Answer:
[tex]4800+183x\geq 8000[/tex]
She must sell at least 18 policies to make an annual income of at least $8,000
Step-by-step explanation:
Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell
We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:
[tex]\frac{3*6,100}{100} =183[/tex]
Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.
We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:
[tex]4800+183x[/tex]
Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:
[tex]4800+183x\geq 8000[/tex]
Let's solve the inequality:
1. Subtract 4800 from both sides
[tex]4800-4800+183x\geq 8000-4800[/tex]
[tex]183x\geq 3200[/tex]
2. Divide both sides by 183
[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]
[tex]x\geq 17.48[/tex]
Since she can't sell a fraction of a policy, we must round the result to the next integer:
[tex]x\geq 18[/tex]
We can conclude that she must sell 18 policies to make an annual income of at least $8,000.
You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds? 121.862 years 12.1862 years 10.155 years 1.0155 years
Answer:
10.153 years
Step-by-step explanation:
The future value of such an investment is given by ...
FV = P·(1 +r/12)^(12t)
where P is the principal invested, FV is the future value of it, r is the annual interest rate, and t is the number of years.
Dividing by P and taking the log, we have ...
FV/P = (1 +r/12)^(12t)
log(FV/P) = 12t·log(1 +r/12)
Dividing by the coefficient of t gives ...
t = log(FV/P)/log(1 +r/12)/12 = log(3000/2000)/log(1 +.003333...)/12 ≈ 121.842/12
t ≈ 10.153 . . . years
PLEASE! Someone help me answer this and explain it
Answer:
12.5
Step-by-step explanation:i did that problem before
What is the equation for the translation of x2 + y2 = 16 seven units to the right and five units up?
(x + 7)2 + (y – 5)2 = 16
(x - 7)2 + (y + 5)2 = 16
(x + 7)2 + (y + 5)2 - 16
(x - 72 + (y – 5)2 = 16
Answer:
[tex](x-7)^2+(y-5)^2=16[/tex].
Step-by-step explanation:
The given circle has equation [tex]x^2+y^2=16[/tex].
This is the equation that has its center at the origin with radius 4 units.
When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).
The equation of a circle with center (h,k) and radius r units is [tex](x-h)^2+(y-k)^2=r^2[/tex].
This implies that, the translated circle will now have equation.
[tex](x-7)^2+(y-5)^2=4^2[/tex].
[tex](x-7)^2+(y-5)^2=16[/tex].
The correct equation for translating the circle x² + y² = 16 seven units to the right and five units up is (x - 7)² + (y - 5)² = 16. Therefore, option D is the correct answer.
The original equation for a circle with a radius of 4 units is x² + y² = 16. A translation of the circle seven units to the right and five units up would involve shifting the x-coordinate by +7 and the y-coordinate by +5. Therefore, the new equation would be (x - 7)² + (y - 5)² = 16.
This is due to the fact that a translation of a geometric figure does not alter its size, shape, or orientation; it simply shifts the figure in the plane. Keeping the radius the same, applying the translation to the circle's center (0,0) results in a new center at (7,5), which translates to the equation above.
What is the value of the discriminant in 3x^2 - 4x + 2 = 0?
Answer:
-8Step-by-step explanation:
[tex]\text{The formula of a discriminant of}\ ax^2+bx+c=0:\\\\b^2-4ac\\\\================================\\\\\text{We have the equation:}\\\\3x^2-4x+2=0\to a=3,\ b=-4,\ c=2\\\\\text{Substitute:}\\\\b^2-4ac=(-4)^2-4(3)(2)=16-24=-8[/tex]
Given: ΔPSQ, PS = SQ Perimeter of ΔPSQ = 50 SQ – PQ = 1 Find: Area of ΔPSQ
Answer:
120 units²
Step-by-step explanation:
Perimeter = PS + SQ + PQ
50 = SQ + SQ + (SQ -1)
51 = 3SQ
17 = SQ
17 -1 = 16 = PQ
The midpoint of the base is one leg of the right triangle whose other leg is the height of this isosceles triangle. That height is ...
h = √(17² -(16/2)²) = √225 = 15
Then the area is ...
A = (1/2)bh = (1/2)(16)(15) = 120 . . . . . square units
3(4x+2)-6x=5x-5(2+x) please solve show your work do not solve for x
Answer:
simplifies to 6x+6=-10x = -8/3 = -2 2/3Step-by-step explanation:
3(4x+2)-6x=5x-5(2+x)
12x +6 -6x = 5x -10 -5x . . . . . eliminate parentheses using the distributive property
6x +6 = -10 . . . . . . . . . . . . . . . collect terms
x +1 = -10/6 . . . . . . . . . . . . . . . divide by 6
x = -1 - 5/3 . . . . . . . . . . . . . . . add -1
x = -8/3 . . . . . . . . . . . . . . . . . simplify
a=8, b=5, C=90 degree; Find c, A, and B
This is for the law of sine and cosine
Answer:
• c = √89 ≈ 9.434
• A = arcsin(8/√89) ≈ 57.995°
• B = arcsin(5/√89) ≈ 32.005°
Step-by-step explanation:
By the law of cosines, ...
c² = a² + b² -2ab·cos(C)
Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.
c = √(8² +5²) = √89 ≈ 9.434
Then by the law of sines (or the definition of the sine of an angle), ...
sin(A) = a/c·sin(C) = a/c = 8/√89
A = arcsin(8/√89) ≈ 57.995°
sin(B) = b/c·sin(C) = b/c = 5/√89
B = arcsin(5/√89) ≈ 32.005°
I need help understanding linear inequalities. I'm trying to solve the following problem:
[tex]\frac{-x}{2}[/tex] < 1
How do I get rid of the 2 on the left side so it's just the x? I know what I do to one side I have to do to the other, and I've broken the problem down to this so far. Any help would be appreciated. Thanks!
All you have to do is treat the inequality like an equation and multiply both sides by 2.
[tex]-x<2 \\ \\ x>-2[/tex]
Answer: x> -2
Step-by-step explanation:
step 1 :take 2 to the other side ,and 1 will multiply by 2 which will give you 2
step 2 : take the negative or -1 to the other side ( you will divide 2 by -1 ) which will result to a -2
step 3: most important thing to remember once you multiply or divide by a negative number you will have to change the inequality sign ( in this case the smaller than sign changes to bigger than because you divided by -1 in step 3 )
hope this helped
Which expression can you substitute in the indicated equation to solve the system below?
x + y = 6
12x + y = 5
1. 6 - y for x in 12x + y = 5
2. 5 + 12x for y in x + y = 6
3. 6 + y for x in 12x + y = 5
4. 5 - x for y in x + y = 6
Final answer:
To solve the system of equations x + y = 6 and 12x + y = 5, substitute 6 - y for x in 12x + y = 5 and solve for y.
Explanation:
To solve the given system of equations x + y = 6 and 12x + y = 5, we need to substitute the value of x or y into the second equation. In this case, substituting 6 - y for x in 12x + y = 5 will allow us to solve for y.
Let's substitute 6 - y for x:
12(6 - y) + y = 5
After simplifying, we get:
72 - 12y + y = 5
Combining like terms:
-11y = -67
Dividing both sides by -11, we find that y = 67/11 or approximately 6.09.
So, option 1: 6 - y for x in 12x + y = 5 is the correct expression to substitute.
If the fourth term of a gwometric progression is -27/4 and the fifth term is 81/4 find a1 and r
Answer:
a1 = 1/4r = -3Step-by-step explanation:
r = a5/a4 = (81/4)/(-27/4) = -3
an = a1·r^(n-1)
-27/4 = a1·(-3)^3 = -27·a1 . . . . fill in the known numbers for n=4
(-27/4)/(-27) = a1 = 1/4
A tree 7ft y’all grows an average 6 in each year which equation models the trees height h after x years
Answer:
h = 7 + 6x
Step-by-step explanation:
Since we are trying to find the height of the tree, we put h on the left side of the equation. Since the tree is 7ft tall at the moment, we write 7ft on the right side of the equation. Knowing that the tree grows 6 inches each year (x) we write 6x on the right side of the equation.
Answer:
H=7+6x
Hope this helps
For which values of P and Q does the following equation have infinitely many solutions ?
Px+57=-75x+Q
Answer:
(P, Q) = (-75, 57)
Step-by-step explanation:
The equation will have infinitely many solutions when it is a tautology.
Subtract the right side from the equation:
Px +57 -(-75x +Q) = 0
x(P+75) +(57 -Q) = 0
This will be a tautology (0=0) when ...
P+75 = 0
P = -75
and
57-Q = 0
57 = Q
_____
These values in the original equation make it ...
-75x +57 = -75x +57 . . . . . a tautology, always true
Use the graph to find the slope and y-intercept to write
the equation in slope-intercept form.
The graph shown is y=
x+
Answer:
Slope = -1/2
Y-intercept is y = -1
Equation of the line: [tex]y=-\frac{1}{2}x-1[/tex]
Step-by-step explanation:
The slope intercept form is y = mx + b
Where, m is slope, and
b is y-intercept
We need 2 points to find these. One point is (-2,0) and second point is (2,-2).
THe formula for slope, m, is m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Plugging the points, we get the slope to be:
[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{-2-0}{2--2}\\=\frac{-2}{4}\\=-\frac{1}{2}[/tex]
y-intercept is the point where the line crosses the y axis. Looking at the graph, y-intercept is y = -1.
Now we plug slope and y-intercept into the slope-intercept form to get:
[tex]y=mx+b\\y=-\frac{1}{2}x-1[/tex]
ANSWER
[tex]y = - \frac{1}{2} x - 1[/tex]
EXPLANATION
The graph passes through (-2,0) and (0,-1).
The slope can be calculated using the formula,
[tex]m= \frac{rise}{run} [/tex]
[tex]m = \frac{0 - - 1}{ - 2 - 0} [/tex]
[tex]m = - \frac{1}{2} [/tex]
The y-intercept is -1.
The equation in slope-intercept form is
y=mx + c
We substitute the slope and y-intercept to obtain
[tex]y = - \frac{1}{2} x - 1[/tex]
What is the solution to the Reimann Hypothesis (If there is one)?
Answer:
Sadly, it is still high in debate. Scientists are still in doubt of the Hypothesis, so no. Some may claim there is a solution, though.
Step-by-step explanation:
Final answer:
The Riemann Hypothesis is an unsolved mathematical problem, with no validated solution as of yet, and remains one of the Millennium Prize Problems in mathematics.
Explanation:
The Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, specifically in the area of number theory. It postulates that all non-trivial zeros of the Riemann zeta function, a complex function important for understanding the distribution of prime numbers, have their real parts equal to 0.5. Despite significant efforts by mathematicians over the years, the solution to the Riemann Hypothesis remains elusive, and no proof or disproof has been universally accepted by the mathematics community.
As of my knowledge cutoff in 2023, researchers continue to explore various mathematical approaches and even computational methods to tackle this problem. However, no experiment or scientific test can validate the hypothesis since it is a purely mathematical conjecture. A resolution of the Riemann Hypothesis would have profound implications for number theory and related fields, yet it remains one of the seven Millennium Prize Problems, with a reward of one million dollars offered for a solution.
Find m∠1 if m∠2=73°, m∠3=107°, m∠4=92°. Justify your response!
Answer:
m∠1 = 92°
Step-by-step explanation:
∠2 corresponds to the supplement of ∠3 if (and only if) lines a and b are parallel. We find that
m∠2 + m∠3 = 73° +107° = 180°
so, the angles are supplementary and lines a and b are parallel.
Angles 4 and 1 are corresponding angles where the line d crosses the parallel lines a and b, so are congruent.
m∠1 = m∠4 = 92°
Find the value of b in the graph of y=3x+b if it is known that the graph goes through the point:
O(3,8)
Answer:
b= -1
Step-by-step explanation:
y=3x+b
8=3(3)+b
8=9+b
b= -1
A bag contains cars numbered from 1 to 14. Find the Probability of:
a) selecting a prime number or multiple of 4
b) selecting a multiple of 2 or 3
c) selecting 3 or 4
d) selecting 8 or a number less than 8
A)
Prime numbers and numbers with a multiple of four that are between 1 and 14 include: 1, 2, 3, 4, 5, 7, 8, 12, 13.
There are 9 numbers listed.
9/14 = ~0.64285... or roghly 65.3%
B) Numbers between 1 and 14 with the multiples of 2 or 3 include: 2, 4, 6, 8, 9, 10, 12, 14.
There are 8 numbers listed.
8/14 = ~0.5714... or, about 57.14%
C) 3 and 4 is a list of two numbers.
2/14 = 1/7 = ~0.1429, or about 14.9%
D) There is a total of numbers equal to or less than 8 in a list of 1 and 14.
8/14 = ~0.5714... or, about 57.14%
Green River State Park has two popular hiking trails: Overlook Trail and High Ridge Trail. On one particular day, 80 hiking groups used the trails: 40 groups used Overlook Trail and 40 groups used High Ridge Trail. Of the 40 groups that used Overlook Trail, 30 groups had children and 10 groups had no children. Of the 40 groups that used High Ridge Trail, 15 groups had children and 25 groups had no children. Consider the following events.
H: A hiking group uses High Ridge Trail.
C: A hiking group has children.
Which statement is true about events H and C?
A. Events H and C are independent and P(H|C) < P(C|H).
B. Events H and C are dependent and P(H|C) < P(C|H).
C. Events H and C are independent and P(H|C) = P(C|H).
D. Events H and C are dependent and P(H|C) = P(C|H).
Answer:
B. Events H and C are dependent and P(H|C) < P(C|H)
Step-by-step explanation:
The ratios of groups with children to hiking groups on the trail are different for the two trails.
P(H|C) = 15/45 = 1/3
P(C|H) = 15/40 = 3/8
1/3 < 3/8 so the comparison of choice B is appropriate.
Drag and drop an answer to each box to correctly complete the proof.
Given: Parallelogram JKLM is a rectangle.
Prove: JL¯¯¯¯¯≅MK¯¯¯¯¯¯¯
Answer:
1. all the right angles are congruent
2. opposite sides of a parallelogram are congruent
3. SAS congruent postulate
4. corresponding parts of a congruent triangle are congruent
Step-by-step explanation:
1. As all the right angles are congruent
∠JML≅∠KLM≅ ∠90°
2. As per the properties of a parallelogram, the opposite sides are congruent.
Hence the sides JM≅KL
3. SAS postulate is defined as Side-Angle-Side postulate. When the side, adjacent angle and the other other adjacent side of two triangle are congruent then the two triangles are said to be congruent. In the given case both the sides JM and ML of ΔJML are congruent to both the sides KL and ML of ΔKLM.
Hence ΔJML≅ΔKLM
4. As proven in part 3, ΔJML≅ΔKLM so the congruent parts of two congruent triangle are congruent.
In given case the side JL(of ΔJML)≅MK(ΔKLM)
!
The completed proof is presented as follows;
Parallelogram JKLM is a rectangle and by definition of a rectangle, ∠JML
and ∠KLM are right angles, ∠JML ≅ ∠KLM because, all right angles are
congruent, [tex]\overline{JM}[/tex] ≅ [tex]\overline{KL}[/tex] because opposite sides of a parallelogram are
congruent, and [tex]\overline{ML}[/tex] ≅ [tex]\overline{ML}[/tex] by reflective property of congruence. By the SAS
congruence postulate, ΔJML ≅ ΔKLM. Because, congruent parts of
congruent triangles are congruent, [tex]\overline{JL}[/tex] ≅ [tex]\overline{MK}[/tex]
Reasons:
The given quadrilateral is a parallelogram, that have interior angles that are right angles, therefore, the figure has the properties of a rectangle, and
parallelogram including;
The length of opposite sides are equalAll right angles are congruent and equal to 90°
The length of a side is equal to itself by reflexive property, therefore, [tex]\overline{ML}[/tex]
≅ [tex]\overline{ML}[/tex]
The Side-Angle-Side SAS postulate states that if two sides and an included
angle of one triangle are congruent to the corresponding two of sides and
included angle of another triangle, the two triangles are congruent.
Learn more here:
https://brainly.com/question/3168048
Given: m arc KP=2m arc IP
, m arc IVK=120°
Find: m∠KJL.
Answer:
40
Step-by-step explanation:
The measure of the angle KJL is 40°.
What is a circle?Circle definition states a shape that consists of points, in a two-dimensional plane, equidistant from a given point. A circle is a closed curve that has no corners or vertices.
Given is a circle O where m arc IVK = 120° and m arc KP = 2 × m arc IP,
We need to find the measure of the angle KJL,
So,
According to the question,
m arc IVK + m arc KPI = 360° [whole circumference of a circle is 360°]
m arc IVK + m arc KP + m arc IP = 360°
120° + m arc IP + 2 × m arc IP = 360°
3 m arc IP = 240°
m arc IP = 80°
Therefore,
m arc KP = 160°
Now, according to the property of a circle,
m ∠KJL = 1/2 × [m arc KP - m arc IP]
m ∠KJL = 1/2 × [160° - 80°]
m ∠KJL = 80°/2
m ∠KJL = 40°
Hence the measure of the angle KJL is 40°.
Learn more about circle click
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#SPJ2
Enter the missing numbers in the boxes to complete the table of equivalent ratios please help me
Answer:
3 : 36 10: 120 6:72
Step-by-step explanation:
60 divided by 5 is 12
3 x 12 = 36
10 x 12 = 120
72/12= 6
3-36
5-60
6-72
10-120
One month equals 12$ saved
need help :) i’m bad at math lol
Answer:
i think it is the last one
Step-by-step explanation:
-2/25^3x^3
What is the volume of the square pyramid with base edges 4 m and height 3 m?
Answer:
Volume of the pyramid = 16m³ or 16 cubic meters.
Step-by-step explanation:
The equation for the volume of a pyramid is:
[tex]V=\frac{b*h}{3}[/tex]
where b = area of base and h = height.
In this case, the base is a square with a side length of 4m.
Area of the square base = (4m)² = b = 16m²
h = 3m
Insert b and a into the volume of a pyramid equation.
[tex]V=\frac{3m*16m}{3}[/tex]
= 16m³
Volume of the pyramid = 16m³ or 16 cubic meters.
You buy a quart of ice cream that comes in a cylindrical tub. A quart has a volume of about 58 cubic inches. The tub has a height of 5 inches. What is the radius of the ice-cream tub? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
Givens
V = 58 in^3
h = 5 inches
pi = 3.14
Formula
V = pi * r^2 * h
Solution
58 = 3.14 * r^2 * 5
58 = 15.7 * r^2
58/15.7 = r^2
3.6942 = r^2
sqrt(r^2) = sqrt(3.6942)
r = 1.922 which when rounded is
r = 1.92
Answer: r=1.92
given what we know about the equation i can determine what steps are needed to solve this :)
volume
1) V = 58 in^3
we know that h=5inches
2) h = 5 inches
heres what pi equals
3) pi = 3.14
then we use pi in the equation
4)= pi * r^2 * h
heres the solution steps
1)58 = 3.14 * r^2 * 5
2)58 = 15.7 * r^2
3)58/15.7 = r^2
4)3.6942 = r^2
5)sqrt(r^2) = sqrt(3.6942)
6)r = 1.922 then we round and get r = 1.92
so final solution is r = 1.92
×║hope this helps║×
Find the equation of the line that is perpendicular to the line 4x+2y=1 and passes through the point (-4,3)
A) y=2x+5
B) y=2x+2
C) y=1/2x+2
D) y=1/2x+5
First find the slope of the given line:
4x +2y = 1
Subtract 4x from each side:
2y = -4x + 1
Divide both sides by 2:
y = -2x +1/2
The slope is -2.
Now use the slope to find the y-intercept. Because the line is perpendicular, you need to use the negative inverse of the slope.
The negative inverse of -2 is 1/2
Now using the point-slope form y - y1 = m(x-x1)
Use the inverse slope for m, and the given point(-4,3) to get:
y - 3 = 1/2(x+4)
Simplify:
y - 3 = x/2 +2
Add 3 to each side:
y = x/2 + 5
Reorder the terms to get y = 1/2x +5
The answer is D.
Hey help me on this??
Answer:
C
Step-by-step explanation:
Use such properties of logarithms:
[tex]\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa[/tex]
Thus,
[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]
Answer:
The answer is C
Step-by-step explanation:
Use such properties of logarithms:
\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa
Thus,
\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).
A bag contains 9 green marbles and 11 white marbles. You select a marble at random. What are the odds in favor of picking a green marble?
Help pls
Answer: 9\20 or 45% hope this helps
The "odds" of picking a green are 9 to 11 .
The "probability" of picking a green is 9/20 or 45% .
why does the function k(f(x)) provide a better model for the scatter plot when 4
Answer:
It reduces the distance from the plotted points to the function curve.
Step-by-step explanation:
The goodness of fit of a model is measured by the "residuals", the differences between the given points and the modeled points. The smaller the residuals, the better the model. Any change to the model that will put it closer to the plotted points makes it a better model. The change proposed in your problem statement does that.
The wholesale cost of a sofa is $520. Based on selling price, the original markup was 69%. Find the final sale price after the following series of price changes occurred: a markdown of 13%, a markup of 30%, and a second markdown of 36%. Round each intermediate selling price to the nearest cent.
Answer:
$1214.19
Step-by-step explanation:
Let c and p represent the cost of the sofa and the original selling price, respectively. The original markup was 0.69·p, so we have ...
c + 0.69p = p . . . . . based on selling price, the original markup was 69%
c = p(1 -0.69) = 0.31p . . . . subtract the markup
p = c/0.31 . . . . . . . . . . . . . divide by the coefficient of c
So, the original selling price was ...
520/0.31 ≈ 1677.42
The first markdown decreased the selling price to ...
1677.42 - 0.13·1677.42 = 0.87·1677.42 ≈ 1459.36
The markup increased the selling price to ...
1459.36 +0.30·1459.36 ≈ 1897.17
And the final markdown decreased the selling price to ...
1897.17 -0.36·1897.17 ≈ 1214.19
The final sale price was $1214.19.
write the equation of the line
Answer:
y = 1/2x -8
Step-by-step explanation:
The two marked points are 1 unit apart vertically and 2 units apart horizontally. The vertical rise is positive for a positive horizontal run, so the slope is ...
rise/run = 1/2
The y-intercept is the leftmost marked point, at y=-8. Then the slope-intercept form of the equation of the line is ...
y = slope·x + y-intercept
y = 1/2x -8