Answer:
9 meters
Step-by-step explanation:
|7.5|+|-1.5|=9
(the || on either side of each number shows that it's representing how far the number is from 0, so it's essentially 7.5+1.5)
Sydney owes her mother $5 and her brother owes her mother $7.Graph the integers that represents the amount they owe their mother as negative integer on a number line.How much more will her brother have to reap their than Sydney ?
Answer:
Sydney will have to pay -5, and her brother will have to pay -7. Her brother will have to pay $2 more than Sydney.
Step-by-step explanation:
Having difficulty with this
For the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.
What is a expression? What is a mathematical equation? What is Equation Modelling? What is differentiation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -
y = f(x)
y' = dy/dx = (d/dx)[f(x)]
We have the following function -
y = 4x⁵
The given function is -
y = 4x⁵
dy/dx = 20x⁴ {y = xⁿ, then y' = nxⁿ ⁻ ¹}
d²y/dx² = 80x³
d³y/dx³ = 160x²
d⁴y/dx⁴ = 320x
Therefore, for the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.
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Solve for x.
412≤1.2x
Responses
x≥334
x is greater than or equal to 3 and 3 over 4
x≤334
x is less than or equal to 3 and 3 over 4
x≥525
x is greater than or equal to 5 and 2 over 5
x≤525
The solution for x in the inequality is x ≥ 343
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
412≤1.2x
Divide both sides of the inequality by 1.2
So, we have
412/1.2 ≤ 1.2x/1.2
Evaluate the quotients
343 ≤ x
Rewrite the expression as
x ≥ 343
Hence, the solution is x ≥ 343
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3F furniture dealer has always sold its merchandise through 4 company-operated
stores. Last year sales were birr 1million and net profit was 8% of sales. Fixed
costs were birr 170,000. As a result of shifting population and increased
competition, the four locations have become less desirable. 3F is considering
eliminating its retail stores in favor of door-to-door selling. It is estimated that
sales would increase by 25% and net profit by birr 30,000. Fixed costs would
increase by birr 30,000 because operations would be moved to a low-rent
warehouse. Required
a) What was the break-even point under the old situation?
b) What will be the break-even point under the proposed situation?
c) What birr sales volume must be obtained under the proposed plan to make as
much profit as last year?
The break-even point under the old situation is 680000, the break-even point under the proposed situation is 806451 and the birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.
Define breakeven point.In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." Although opportunity costs have been paid and capital has obtained the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."
In the given question, last year sales= birr 100000
net profit= 8% of sales
Fixed costs= birr 170000
Estimated sales increase= 25%
Estimated net profit= birr 30000
Increase in fixed cost due to moving to low-rent warehouse= birr 30000
(a) The break-even point under the old situation (X):
= 100,000 * a - 170,000
=1,000,000 * 8%
a= 25% (net profit)
X*a= 1170,000
X=680,000
That is, the break-even point under the old situation is 680000.
(b) The break-even point under the proposed situation is:
= 1,250,000 x b - 170,000- 30,000
= 80,000 + 30,000
b= 24.8%
X*b=200,00
X=806451
The break-even point under the proposed situation is 806451 and
(c) The birr sales volume must be obtained under the proposed plan to make as much profit as last year is:
X*b -200,000= 80,000
X*b = 280,00
X= 1,129,032
The birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.
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Find X and RDB
X= ______
RDB=______
Using the secant-secant theorem,
[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]
The measure of the angle ∠RDB will be 45°.
What is the angle of the chord?In geometry, a chord of a circle is a straight line segment whose endpoints both lie on the circle. A diameter of a circle is the longest chord, and it passes through the centre of the circle.
Calculate the value of x as below,
( 13x + 7 - 60 ) / 2 = 5x - 10
13x - 53 = 10x - 20
3x - 53 = -20
3x = 33
x = 11
The measure of the angle ∠RDB is,
∠RDB = 5x - 10
∠RDB = ( 5 x 11 ) - 10
∠RDB = 45°
Therefore, the value of an angle ∠RDB will be 45°.
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This is NOT multiple choice
Solve the equation 15e^4x = 12 for x
Show your work please
A) identify the exact solution
B) approximate the solution to the nearest thousandth.
Step-by-step explanation:
15 e^(4x) =12
divide both sides by 15
e^(4x) = 0.8
if e^y = X
then y = ln x
4x=ln 0.8
4x=-0.22314
dividing both sides by 4
4x/4= -0.22314/4
x = -0.0558
Consider a political discussion group consisting of 9 Democrats, 9 Republicans, and 5 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting two Democrats.
Hence, the probability of selecting two Democrats is [tex]45[/tex].
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
The meaning of probability is basically the extent to which something is likely to happen.
Here given that,
Consider a political discussion group consisting of [tex]9[/tex] Democrats, [tex]9[/tex] Republicans, and [tex]5[/tex] Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention.
Let us assume ,
The discussion of the democratic is [tex]x_1=9[/tex].
The discussion of the democratic is [tex]x_2=9[/tex].
The discussion of the democratic is [tex]x_3=5[/tex]
So, the total number of candidates are
[tex]x_t=x_1+x_+x_3\\\\=9+9+5\\\\=23[/tex]
Probability of independate candidate from the group of candidates is
[tex]P_1=\frac{x_3}{x_t}\\\\P_1=\frac{5}{23}\\\\[/tex]
As, the remaining number of candidates after the selectio of the independent candidate is
[tex]x_r=x_t-1\\\\x_r=23-1\\\\x_r=22[/tex]
Now, the remaining number of candidates from the group of total remaining candidates is
[tex]P_2=\frac{x_1}{x_r}\\\\P_2=\frac{9}{22}[/tex]
So, the probability of an independent Democrat using the probability is
[tex]P=P_1[/tex] × [tex]P_2[/tex]
[tex]P=\frac{5}{23}[/tex] ×[tex]\frac{9}{22}[/tex]
[tex]P=\frac{110(207)}{506}\\\\P=\frac{22770}{506}\\\\P=45[/tex]
Hence, the probability of selecting two Democrats is [tex]45[/tex].
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please help with this
Answer: There are multiple answers.
Step-by-step explanation: To find x...simply ad together what you have (The numbers given) and subtract from 180.
(I did this a while ago, don't take my word for it)
Last month the price of one pound of carrot was $2 1/5 and joe sold 12 1/12
Answer:[tex]26\frac{7}{12}[/tex]
Step-by-step explanation:
2 1/5 * 12 1/2 = 319/12
319/12 = [tex]26\frac{7}{12}[/tex]
Which of the following shows an example of the identity property of 0?
Answer:is 1
identity property of 0 the definition is adding 0 to any number results in the number itself. and one 1 is have the same but other 3 is not.
If a boy grows 5 inches, he will be one half as tall as his sister , his sister is 68 inches tall. How tall is the boy?
What is an equation of the line that passes through the points (4, 4) and (8, 5)?
Answer:
y=0.25x+3
Step-by-step explanation:
use desmos graphing calculator and put the coordinates into a table
Which statement best describes the functions represented in the graphs?
A.Both functions are continuous and linear.
B.Only function p is continuous and linear.
C.Both functions are discrete and exponential.
D.Only function a is discrete and exponential.
The statement that best describes the functions represented in the graphs is B. Only function p is continuous and linear.
What is a linear function?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
How to know continuous function?A function at a place can only be continuous if it is defined there, has a limit there, and its value at that point is equal to the value of the limit there.
The graph of function p is linear and continuous
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A rectangular flowebed is 6.1 meters long.and 3.6 meters wide. What is the area of the flower bed? Use the area model to solve?
For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−90)2+4,050 . The maximum capacity of the company is 150 items.
Assuming that the company sells all that it produces, what is the profit function?
P(x)=
What is the domain of P(x) ?
The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 40 items =
Profit when producing 50 items =
Can you explain, from our model, why the company makes less profit when producing 10 more units?
The profit function is P(x) = −0.5x² + 40x - 100
The domain is 3 < x < 75Profit when producing 40 items = 700Profit when producing 50 items = 650The company makes less profit when they produce moreHow to determine the profit function?From the question, we have the following equations that can be used in our computation:
Cost function, C(x) = 50x + 100
Revenue function, R(x) = −0.5(x − 90)² + 4050
The profit function is the difference between the revenue and the cost
So, we have
P(x) = R(x) -CP(x)
Substitute the known values in the above equation, so, we have the following representation
P(x) = −0.5(x − 90)² + 4050 - 50x - 100
Evaluate the like terms
P(x) = −0.5(x − 90)² - 50x + 3950
Expand
P(x) = −0.5(x² − 180x + 8100) - 50x + 3950
Expand
P(x) = −0.5x² + 90x - 4050 - 50x + 3950
Evaluate the like terms
P(x) = −0.5x² + 40x - 100
The domain of the functionIn (a), we have
P(x) = −0.5x² + 40x - 100
Using a graphing calculator, the reasonable domain is
3 < x < 75
So, the domain is 3 < x < 75
The profit at each productHere, we have
x = 40 or 50
So, we have
P(40) = -0.5(40)² + 40(40) - 100 = 700
P(50) = -0.5(50)² + 40(50) - 100 = 650
Why the profit makes less profitIn (d), we have
P(40) = 700
P(50) = 650
This means that the profit reduces as they produce more
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DUE SOON! PLEASE SHOW WORK! JUST DONT KNOW WHERE TO START! BEEN STUCK ON THIS FOREVER ITS DUE SOON!!
Answer:
(0,-7)
Step-by-step explanation:
Plug in the X and Y's from the answer choices to get your answer. If the left of the equation (Y) is less than the right side (-1/2x - 6) it is correct!
Hope this helps!
Kathryn invests $1000 in one account and $2200 in an account paying 3 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest?
She invested $1000 at 2% and 2200 at 5% simple interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P₁ = 1000, P₂ = 2200, assuming r₁ = x% and r₂ = (x + 3)% and the sum of simple interest obtained from both these investments is $130.
∴ (1000×x×1)/100 + {(2200×(x + 3)×1}/100 = 130.
10x + 22x + 66 = 130.
32x = 64.
x = 2.
So, the rate of interest is 2% and 5%.
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At a certain high school, the Prom Committee is going to choose new members. There are 10 students from the Junior class and 3 students from the Senior
class who are willing to be new members. In how many ways can 7 new members be chosen if 2 or fewer must be from the Senior class?
The number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is; 705 ways
How to solve permutation and combination?The formula for probability combination is;
nCr = n!/(r! * (n – r)!)
where;
n is the total number of items.
r is the number of things that may be selected at one time.
The number of ways that 2 students can be selected from the senior class is;
N(2 students from the SR class) = 3C2 * 10C2 = 135 ways
Similarly;
N(1 student from the SR class) = 3C1 * 10C3 = 360
N(0 students from the SR class) = 3C0 * 10C4 = 210
Thus, number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is;
135 + 360 + 210 = 705 ways
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Answer PLEASE!!!! 30 points
Simplify −4r(−15r + 3r − 10).
−48r2 + 40r
−48r2 − 40r
48r2 + 40
48r2 + 40r
Answer:
[tex]\huge\boxed{\sf 48r\² + 40r}[/tex]
Step-by-step explanation:
Given expression:= -4r(-15r + 3r - 10)
Add -15r and 3r
= -4r(-12r - 10)
Distribute
= (-4r)(-12r) - (-4r)(10)
= 48r² - (-40r)
= 48r² + 40r[tex]\rule[225]{225}{2}[/tex]
5. Find the volumes of the following sugar containers. Round to
Domino 1 decimal place.
SUGAR
a. Domino granulated sugar in canister: radius-1.56 inches;
height-6.93 inches
in³
b. Domino sugar cubes in box: length-15.5 cm; width-8.6 cm;
height-3.8 cm.
Domino
SUGAR CUBES
cm³
The volume of the canister is 36.7 in³. The volume of box is 482.6 cm³
To find the volume of a canister, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, the canister has a radius of 1.56 inches and a height of 6.93 inches,
volume of canister = π × (1.56 inches)² × 6.93 inches
volume of canister = 36.7 in³
To find the volume of a box, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
In this case, the box has a length of 15.5 cm, a width of 8.6 cm, and a height of 3.8 cm
volume of box = 15.5 cm × 8.6 cm × 3.8 cm
volume of box = 482.6 cm³
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Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 17 centimeters and a height of 13 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
3,203 cm2
2,295 cm2
1,020 cm2
731 cm2
Answer:
283 cm^2
Step-by-step explanation:
hi your welcome
Answer:
Step-by-step explanation:
radius = r = 17
height = h = 13
First calculate the total surface area =
2πr (r + h)
2 (3.14) 17 (17 + 13)
2 (3.14) 17 (30)
6.28 (17)(30)
106.76 (30)
3202.80 cm²
Then subtract the area of the bottom base of the cake:
Base of the cake is the area of the round base
π r² = 3.14 (17)²
3.14 (289) = 907.46 cm²
Subtract area of base from total surface area:
I am rounding:
3203 - 908 = 2295 cm²
Second option or B
Use the graph below to fill in the blank with the correct number:
f(2)=
Answer:
1
Step-by-step explanation:
[tex]f(2)[/tex] is equal to the [tex]y[/tex] coordinate of the point on the graph of the function with [tex]x[/tex] coordinate 2.
HELP PLEASE!
The answer choices are
A) 240
B) 270
C) 210
D) 120
If the rotation is clockwise the angle is 120°.
If the rotation is counterclockwise the angle is 240°
The correct options are A and D.
What is the angle of rotation that maps P to G?
We assume that the rotation is clockwise.
First, we can see that the rotation from P to F is just a rotation of 90°.
(point P as at 9 on a clock and point F is at 12 on a clock).
To go from point F to G, we need to move one of the sections defined by the dashed lines, and we know that each one of these measures 30°, then we need to add another 30° to the angle.
90° + 30° = 120°
Then the angle of rotation to map P to G is 120°.
The correct option is D.
Then if the rotation is counterclockwise, the rotation will be of 240°.
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The polynomial
p(x)=24x3−46x2+29x−6
has three real roots. One of them is x=2/3 Find the others and list them in increasing sequence:
The other roots of the cubic equation p(x) = 24·x³ - 46·x³ + 29·x - 6 are;
x = 1/2
x = 3/4
What is a cubic equation in mathematics?A cubic equation is an equation that has 3 as the highest index.
The specified polynomial in the question is presented as follows;
P(x) = 24·x³ - 46·x² + 29·x - 6
The solution of the equation is; x = (2/3)
Therefore, (x - 2/3) is a factor of the equation and we get;
(24·x³ - 46·x² + 29·x - 6) ÷ (x - 2/3) has a remainder of 0
Dividing the above expression using long division, we get;
24·x² - 30·x + 9
(x - 2/3) [tex]{}[/tex] |(24·x³ - 46·x² + 29·x - 6)
[tex]{}[/tex] 24·x³ - 16·x² + 29·x - 6
[tex]{}[/tex] -30·x²
[tex]{}[/tex] -30·x² + 20·x
[tex]{}[/tex] 9·x - 6
[tex]{}[/tex] 9·x - 6
The other real roots of the specified equation can be found as follows;
The equation for the roots is; P(x) = 24·x³ - 46·x² + 29·x - 6 = 0
From the above long division, therefore;
24·x³ - 46·x² + 29·x - 6 = (24·x² - 30·x + 9) × (x - 2/3) = 0
Which indicates; (24·x² - 30·x + 9) = 0 or (x - 2/3) = 0
The other solution are;
24·x³ - 30·x + 9 = 0
3·(·8·x² - 10·x + 3) = 0
8·x² - 10·x + 3 = 0
Solutions for the above equation in the form; a·x² + b·x + c = 0 can be obtained using the quadratic formula as follows;
The quadratic formula; x = [tex]\dfrac{-b\pm\sqrt{b^2 - 4\cdot a\cdot c} }{2\cdot a}[/tex]
By comparing the equation, 8·x² - 10·x + 3 = 0 to the equation, a·x² + b·x + c = 0, we get;
a = 8, b = -10, and c = 3
Therefore;
x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8)
((-10)² - 4 × 8 ×3) = 2
Therefore;
x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8) = (10 ± 2)/(16)
x = 3/4, and x = 1/2
Therefore, the other other roots in increasing sequence are;
x = 1/2 and x = 3/4
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Having a really hard time with this question, so if anyone kindly can let me know.
Answer:
Plane PQY
Step-by-step explanation:
A plane is defined by 3 non-linear points. This is because if 3 linear points are given, only a line has been defined; its plane could be at any angle. The only answer choice that has non-linear points is PQY.
If 9 cows can fit in a field, how many fields are necessary to make sure 65 cows are all in a field?
fields
Answer: 8 fields are needed
Step-by-step explanation:
65 ÷ 9 = 7.222
You can't have a partial field, so you round up to find the number of fields for all 65 cows.
8 fields will fit 65 cows
Answer: 8
Step-by-step explanation:
you divide 65 by 9 but you cant have 7.222 cows so its 8
Which is the best estimate of 756 ÷ 26?
The division between 756 and 26 can be represented as a fraction or decimal as 378/13 or 29.1 respectively
FractionsFractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
We can say the fraction of a number is a ratio between the numerator and denominator of two numbers.
Fractions are often as a result of dividing two numbers and they probably don't give a whole number.
In this case, the division between 756 and 26 will result in a fraction because both numbers are not completely divisible by one another.
To divide 756 by 26;
756 ÷ 26 =
Divide both sides by 2
756 ÷ 26 = 378 / 13
Both numbers are not divisible by one another from here, but we can represent this as a fraction of one another;
756 ÷ 26 = 29.076923
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A student bikes 5000 m East to school in 30.0 min (1800 seconds), realizes he forgot his calculator for physics, spends 30.0 min (1800 seconds) going back going home, and then races back to school in 27.0 minutes (1620 seconds).
What is the student’s total distance traveled?
_______ meters
The number of seconds it took the student to travel back and forth is ________
seconds.
Determine the student’s average speed. ________
m/s
The total distance covered is 15000 m. The total time taken is 5220 seconds and the speed is 2.87 m/s.
What is the speed?We know that speed has to do with the ratio of the distance that has been covered to the time taken. The speed is a scalar quantity and as such we do not consider the direction hence we would not consider that going back in the opposite direction. The total distance can be obtained algebraically.
The total distance that the student travelled can be obtained from;
5000 m + 5000 m + 5000 m
= 15000 m
The total time taken in seconds = 1800 seconds + 1800 seconds + 1620 seconds
= 5220 second
Speed = Distance/ Time
= 15000 m/5220 second
= 2.87 m/s
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Suppose you have the Exam 1 and Exam 2 scores of all
students enrolled in U.S. History. The slope of the
regression line for predicting the scores on Exam 2 from
the scores on Exam 1 is 0.51. The standard deviation for
Exam 1 scores is 11.6, and the standard deviation for Exam
2 scores is 7.0. Use only this information to find the
correlation between Exam 1 scores and Exam 2 scores.
The correlation coefficient between Exam 1 scores and Exam 2 scores is given as follows:
0.8452.
How to obtain the correlation coefficient?The equation for this problem is given as follows:
b = r x Sy/Sx.
The variables of the equation are given as follows:
b is the slope.r is the correlation coefficient.Sy is the standard deviation of the output variable.Sx is the standard deviation of the input variable.The input and the output variables in this problem are given as follows:
Input variable: Exam 1 score.Output variable: Exam 2 score.Hence the values of the parameters are given as follows:
b = 0.51, Sx = 11.6, Sy = 7.
Hence the numeric value of the correlation coefficient is obtained as follows:
b = r x Sy/Sx.
r x 7/11.6 = 0.51
0.6034r = 0.51
r = 0.51/0.6034
r = 0.8452.
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Find the average rate of change from x=4 to x=14
The average rate of change is given by -2/5. The correct option is (d).
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given graph shows different values of y at x = 4 and x = 14 as follows,
At x = 4, y = 7
And at x = 14, y = 3.
Now, the average rate of change can be determined by taking the ratio of the difference of the values of y to that of x as follows,
(3 - 7)/(14 - 4)
= -4/10
= -2/5
Hence, the average rate of change x = 4 to x = 14 is given as -2/5.
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