You invested 11000 in in 2st fund and 9000 in 2nd fund
Solution:Given that, You invested money in two funds.
Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.
This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500.
Let the amount in Fund I be $x and amount in Fund II be $ y
Then, for last year ⇒ 0.08x+0.05y=1330 ----- eqn (1)
And for this year ⇒ 0.12x+0.02y=1500 ------- eqn (2)
Multiply (1) by 2 ⇒ 0.16 x + 0.1 y = 2660
Multiply (2) by 5 ⇒ 0.6 x + 0.1 y = 7500
Subtract the two equations
(2) ⇒ 0.6x + 0.1y = 7500
(1) ⇒ 0.16x + 0.1y = 2660
(-) --------------------------------
0.44x + 0 = 4840
x = 11000
Now, from eqn (2)
0.12(11000) + 0.02y = 1500
0.02y = 1500 – 1320
0.02y = 180
y = 9000
Hence, he invested 11000 in in 2st fund and 9000 in 2nd fund
1. Two pieces of equipment were purchased for a total of $4000. If one piece cost $850 more fean
the other, find the price of the less expensive piece of equipment. Assume all data ze 2002
to two significant agits unless grezier 20curacy is given
Answer:
$1,575
Step-by-step explanation:
x = the cost of the less expensive piece of equipment
x+850 = the cost of the more expensive piece of equipment
x + (x+850) = 4,000 the. two pieces together cost 4,000, so I added up the cost of the less expensive piece and the more expensive piece, and equaled it to 4,000
solve the equation:
x + (x+850) = 4,000
2x+850=4,000
2x=3,150
÷2
x=1,575
What is the domain of the function shown in the mapping?
Input
Output
{x|x=-5, -3, 1, 2, 6}
{yl y = -9,6, 0, 2, 4}
{x|x = -9, -6, -5, -3,0, 1, 2, 4, 6}
{yly = -9, -6, -5, -3,0, 1, 2, 4, 6}
{x|x=-5, -3, 1, 2, 6} is the domain of the function shown in the mapping?.
Step-by-step explanation:
The function’s domain is the whole group of the possible values for the independent variables. Generally, this definition explains:
A domain is a group of all possible x values that cause a "function work" to perform true y values.
When finding your domain, pay attention to the following:
• The denominator (in bottom) must not be zero
• The number below the square root must be positive in the section.
From the given mapping figure, Domain: {x| x = -5, -3, 1, 2, 6}
What is the volume of this rectangular prism?
4.8 cm
4.1 cm
15 cm
Answer:
those are the dimentions
Step-by-step explanation:
If a figure has been dilated by a scale factor of 1/3, which transformation could be used to prove the figures are similar using the AA similarly postulate?
One batch of cookies requires the following ingredients:
2 1/3 cups of flour
3/4 of a cup of chocolate chips
2/5 of a cup of chopped almonds
1 1/2 cups of brown sugar
3/8 of a cup of white sugar
1/2 of a teaspoon of salt
Eric wishes to triple the recipe. How much of each ingredients should he use? Select all that apply
A) 6 1/3 cups of flour
B) 1/6 of a teaspoon of salt
C) 1 1/8 cups of white sugar
D) 9/12 cup of chocolate chips
E) 6/5 cups of chopped almonds
F) 2 1/2 cups of brown sugar
Answer:
it saids all that apply its A and what ????
Step-by-step explanation:
The correct options are:
(A) 6 (1/3) cup of flour
(E) 6/5 cups of chopped almonds.
Step-by-step explanation:
Given information:
One batch of cookies requires the ingredients:
2 (1/3) cup of flour.
3/4 of a cup of chocolate chips
2/5 of a cup of chopped almonds
1 (1/2) cup of brown sugar
3/8 of a cup of white sugar
1/2 of teaspoon of salt
Now if Eric wishes to triple the recipe, He needs to triple all the ingredients.
So the new list of ingredients will be triple of pervious one.
That will be:
6 (1/3) cup of flour
3 (3/4) cup of chocolate chips
3 (2/5) cup of chopped almonds
3 (1/2) cup of brown sugar
3 (3/8) cup of white sugar
3 (1/2) tea spoon of salt
So the correct options are:
(A) 6 (1/3) cup of flour
(E) 6/5 cups of chopped almonds.
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Evaluate n+2x2 when n=3 and x=−2.
Answer:
When n=3 and x=−2 the answer is 11.
Step-by-step explanation:
Given:
Let p (n,x) be the function such that
[tex]p (n,x) = n + 2x^{2}[/tex]
To Find:
p (n,x) = p ( 3, -2) = ?
Solution:
[tex]p (n,x) = n + 2x^{2}[/tex]
Substituting n = 3 and x = -2 we get
[tex]p (3, -2) = 3 + 2(-2)^{2}[/tex]
Negative square gives positive number therefore (-2)²=4
[tex]p (3, -2) = 3 + 2\times 4[/tex]
[tex]p (3, -2) = 3 + 8\\p (3, -2) = 11[/tex]
When n=3 and x=−2 the answer is 11.
Final answer:
When evaluating the expression n+2x^2 with n=3 and x=-2, we substitute the values to get 3 + 2(-2)^2, which simplifies to 3 + 8. The final evaluated expression is 11.
Explanation:
To evaluate the expression n+2x² with given values for n and x, we need to substitute the values into the expression and simplify it.
In this case, n = 3 and x = -2. Substituting these values in, we get:
3 + 2(-2)²
First, we calculate the square of -2:
3 + 2(4)
Now, we multiply 2 by 4:
3 + 8
Finally, we add 3 and 8 together:
11
Therefore, the evaluated expression is 11.
for the function below, state the x-coordinate of the x-intercept that is located to the left of the origin
f(x)=4x^3-12x^2 - x + 15
Answer:
The x-coordinate of the x-intercept that is located to the left of the origin is equal to -1
Step-by-step explanation:
we have the function
[tex]f(x)=4x^3-12x^2-x+15[/tex]
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
using a graphing tool
The function has three x-intercepts
The x-intercepts are the points
(-1,0),(1.5,0) and (2,5,0)
see the attached figure
The x-intercept that is located to the left of the origin is the point (-1,0)
therefore
The x-coordinate of the x-intercept that is located to the left of the origin is equal to -1
Answer:
The x-coordinate of the x-intercept is -1.
Step-by-step explanation:
Stephanie left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 56
miles per hour. Half an hour later, Tina left Riverside in her car on the same route as Stephanie, driving 70 miles per hour.
Solve the system
Answer:
2.5
Step-by-step explanation:
56(t+1/2)=70 t
56T + 28= 70T
28=70T-56T
28=14
2=T
s=T+ 1/2
S=2+ 1/2
S=2.5 hours
Tina traveled for 2 hours at a speed of 70 miles per hour, covering a distance of 140 miles.
Stephanie traveled for 2.5 hours at a speed of 56 miles per hour, also covering a distance of 140 miles.
What's the expression about?The distance traveled by a vehicle is given by the formula: distance = speed × time.
For Stephanie:
Distance_stephanie = Speed_stephanie × Time_stephanie
Distance_stephanie = 56 × (t + 0.5)
For Tina:
Distance_tina = Speed_tina × Time_tina
Distance_tina = 70 × t
Since both Stephanie and Tina are traveling the same route, the distances they travel should be equal:
Distance_stephanie = Distance_tina
Substitute the expressions for distances:
56 × (t + 0.5) = 70 × t
Now solve for "t":
56t + 28 = 70t
28 = 14t
t = 28 / 14
t = 2
So, Tina traveled for 2 hours.
Now we can find the distance traveled by both Stephanie and Tina:
Distance_tina = 70 × t
Distance_tina = 70 × 2
Distance_tina = 140 miles
Distance_stephanie = 56 × (t + 0.5)
Distance_stephanie = 56 × (2 + 0.5)
Distance_stephanie = 56 × 2.5
Distance_stephanie = 140 miles
Both Stephanie and Tina traveled a distance of 140 miles.
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Three consecutive integers have a sum of 132?
Answer:
43 , 44 ,45
Step-by-step explanation:
X + X + 1 + X + 2 = 132
3X + 3 = 132
3X = 132 - 3
3X = 129
X = 129/3
X = 43
so first number is 43.
second number will be 43 + 1 = 44
third number will be 43 + 2 = 45
The third angle of a triangle is the same size as the first. The second angle is 4 times the third. Find the measure of angles.
Answer:
1st angle 30°
2nd angle 120°
3rd angle 30°
Step-by-step explanation:
Let's call
A = 1st angle
B = 2nd angle
C = 3rd angle
In every triangle it holds
A + B + C = 180°
Now, if the third angle of the triangle is the same size as the first
A = C
If the second angle is 4 times the third
B = 4C
we have then
C + 4C + C = 180° ===> 6C = 180° ===> C = 30°
If C = 30° then A = 30° and B = 120°
what are associative on rational numbers
Answer:yo7 can add or multiply numbers regardless how they are grouped
Step-by-step explanation:
What is the area of the triangle with a base of 5 1/2 cm and a height of 3 1/2 cm?
Answer:
9.63
Step-by-step explanation:
Estimate the size of a crowd walking in a charity fundraising march that occupies a rectangular space with dimensions of 10 feet by 1,200 feet (to the nearest whole number). Assume that 40 people occupy a rectangle measuring 10 feet by 12 feet.
Answer:
4000 is size of a crowd walking in a charity fundraising March.
Step-by-step explanation:
Given:
Dimensions of rectangular space 10 feet by 12000 feet
So we can say that,
Length = 1200 ft
Width = 10 ft
Now we will calculate the area of rectangular space which is given by
Hence Area will be = [tex]length\times width= 10\ ft \times 1200 \ ft= 12000 \ ft^2[/tex]
Now we know that 40 people occupy a rectangle measuring 10 feet by 12 feet.
Length = 12 ft
Width = 10 ft
Area = [tex]length\times width= 10\ ft \times 12 \ ft= 120 \ ft^2[/tex]
It says that 40 people are occupied in 120 [tex]ft^2[/tex]
So how many people will be there in 12000 [tex]ft^2[/tex]
By using unitary method we get,
Number of people = [tex]\frac{40\times 12000 \ ft^2}{120 \ ft^2} = 4000 \ peoples[/tex]
Size of a crowd walking in a charity fundraising March is 4000.
Answer:
4,000 people
Step-by-step explanation:
49 people occupy 120 ft^2
Dimensions of crowd: 10×1,200=12,000
120 ft^2/40 people = 12,000 ft^2/x people
X=4,000
What minus -4 2/3 equals a positive number
Answer:-4 2/3
Step-by-step explanation: negative number minus itself will always be positive.
Mary and Lamar establish a tutoring service at a local mall. They tutor college students in math and English. They charge $40 per hour for tutoring. In the month of January they charged for 200 tutoring hours. The expenses of their business are given in the table below. Expense Amount/Month Rent of Space $4000 Electricity $325 Advertising $375 Using the formula Profit = $40(number of hours) – (expenses) , calculate their profit for the month of January.
The profit is $3300 for the month of January.
Step-by-step explanation:
Per hour charge = $40
Total number of tutoring hours = 200
Rent of space = $4000
Electricity = $325
Advertising = $375
Total expenses = 4000+325+375 = $4700
Profit = $40(number of hours) - (expenses)
[tex]Profit=\$40(200)-4700\\Profit=\$8000-4700\\Profit=\$3300[/tex]
The profit is $3300 for the month of January.
Keywords: profit, addition
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In a recent poll, 370 people were asked if they liked dogs, and 7% said they did. Find the margin of error of this poll, at the 90% confidence level. Give your answer to three decimals.
Answer:
[tex] ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218[/tex]
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]p[/tex] represent the real population proportion of interest
[tex]\hat p=0.07[/tex] represent the estimated proportion for the sample
n=370 is the sample size required (variable of interest)
[tex]z[/tex] represent the critical value for the margin of error
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.10[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And replacing into formula (a) the values provided we got:
[tex] ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218[/tex]
The margin of error on this case would be ME=0.0218
Tommy's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 51 regular sodas and 34 diet sodas. What percentage of the sodas served were regular?
Answer:
60%
Step-by-step explanation:
51+34=85
51/84= 0.60 or 60%
PLEASE HELP QUICKLY 25 POINTS
What is the common difference,d,of the sequence ?
-92,-74,-54,-38,-20
Enter your answer in the box
D = [ ]
Answer:
+18
Step-by-step explanation:
A = {1, 2, 5, 7} B = {3, 4, 6, 7} C = {0, 5, 8, 9} Find A U B U C. A) {0,1,2,3,4,5,6,7,8,9} B) {1,2,3,4,5,6,7} C) {3,4,5,6,7} D) {3,4,7}
A) {0,1,2,3,4,5,6,7,8,9} is the right answer
Step-by-step explanation:
Given
A = {1, 2, 5, 7}
B = {3, 4, 6, 7}
C = {0, 5, 8, 9}
We hvae to find the union of all thre sets. In union, the elements of involved sets are combined. The repating elements are only written once
So,
[tex]AUBUC = \{1, 2, 5, 7\}U\{3, 4, 6, 7\}U\{0, 5, 8, 9\}\\= \{0,1,2,3,4,5,6,7,8,9\}[/tex]
Hence,
A) {0,1,2,3,4,5,6,7,8,9} is the right answer
Keywords: Sets, Union
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Select the equation of the line that passes through the point (3, 5) and is
perpendicular to the line x= 4
O 1) y = 5
O2)x= 5
O3) y = 4
O4) x = 3
Answer:
1) y = 5Step-by-step explanation:
x = 4 it's a vertical line.
Perpendicular line to a vertical line is a horizontal line.
A horizontal line has equation y = a.
A horizontal line passes through the point (3, 5) → x = 3 and y = 5.
Therefore the equation is y = 5
Justin opens a savings account with $4. He saves $2 each week. Does a linear function or a nonlinear function represent this situation? Explain.
Yes , the situation can be represented by a linear function where the equation is A = 2x + 4 where x is the number of weeks
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
The initial amount in Justin's savings account = $ 4
The amount saved by Justin every week = $ 2
Let the number of weeks be = x
So , the amount saved by Justin in x weeks = 2x
Now , the total amount saved by Justin in savings account A = initial amount in Justin's savings account + amount saved by Justin in x weeks
Substituting the values in the equation , we get
A = 4 + 2x
On simplifying the equation , we get
A = 2x + 4
which is of the form of a linear equation of line
Hence , the linear equation is A = 2x + 4 , where x is the number of weeks
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What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?
y+1=4(x+3)
y−1=4(x−3)
y+3=4(x+1)
y−3=4(x−1)
Answer:
y + 3 = 4(x + 1)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 4 and (a, b) = (- 1, - 3), thus
y - (- 3) = 4(x - (- 1)), that is
y + 3 = 4(x + 1)
Answer:
its C can i have
Step-by-step explanation:
P(A) = 8/15
P(B) = 6/15
P(A n B) = 1/5
Find P(AUB)
A. 2/15
B. 11/15
C. 1/15
D. 4/15
Answer:
Step-by-step explanation:
note : P(AUB) = p(A)+p(B) - p(A∩B)
P(AUB) = 8/15+6/15- 1/5 = 8/15+6/15-3/15 = 11/15 answer : B
Probability helps us to know the chances of an event occurring. The correct option is B.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that P(A) = 8/15, P(B) = 6/15, and P(A n B) = 1/5. Therefore, the value of P(AUB) will be,
P(AUB) = P(A) + P(B) + P(A n B)
= 8/15 + 6/15 - 1/5
= 11/15
Hence, the correct option is B.
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sec squared 55 - tan squared 55
Answer:
sec squared 55 – tan squared 55 = 1
Explanation:
Given, sec square 55 – tan squared 55
We know that,
[tex]\sec \Theta=\frac{\text {hypotenuse}}{\text {base}}[/tex]
And,
[tex]\tan \theta=\frac{\text { perpendicular }}{\text { base }}[/tex]
where Ө is the angle
Substituting the values
[tex]\left(\frac{\text {hypotenuse}}{\text {base}}\right)^{2}-\left(\frac{\text { perpendicular }}{\text {base}}\right)^{2}[/tex]
Solving,
[tex]\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}[/tex]
According to Pythagoras theorem,
[tex]\text { (hypotenuse) }^{2}-\text { (perpendicular) }^{2}=(\text { base })^{2}[/tex]
Putting this in the equation;
squared 55 - tan squared 55 =
[tex]\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}=\frac{(\text {base})^{2}}{(\text {base}) *(\text {base})}=1[/tex]
Therefore, sec squared 55 – tan squared 55 = 1
The value is always 1.
To solve the expression sec²(55°) - tan²(55°), we can use a trigonometric identity. Recall the Pythagorean identity for tangent and secant:
sec²(θ) - tan²(θ) = 1
Using this identity, we substitute θ with 55°:
sec²(55°) - tan²(55°) = 1This simplifies our expression immediately, as the value is always 1 regardless of the angle, as long as the identity holds.
So, sec²(55°) - tan²(55°) = 1.
A rational function is a function whose equation contains a rational
expression.
A. True
B. False
Answer:
True
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
in a sale normal prices are reduced by 10% nathelie bought a pair of shoes in the sale for £54 what was the original price of the shoes
Answer:
Step-by-step explanation:
10% of £54=£5.4 (price reduced by 10%)
Normal price should be £5.4 +£54= £59.4
Hey! How are you? My name is Maria, 19 years old. Yesterday broke up with a guy, looking for casual sex.
Write me here and I will give you my phone number - *pofsex.com*
My nickname - Lovely
How many pounds of ground beef are needed to make 80 hamburger patties if each uncooked patty weighs 4.8 ounces?
A
10.4 pounds
B
24 pounds
C
61.4 pounds
D
96 pounds
The right answer is Option B.
Step-by-step explanation:
Beef per patty = 4.8 ounces
Number of hamburgers = 80
Beef required = Number of hamburgers * beef per patty
Beef required = [tex]80*4.8 = 384 \ ounces[/tex]
As we know,
16 ounces = 1 pound
1 ounce = [tex]\frac{1}{16} \ pounds[/tex]
384 ounces = [tex]\frac{1}{16}*384[/tex]
384 ounces = 24 pounds
24 pounds of beef is required to make 80 hamburger patties.
The right answer is Option B.
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Solve the system of linear equations. 2x + 5y = 12 4x − y = 2
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
2x+5y=12
4x-y=2
--------------
y=4x-2
2x+5(4x-2)=12
2x+20x-10=12
22x-10=12
22x=12+10
22x=22
x=22/22
x=1
4(1)-y=2
4-y=2
y=4-2=2
y=2
Answer:
x = 1, y = 2 → (1, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+5y=12\\4x-y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+5y=12\\20x-5y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad22x=22\qquad\text{divide both sides by 22}\\.\qquad x=1\\\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\4(1)-y=2\\4-y=2\qquad\text{subtract 4 from both sides}\\-y=-2\qquad\text{change the signs}\\y=2[/tex]
Marco needs $57 to buy new basketball shoes. If Marco earns $3 per day working and already has $12 saved, which equation shows how many days Marco must work before he can afford the shoes?
Answer:
3x+12=57
x= how many days
Step-by-step explanation:
Answer:
[tex]3x+12=57[/tex]
Step-by-step explanation:
Let x represent number of days.
We have been given that Marco earns $3 per day working. So amount earned in x days would be [tex]3x[/tex].
We are also told that Marco already has $12 saved, so total amount saved by Marco in x days would be [tex]3x+12[/tex].
Now we will equate total amount saved by Marco in x days with 57 as Marco needs to save $57 to buy new shoes.
[tex]3x+12=57[/tex]
Therefore, the equation [tex]3x+12=57[/tex] shows the number of days (x) that Marco must work before he can afford the shoes.
The circumference of a circle is 15 ft. What is the length of the radius? Use 3.14 for π. Round your answer to the nearest tenth of a foot.
Answer:
The radius of the circle is 2.4ft
Step-by-step explanation:
circumference of circle = 2πr
circumference = 15ft
2πr = 15
(2×3.14)r = 15
6.28r = 15
r = 2.4ft (near. tenth)
Answer:
The answer is 2.4 ft.
Step-by-step explanation:
C= 2πr
15= 2(3.14)r
15= 6.28r
15÷6.28= 6.28r÷ 6.28
2.4= r