^2}}=\dfrac{m^2n^3}{p^3}\cdot\dfrac{n^2}{mp}\\\\=\dfrac{m^2n^3n^2}{p^3mp}=\dfrac{m^{2-1}n^{3+2}}{p^{3+1}}=\dfrac{mn^5}{p^4}[/tex]
_____
The applicable rules are ...
[tex]a^ba^c=a^{b+c}\\\\\dfrac{a^b}{a^c}=a^{b-c}[/tex]
evaluating functions
(-1/4)x + 2 = 8
Multiply all terms by 4.
(-1)x + 8 = 32
Simplify.
-x + 8 = 32
Subtract 8 from both sides.
-x = 24
Multiply both sides by -1.
x = -24.
The value of x is equal to -24.-1/4(-24) + 2 = 8
Evaluating functions is the process of substituting a specific value in place of the variable in a function to compute a result. For example, given the function f(x) = x^2, if asked to find f(2), you would replace x with 2 resulting in 4.
Explanation:Evaluating functions in mathematics involves inserting a specific numerical value or a variable into a function to compute a result. For example, if you're given the function f(x) = x^2, and you're asked to find f(2), you simply substitute 2 in place of x in the function, resulting in 2^2, which equals 4.
For instance, if we were to evaluate f(5) for the given function, it would give the result 25 because 5^2 = 25. Hence, simply put, to evaluate a function is to replace the variable with the input value, and compute the result.
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In the figure angle B is a right angle, side AB is 4 units long, and side BC is 6 units long. How many units long is side AC?
We know that , According to Pythagorean Theorem :
In a Right Angled Triangle :
✿ (Hypotenuse)² = (First Leg)² + (Second Leg)²
In the Figure : AC is the Hypotenuse and AB and BC are Two Legs
Given : Length of AB = 4 and Length of BC = 6
⇒ (AC)² = (AB)² + (BC)²
⇒ (AC)² = 4² + 6²
⇒ (AC)² = 16 + 36
⇒ (AC)² = 52
[tex]\mathsf{\implies AC = \sqrt{52}}[/tex]
[tex]\mathsf{\implies AC = 2\sqrt{13}}[/tex]
3rd Option is the Answer
I need help fast please!!!!!!!!!!!!!!!!!
Answer:
HL
Step-by-step explanation:
The two hypotenuses of these right triangles are marked congruent, and the leg QS is shared, hence congruent.
The HL theorem applies.
Modeling Circular Motion, Picture attached to the question.
The boat is traveling at a rate of 1 meter per second.
How long does it take the barnacle to get back to its starting point?
Answer:
2π secondsStep-by-step explanation:
The circumference of a circle of radius r is given by
... C = 2πr
When r = 1 m, then
... C = 2π(1 m) = 2π m
The relation between time, distance, and speed is ...
... time = distance/speed
... time = (2π m)/(1 m/s) = 2π s
_____
Comment on the scenario
We have a hard time imagining what sort of scenario this is modeling, as it appears the "boat" is rotating in such a way as to place the barnacle above and below the water level. This problem may be nonsensical, but at least it is workable. (Some aren't.)
Answer:2 pi
Step-by-step explanation:
The ratio of students that ride the bus as compared to those that walk is 10:1. Does this school have more students that ride the bus or walk? how so you know?
Answer:
more that ride the bus10:1 is more than 1:1Step-by-step explanation:
riders : walkers = 10 : 1
The ratio tells you that 10 students ride the bus for every 1 student that walks. Since 10 is more than 1, more students ride the bus.
We know more students are riders, because we know that 10 is more than 1.
Pvc pipe is manufactured with a mean diameter of 1.01 inch and a standard deviation of 0.003 inch. the diameters are known to be normally distributed. find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.
Answer:
about 82%
Step-by-step explanation:
The distribution of sample means has a standard deviation that is the pipe standard deviation divided by the square root of the sample size. Thus, the standard deviation of the sample mean is 0.003/√9 = 0.001.
Then the limits on sample mean are 1.010 - 1×0.001 = 1.009 and 1.010 +2×0.001 = 1.012. The proportion of the normal distribution that lies between -1 and +2 standard deviations is about 81.9%.
The problem involves statistical calculation involving mean, standard deviation, and Z-scores of a normal distribution. We first calculate sample standard deviation, then the Z-scores for the given range. After finding probabilities for the Z-scores, we subtract to get the final probability of 0.8185.
Explanation:The problem at hand involves the field of statistics, specifically, the normal distribution, sample mean, and standard deviation. We can use the following steps to solve the problem:
Determine the standard deviation of the sample. Given the standard deviation of the population (σ population) is 0.003 inch and the sample size (n) is 9, we use the formula σ sample = σ population/sqrt(n), which gives 0.003/sqrt(9) = 0.001.Calculate the Z-scores for 1.009 and 1.012. The Z-score is determined by the formula: Z = (X - μ) / σ. For X=1.009, Z1 = (1.009-1.01)/0.001 = -1. For X=1.012, Z2 = (1.012-1.01)/0.001 = 2.Using a Z-table or appropriate statistical software, find the probability corresponding to these Z-scores. The probability for Z1=-1 is 0.1587, and for Z2=2, it is 0.9772.Lastly, subtract the smaller probability from the larger one to get the probability that a sample mean is greater than 1.009 but less than 1.012. So, the answer is 0.9772 - 0.1587 = 0.8185.Learn more about Normal Distribution here:https://brainly.com/question/34741155
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triangles abc and def are similar. The length of each side of triangle abc is 8 times the length of each corresponding side of triangle def. How many times greater is the area of triangle abc than the area of triangle def
64
Step-by-step explanation:If each side length is multiplied by 8, the product of two side lengths will be multiplied by 8×8 = 64.
Area is proportional to the product of two side lengths, so will be multiplied by 64.
Hi! I need help on this. thank you
Answer:
5^(3m+10)
Step-by-step explanation:
There are several ways you can go at this. One is to do the division of fractions the way you often do division with fractions: multiply by the inverse of the denominator.
= (5^(m+4)) · (25^(m+3))
= (5^(m+4)) · ((5^2)^(m+3))
= (5^(m+4)) · (5^(2m+6))
= 5^(m+4+2m+6)
= 5^(3m+10)
URGENT !! What is the value of Y?
Answer:
B. 68°Step-by-step explanation:
We know:
The sum of the measures of the angles of the triangle is equal to 180 °.
Therefore we have the equation:
[tex]y+(y-12)+56=180[/tex] combine like terms
[tex]2y+44=180[/tex] subtract 44 from both sides
[tex]2y=136[/tex] divide both sides by 2
[tex]y=68[/tex]
Which angle has a positive measure?
Answer:
The measure of angle B is positive
Step-by-step explanation:
we know that
Positive angles are those measured counterclockwise.
therefore
in this problem
The measure of angle B is positive
Find the missing side. Round to the nearest tenth.
Answer:
[tex]x=7.2\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle of the figure
The tangent of angle of 67 degrees is equal to divide the opposite side to the angle of 67 degrees (17 units) by the adjacent side to angle of 67 degrees (x units)
[tex]tan(67\°)=17/x[/tex]
Solve for x
[tex]x=17/tan(67\°)[/tex]
[tex]x=7.2\ units[/tex]
What is the simplified value of the expression below?
A. 18.25
B. 21.38
C. 27.56
D. 42.75
Answer:
A. 18.25
Step-by-step explanation:
After you do the multiplications, the problem is
... (56 +90)/8 = 146/8 = 18.25
_____
The division bar is a grouping symbol, equivalent to parentheses around both numerator and denominator. You must evaluate the numerator before you can divide by the denominator, which also must be evaluated before that division.
PLEASE HELP
Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the number of years since it was last purchased.
What equation models this function?
(My graph is below)
Enter your answer in the box.
f(x)=
f(x) = 8·1.25^x
Step-by-step explanation:An exponential function has the form ...
... f(x) = a·b^x
Then f(0) = a. Your graph shows f(0) = 8.
The base "b" can be found from any other point on the graph. You have marked the point (1, 10), so we can find "b" from ...
... f(1) = 10 = 8·b^1 = 8b
... 10/8 = b = 1.25 . . . . . . . divide by the coeffiicient of b
Now, we know the exponential function is ...
... f(x) = 8·1.25^x
Answer:
The correct answer is f(x) = 8·1.25^x
Step-by-step explanation:
A town's population is 53,075. About 100 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 55,825. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
If we let m represent the number of months, then the population increase of the first town is 100m and its decrease is 200m. The population decrease of the second town is 175 m.
We want to find m such that the increases and decreases make the towns' populations equal. We add the increases and subtract the decreases to the base population in each case.
... first town population = second town population
... 53075 -100m +200m = 55825 -175m . . . . . the model equation
Solution
... 100m = 2750 -175m . . . . . collect terms, subtract 53075
... 275m = 2750 . . . . . . . . . . add 175m
... m = 10 . . . . . . . . . . . . . . . . . divide by 275
The populations will be equal in 10 months.
Answer:
175m-125m+38,200=40,600-150m
Step-by-step explanation:
I just completed it on imagine math
A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost, 2 fewer loaves of bread will be sold per day. Let x represent the number of $0.50 increases in the cost of a loaf of bread.For what number of $0.50 increases in the cost of a loaf of bread will the grocer's generated revenue be greater than zero?
A. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 20.
B. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 20.
C. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 15
.
D. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 15.
Answer:
none of the above
Step-by-step explanation:
The grocer's revenue will be the product of the number of loaves sold (30-2x) and their price (2.50+0.50x).
Revenue will be positive for values of x between those that make these factors be zero. The number of loaves sold will be zero when ...
... 30 -2x = 0
... 15 -x = 0 . . . . . divide by 2
... x = 15 . . . . . . . add x
The price of each loaf will be zero when ...
... 2.50 +0.50x = 0
... 5 + x = 0 . . . . . . . multiply by 2
... x = -5 . . . . . . . . . . subtract 5
Revenue will be positive for any number of increases greater than -5 and less than 15.
_____
D is the best of the offered choices, but it is incorrect in detail. -5 is a number less than 15, but will give zero revenue.
Find the quantity represented by each percent.
5.) 48% of 725 kg
6.) 15% of 138 lb.
Find the missing value.
7.) 45% of _____is 108.
Answer:
5.) 348 kg
6.) 20.7 lb
7.) 240
Step-by-step explanation:
5.) 48% of 725 kg
48 × 725 ÷ 100 = 348 kg
6.) 15% of 138 lb
15 × 138 ÷ 100 = 20.7 lb
7.) 45% of _____is 108.
100 × 108 ÷ 45 = 240
Thus, 5.) 348 kg; 6.) 20.7 lb; 7.) 240
-TheUnknownScientist
What is the probability of flipping a coin 15 times and getting heads 10 times? Round your answer to the nearest tenth of a percent.
The coin is flipped 15 times and you get 10 heads, is written as 10/15.
10/15 = 0.66666 = 66.7%
Answer:
9.2%
Step-by-step explanation:
The sum of two numbers is 52 . The smaller number is 16 less than the larger number.What are the numbers?
Answer:
This question is not as hard as it seems.
Let the first number = x.
The other number will be x - 16.
The sum of both the number is 52.
So, x+x-16 = 52
Which would simplify to 2x -16 = 52.
When I add 16 to both sides, it would give me 2x = 68.
Then, divide both sides by 2.
This leaves us with x = 34.
Since we have x, now x-16 would be 34-16 = 18.
The two numbers are 34 and 18, this answer is correct because both of them add up to give me 52.
HOPE THIS HELPS!
Question
The sum of two numbers is 52 . The smaller number is 16 less than the larger number.What are the numbers?
Answer:
18 and 34
Step-by-step explanation:
[(52 - 16) : 2] + 16 =
(36 : 2) + 16 =
18 + 16 =
34
-----------------------
Check
34 - 18 = 16
34 + 18 = 52
the answer is good
Noel has 5/6 of a yard of purple ribbon and 9/10 of a yard of pink ribbon. How much ribbon does she have altogether?
I need help with my Geometry! i clipped the photo below
Try this solution:
a) the property of the inscribed quadrilateral is: m∠A+m∠G=m∠H+m∠F=180°.
It means (for m∠A+m∠G=180°), 21x-2+38x+5=180°, ⇒ x=3, m∠G=63-2=61°.
b) m(arcFAH)=2m∠FGH=2m∠G=122°.
c) x²-2x+y²-4y=11; ⇔ (x²-2x+1)+(y²-4y+4)=16; ⇔ (x-1)²+(y-2)²=4², where (1;2) is the centre and 4 - radius of this circle.
What are the solutions to the equation?
x2 + 6x = 40
x = −10 and x = 4
x = −8 and x = 5
x = −5 and x = 8
x = −4 and x = 10
Answer:
x = −10 and x = 4
Step-by-step explanation:
x2 + 6x = 40
Subtract 40 from each side
x^2 + 6x -40 =0
Factor, what 2 numbers multiply to -40 and add to 6
10 * -4 = -40 10+-4 = 6
(x+10) (x-4) = 0
Using the zero product property
x+10 =0 x-4=0
x=-10 x=4
Answer:
x = −10 and x = 4
Step-by-step explanation:
We are given the following quadratic equation and we are to solve it to find the two solution for the variable x:
[tex]x^2+6x=40[/tex]
Rearranging the equation by putting the constant on the same side as the variables to get:
[tex]x^{2} +6x-40=0[/tex]
Now factorizing it to get:
[tex]x^{2} -4x+10x-40=0\\\\x(x-4)+10(x-4)=0\\\\(x+10)(x-4)=0\\\\x= -10, x= 4[/tex]
Therefore, the solution to the given quadratic equation [tex]x^2+6x=40[/tex] are x = −10 and x = 4.
EASY PLZ HELP!
Solve for x. (Show your work)
2x + 3 > 5
Answer:
x > 1
Step-by-step explanation:
Firstly, the +3 must be moved over to the other side, making it a -3:
2x > 5 - 3
2x > 2
Then, divide both sides by two to get 1x:
x > 1
Hi there!
Answer:
X>1
*The answer must have a positive sign and greater than symbol.*
Step-by-step explanation:
First, you subtract by 3 from both sides of an equation.
[tex]2x+3-3>5-3[/tex]
Then, you subtract by the numbers from left to right.
[tex]5-3=2[/tex]
[tex]2x>2[/tex]
You can also divide by 2 from both sides of an equation.
[tex]\frac{2x}{2}>\frac{2}{2}[/tex]
Finally, you divide by the numbers from left to right.
[tex]2/2=1[/tex]
Final answer is x>1
I hope this helps you!
Have a nice day! :)
:D
-Charlie
Thank you so much! :)
:D
In the game of backgammon, you get to double how much you move if you roll “doubles" on two dice (that is: 1 and 1, 2 and 2, 3 and 3, etc.). The next three questions concern this situation. 23. What is the probability of rolling doubles on any one roll?
(a) 1/6
(b) 1/12
(c) 1/36
(d) 5/36
(e) 1/2
Consider the system of equations:
2x - 3y = 7
x + 4y = 9
What is the solution to the system?
( use elimination or substitution )
Answer:
(x, y) = (5, 1)
Step-by-step explanation:
To eliminate x, you can double the second equation and subtract the first.
... 2(x +4y) -(2x -3y) = 2(9) -(7)
...11y = 11 . . . . . simplify
... y = 1 . . . . . . divide by 11
Using the second equation to find x, we have ...
... x + 4·1 = 9
... x = 5 . . . . . subtract 4
_____
Check
2·5 -3·1 = 10 -3 = 7 . . . . agrees with the first equation
(Since we used the second equation to find x, we know it will check.)
Translate the difference of five squared and n into symbols.
5^2- n
5^2+ n
5^2x n
5^2 ÷ n
Answer:
5² - n
Step-by-step explanation:
Five squared = 5²
n = n Subtract n from 5²
Diff. = 5² - n
We indicate "taking the difference" by a "minus" sign, so all the other options are wrong.
Answer:
5² - n
Step-by-step explanation:
Five squared is written as = 5²
The symbol of n is n.
The term difference is subtraction.
The difference of five squared and n ⇒ 5² - n
please answer quickly thank you
For this case, we have that by definition:
Let "x" be an angle of any vertex of a right triangle.
[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]
So, if we want to find the angle x of the triangle shown we have:
[tex]tangent (x) = \frac {13} {6}\\x = arc \ tangent (\frac {13} {6})\\x = 65.23[/tex]
Rounding:
[tex]x = 65\ degrees[/tex]
Answer:
65 degrees
Option d