Answer:
$14500
Step-by-step explanation:
$10 per unit means 1 unit is equivalent to 10 dollars.
∴Unit multiplier = [tex]\frac{10 dollars}{unit}[/tex]
$5 per unit means 1 unit is equivalent to 5 dollars
∴Unit multiplier = [tex]\frac{5 dollars}{unit}[/tex]
Remaining units = 1000 - 100 = 900 units
The unit multipliers are arranged in such a way that the "units” in the numerator and denominator will cancel each other out leaving us with “dollars” in the numerator. Our answer should be expressed in dollars
since the question requires us to calculate the bill
Bill of the House = Charge of first 100 units + Charge of remaining units
= (1000 units)([tex]\frac{10dollars}{unit}[/tex]) + [(900)units][[tex]\frac{5dollars}{unit}[/tex]]
= $10000 + $4500
= $14500
Find the length of QS
Answer:
112
Step-by-step explanation:
you have to find the length of QT and ST, then QS will be the hypotenuse (opposite of the right angle) of the triangle QTS.
use the formula:
c²=a²+b²
a²=c²-b²
1. to find QT:
QT²=53²-45²
QT²=2,809-2,025
QT²=784
QT=28
2.to find ST:
ST²=117²-45²
ST²=13,689-2,025
ST²=11,664
ST=108
3. find QS:
QS²=28²+108²
QS²=784+11,664
QS²=12,448
QS=111.570605
QS≈112
Use the image to determine the line of reflection. Graph of polygon ABCDE with point E at negative 3 comma 1. A second polygon A prime B prime C prime D prime E prime with E prime at negative 3 comma negative 3. Reflection across the x-axis Reflection across the y-axis Reflection across y = −1 Reflection across x = −3
The line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
A line section is what?Two different points on a line define the boundaries of a line segment in geometry. Or, a line segment is a section of the line that links two points, as another alternative. In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are set or identifiable.
According to the given information:From the given image, we can see that the original polygon ABCDE has point E at (-3, 1), and the reflected polygon A'B'C'D'E' has point E' at (-3, -3). This means that the reflection must have occurred across the horizontal line passing through the point (-3, -1), which is the midpoint of the line segment joining E and E'.
Therefore, the line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
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How much money should be deposited today in an account that earns 3.5% compounded monthly so that it will
accumulate to $12,000 in 3 years?
Click the icon to view some finance formulas.
The amount of money that should be deposited is
(Round up to the nearest cent as needed.)
orre
The amοunt οf mοney that shοuld be depοsited tοday is apprοximately $9,786.04 (rοunded up tο the nearest cent).
What dοes the mathematical term "cοmpοund" mean?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest.
It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest. Cοmpοund interest is cοmmοnly abbreviated C.I. in mathematics.
The amοunt that has tο be depοsited tοday can be determined using the calculatiοn fοr the future value οf an annuity.
FV is equal tο P * [(1 + r/n)(nt) - 1] / (r/n)
where:
$12k in future value P = principle (the amοunt tο be depοsited tοday)
3.5% as the annual interest rate
12 times every year are added tο the number n. (cοmpοunded mοnthly)
If t Equals time in years, then 3
When we enter the values, we οbtain:
[tex]12,000 = P * [(1 + 0.035/12)^{(12*3)} - 1] / (0.035/12)[/tex]
Simplifying:
[tex]12,000 = P * (1.035^{36} - 1) / (0.00291667) (0.00291667)[/tex]
[tex]P = 12,000 * (0.00291667) / (1.035^{36 }- 1)[/tex]
P ≈ $9,786.04
The sum that shοuld be depοsited as a result is abοut $9,786.04 tοday (rοunded up tο the nearest cent).
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MATHEMATICS
1. If each interior angle of a regular polygon is five times the exterior angle, how many sides has the polygon? x° зх°6x° 4xº 4x° 2x⁰ 2. Find the value of X in the polygon drawn above.
1. The number of sides of the polygon is 8
2. The value of x is 36
What is a polygon?A polygon can be defined as a flat or plane. The sum of a regular polygon is expressed as (n-2)180. The sum of exterior angle of a polygon is 360.
Therefore the sum of the interior is 5 times the exterior.
(n-2)180 = 5×360
180n - 360 = 1800
180n = 1800-360
180n = 1440
divide both sides by 180
n = 1440/180
n = 8
therefore the number of sides of the polygon is 8
2. The number of sides of the polygon is 6
Therefore the sum of angle in the polygon = 6-2)180 = 4× 180
= 720°
x+3x+6x+4x+4x+2x = 720
20x = 720
x = 720/20
x = 36
therefore the value of x is 36
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√15y^3
Simplify.
Remove all perfect squares from inside the square root.
the answer would be 3.872983 but rounding that off would be 3.9
answer: 3.9
144 is 90% what is the other 10 percent
Answer:
the missing 10% of 144 is 16. The whole amount would be 144 + 16 = 160.
Step-by-step explanation:
To find the missing 10%, you can use the fact that 100% is equal to the whole amount, and set up a proportion:
90/100 = 144/x
Simplifying this proportion, you can cross-multiply:
90x = 100 * 144
Then, you can solve for x:
x = (100 * 144) / 90
x = 160
Therefore, the missing 10% of 144 is 16. The whole amount would be 144 + 16 = 160.
Find the derivative if x= -2
Answer:
-27e^(-2).
= -3.654 to 3 decimal places.
Step-by-step explanation:
d/dx((3x^2 + 3)e^-x)
Using the Product Rule:
Derivative = (3x^2 + 3) d/dx(e^-x) + e^-x d/dx(3x^2 + 3)
= -e^-x(3x^2 + 3) + e^-x(6x)
= e^-x(6x -1*(3x^2 + 3))
= e^-x(6x - 3x^2 - 3)
= 3e^-x(2x - x^2 - 1)
= -3e^-x(x^2 - 2x + 1)
= -3e^-x(x - 1)^2
When x = -2,
Derivative = -3e^(-2)(-2-1)^2
= -27e^(-2)
What is the square root of 121. Please explain and show your work, I need it for the problem lol. thx
The value for the square root of 121 is 11.
We have,
The square root of 121 is 11.
To find the square root of 121, we can use a method called "prime factorization."
Begin by finding the prime factors of 121:
121 = 11 x 11
Since both factors are the same, we can pair them together:
11 x 11 = 11²
The exponent 2 indicates that the number 11 is repeated twice.
Therefore,
The value for the square root of 121 is 11.
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If Haechan has 1 apple and Mark has 2 and Jungwoo has 7 how much apples are there combined?
Answer:
9 apples
Step-by-step explanation:
1 apple + 2 apples + 7 apples= 9 apples
Answer:
1+7+2= 10
Step-by-step explanation:
1 apple + 7 apples + 2 apples = 10 apples
Fill the missing number: 0, 3, 8, 15, …….
Answer:
The next number is 24
Step by step explanation:
Write all the numbers down and make sure they are separated from each other. Example, 0 3 8 15.Find the difference between the numbers.0 3 8 15
+3 +5 +7(the difference here is 2) so the next one will be +9. 15+9=24.
How to solve this problem
This table shows the amount of money that Bradford saved in his savings account after different amounts of time.
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
Responses
0.08
0.08
12.5
12.5
25
25
50
Answer:
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
The constant of proportionality is 25.
Step-by-step explanation:
please someone help me
The perimeter of the triangle JKL, obtained using the two tangent theorem, is 138 units
What is the two tangent theorem?The two tangent theorem states the segments from the circle to the point at which two tangents to the circle meet are congruent.
The two tangent with common external point theorem indicates that the relationships between the lengths of the segments are;
5·x - 8 = 8·x - 35
8·x - 35 = 5·x - 8
8·x - 5·x = 35 - 8 = 27
3·x = 27
x = 27/3 = 9
x = 97·y - 9 = 2·y + 11
7·y - 2·y = 11 + 9 = 20
5·y = 20
y = 20/5 = 4
y = 4LO = 32 - (2·y + 11)
Therefore; LO = 32 - (2 × 4 + 11) = 13
LO = 13The two tangents theorem, indicates that we get;
LM = LO = 13The perimeter, P, of the triangle JKL is therefore;
P = (5·x - 8) + (8·x - 35) + (7·y - 9) + (2·y + 11) + LM + LO
P = (5×9 - 8) + (8×9 - 35) + (7×4 - 9) + (2×4 + 11) + 13 + 13 = 138
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what is the anwser to finding the radius
The radius of the circle is r = 3.75
What is the radius of a circle?The radius of a circle is the distance from its center to its circumference.
To find the radius of the circle, we see that there is a right-angle triangle there. So, using Pythagoras' theorem, we have that
AC² = AB² + BC²
(6 + r)² = 9² + r²
Expanding the brackets, we have that
36 + 12r + r² = 81 + r²
Cancelling out r², we have that
36 + 12r = 81
Subtracting 36 from both sides, we have that
12r = 81 - 36
12r = 45
r = 45/12
r = 15/4
r = 3.75
So, the radius is r = 3.75
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You deposit $6000 in an account earning 6% interest compounded quarterly. How much will you have in the account in 15 years? Round your answer to the nearest cent.
Step-by-step explanation:
The formula to calculate the future value of a present value deposit with compounding interest is:
FV = PV × (1 + r/n)^(n*t)
Where:
PV = Present Value (the initial deposit)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
Using this formula, we can calculate the future value of the $6000 deposit after 15 years:
PV = $6000
r = 6% = 0.06
n = 4 (compounded quarterly, i.e. 4 times per year)
t = 15 years
FV = $6000 × (1 + 0.06/4)^(4*15)
FV = $6000 × 1.458^60
FV = $6000 × 6.2565
FV = $37,539.00
Therefore, the future value of the $6000 deposit after 15 years with quarterly compounding at 6% interest rate is $37,539.00.
24. A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table.
According to this data, which was the most likely distribution of the colors of candies in the bag before it was opened?
A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange
B. 300 red, 250 blue, 200 green, 100 yellow, and 150 orange
C. 200 red, 200 blue, 200 green, 200 yellow, and 200 orange
D. 200 red, 200 blue, 200 green, 100 yellow, and 100 orange
A. 250 red, 250 blue, 250 green, 125 yellοw, and 125 οrange is the mοst likely distributiοn οf the cοlοrs οf candies in the bag befοre it was οpened
What is equatiοn?A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.
We must make use οf the data the students cοllected in οrder tο calculate the mοst likely distributiοn οf the candy cοlοurs in the bag befοre it was οpened. Nοw, let's determine the tοtal amοunt οf sweets the pupils pulled οut:
40 sweets divided by 4 pupils is 80 candies.
We may assume that there were twice as many red candies in the bag befοre it was οpened if the kids tοοk οut 40 οf them:
4 x 250 = 1,000
By emplοying this technique, we may determine hοw many candies οf each hue were included in the bag priοr tο its οpening.
Thus, A. 250 red, 250 blue, 250 green, 125 yellοw, and 125 οrange is the mοst likely distributiοn οf the cοlοrs οf candies in the bag befοre it was οpened
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Calculate the arithmetic mean of the numbers. -12 and 7
Plssss its an emergeny i will give brainliest
Therefore , the solution of the given problem of arithmetic mean comes out to be -12 and 7 have an algebraic mean of -2.5.
What is arithmetic mean, exactly?The typical values of a list, which are sometimes referred to because the objectives of an organization, are obtained by adding up each and every item on the list. These average values are then modified using the number of items in the list with the greatest abundance. Growth patterns in mathematics are comparable. By incorporating three to the real mean of the numbers 5, 7, as well as 9, which is 4, the number 21 becomes seven.
Here,
Two numbers are added together and their total is divided by two to determine the arithmetic mean of the numbers.
The arithmetic mean of the integers -12 and 7 is
=> {-12 + 7}/ {2}
=> {-5}/{2}
=> -2.5
As a result, -12 and 7 have an algebraic mean of -2.5.
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You are conducting a study testing whether depression symptoms are lower after participating in therapy compared to before. Given this information, complete the hypotheses in symbols:
Given this information, the complete hypotheses in symbols for the study is:
H0:μ_Post-μ_pre ≥ 0H0:μ_Post-μ_pre < 0What are the hypotheses symbol?In statistics, the null hypothesis is usually represented by the letter H with the subscript '0' (zero), as in H0. It's spelled H-null, H-zero, or H-nought. Simultaneously, the alternative hypothesis expresses the observations caused by the non-random cause. It is represented by the letters H1 or Ha.
The null and alternative hypotheses in symbols would be:
H0: μafter ≤ μbeforeHa: μafter < μbeforeNote: Where: H0 = null hypothesis, Ha = alternative hypothesis, μafter = population mean of depression symptoms after therapy and μbefore = population mean of depression symptoms before therapy
The null hypothesis states that the mean depression symptoms after therapy is less than or equal to the mean depression symptoms before therapy. The alternative hypothesis states that the mean depression symptoms after therapy is less than the mean depression symptoms before therapy.
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HELP HELP FAST FAST QUICK BRAINLIEST
Answer:
the answer is 2 pls mark me brainliest
Ingrum Corporation produces and sells two products. In the most recent month, Product R38T had sales of $33,000 and variable expenses of $8,840. Product X08S had sales of $54,000 and variable expenses of $32,050. The fixed expenses of the entire company were $36,130. The break-even point for the entire company is closest to:
Answer:
Therefore, the break-even point for the entire company is approximately 0.784 or 78.4%.
Step-by-step explanation:
To calculate the break-even point, we need to find the total contribution margin, which is the difference between the total sales revenue and total variable expenses.
For Product R38T, the contribution margin is $33,000 - $8,840 = $24,160.
For Product X08S, the contribution margin is $54,000 - $32,050 = $21,950.
The total contribution margin for both products is $24,160 + $21,950 = $46,110.
To calculate the break-even point, we divide the total fixed expenses by the total contribution margin:
Break-even point = Total fixed expenses / Total contribution margin
= $36,130 / $46,110
= 0.784
Therefore, the break-even point for the entire company is approximately 0.784 or 78.4%.
plot and label point Z
Answer: Sorry, I need more info.
Step-by-step explanation:
Can you please post the graph and the value of point Z? It's impossible to answer without this information. I'm sorry I couldn't help very well.
2.
3.5 in.
4 in.
6 in.
What is surface area
Given that three factors are given and the surface area is required, this means that we are dealing with a three-dimensional shape. Where the above is a rectangular prism, the surface area = 118 In².
What is the explanation for the above response?
Surface area is the measure of the total area that the surface of a three-dimensional object occupies.
To calculate the surface area of an object, you need to add up the areas of all its faces. The formula for finding the surface area of a rectangular prism, which has three pairs of congruent rectangular faces, is:
Surface area = 2(lw + lh + wh)
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
So, if we have a rectangular prism with the following dimensions:
Length (l) = 3.5 inches
Width (w) = 4 inches
Height (h) = 6 inches
The surface area can be calculated as follows:
Surface area = 2(lw + lh + wh)
= 2(3.5 x 4 + 3.5 x 6 + 4 x 6)
= 2(14 + 21 + 24)
= 2(59)
= 118In²
Therefore, the surface area of this rectangular prism is 118 In².
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Full Question:
Although part of your question is missing, you may be referring to this full question:
Given a rectangular prism with the following dimensions:
3.5 in.
4 in.
6 in.
What is surface area?
1. Determine if the polygons are similar. Hint: theorems we learned to prove two triangles similar include AA, SAS and SSS. Are the triangles similar (yes or no)? yes
Triangle with smaller triangle inside H R J S T K 10 6 4.8 8
Work or explanation:
Which theorem can you use to prove the two triangles similar? SAS
Yes triangles are similar.
SAS theorem is used to prove triangles are similar.
Define Side-Angle-Side Similarity Criteria, or SASThe SAS similarity theorem states that if any two sides of the first triangle are exactly proportional to any two sides of the second triangle and the angle created by these two individual triangles is identical, then the two triangles must be similar. When we only know the length of two sides and the angle produced between those two sides in each triangle, this rule is often implemented.
ΔRST and ΔHJK triangles are similar.
According to the SAS theory,
∠ S=∠J (angles are equal)
SR/HJ=ST/JK
6/10=4.8/8.6=.6( both sides are proportional)
Triangles ΔRST and ΔHJK are hence identical.
Two triangles can be compared using the Side-Angle Theorem.
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The area of a square frame is 55 square inches find the length of one side of the frame. explain
a. to the nearest whole inch
b. to the nearest tenth of an inch
Answer:
a. To the nearest whole inch:
To find the length of one side of the square frame, we need to take the square root of the area. So:
√(55) ≈ 7.4
Rounding 7.4 to the nearest whole inch, we get 7 inches. Therefore, the length of one side of the frame is 7 inches.
b. To the nearest tenth of an inch:
Again, we take the square root of the area:
√(55) ≈ 7.4161984
Rounding 7.4161984 to the nearest tenth of an inch, we get 7.4 inches. Therefore, the length of one side of the frame is 7.4 inches.
Step-by-step explanation:
In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer. m 4 + m 5 + m 6 = 180. 1 and 4 are alternate interior angles. m 5 = m 3 + m 2. m 5 + m 1 = 180.
m4 + m5 + m6 = 2m4 + m5 = 180, which proves that the interior angles of a triangle have a sum of 180 degrees.
What is interior angles of a triangle?Interior angles of a triangle are the angles formed inside a triangle at each of its vertices. The sum of these angles is always 180 degrees in a Euclidean plane.
This statement can be used because lines l and m are parallel, which means that m4 and m6 are corresponding angles and are congruent. This means that m4 = m6. Also, m5 and m4 are alternate interior angles, which means that they are congruent as well.
we can substitute m6 with m4 in the first equation to get:
m4 + m5 + m4 = 180
2m4 + m5 = 180
Therefore, the equation simplifies to:
2(180 - m5) + m5 = 180
360 - 2m5 + m5 = 180
m5 = 180 - 360 + 2m5
m5 = 2m5 - 180
m5 = 180
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Find the linear function with the following properties.
f(−7)=5
f(1)=2
Look at the picture below
The arc length is 2.2π
What is the centre angle?The central angle is an angle with twο arms and a vertex in the middle οf a circle. The twο arms οf the circle's twο radii intersect the circle's arc at twο different lοcatiοns. A circle can be divided intο sectοrs by using the central angle. A central angle might be fοund οn a pizza slice.
Given that the radius οf the circle is 18 inches.
The fοrmula circumference οf a circle is 2πr.
The circumference οf a circle is 2×π×18 =36 π inches.
The tοtal degree οfa circle is 360°.
The arc length with a central angle 360° is 36 π
Apply unitary methοd:
The arc length with a central angle 1° is 36 π/360°.
The arc length with a central angle 22° is (36 π×22°)/360° = 2.2π
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ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 how old is ngozi
The age of Ngozi if ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 is 3.68 years.
How old is Ngozi?Let
Ada age = x
Agnes age = 13 1/3x
Ngozi age = 2x
30 = x + 13 1/3x + 2x
30 = 3x + 40/3x
30 = 49/3x
divide both sides by 49/3
x = 30 ÷ 49/3
multiply by the reciprocal of 49/3
x = 30 × 3/49
x = 1.84 years
Ngozi age = 2x
= 2(1.84)
= 3.68 years
Therefore, Ngozi is 3.68 years old
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fill in the sentence below with the description that most specially applies to the quadrilateral below
The quadrilateral is most specifically a parallelogram because the opposite sides are parallel to each other
What is a parallelogram?
A parallelogram is a geometric shape with four sides, where opposite sides are parallel and congruent (having the same length), and opposite angles are also congruent (having the same measure).
In other words, a parallelogram is a quadrilateral (a polygon with four sides) where both pairs of opposite sides are parallel.
The opposite sides of a parallelogram are equal in length, and its diagonals bisect each other. The area of a parallelogram is equal to the product of its base (one of its sides) and its height (the perpendicular distance between the base and the opposite side).
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Seth's father is thinking of buying his son a six-month movie pass for $40.
With the pass, matinees cost only $1.00 each.
What is the slope and what does it mean in the context of this problem?
What is the y-intercept and what does it mean in the context of this
problem?
Answer:
The slope is 1. This is the cost of each matinee.
The y intercept is 40. This is the cost of the pass.
Step-by-step explanation:
Equation:
y = x + 40
y represent the total spend on seeing movies. Seth's dad pays a one time 40 fee and then 1 for each movie. The x represents the number of movies that he goes to see.
Examples:
His total cost if he goes to see one movie is
y = x + 40
y = 1 + 40
y = 41
His total cost if he goes to see 10 movies is
y = x + 40
y = 10+ 40
y = 50
His total cost if he goes to see 15 movies is
y = x + 40
y = 15 + 40
y = 55
Helping in the name of Jesus.