Answer:
$10,000 invested at 5%
$20,000 invested at 8%
Step-by-step explanation:
1. Let x = the amount of money invested at 5%, and y = the amount of money invested at 8%.
x + y = 30,000 (the total amount invested)
0.05x + 0.08y = 2,100 (the total interest earned)
2. Solve the system by whatever method you choose.
The expression 43πr3 represents the volume of a sphere, with radius r. Why is this expression a monomial?
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
It is the product of a number, represented by Response area, and a variable with a whole number exponent, represented by Response area.
Question 2
What is the degree of the monomial?
The degree is
.
Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
WE have been given an expression as 43πr³ represents the volume of a sphere, with radius r.
Terms can be added or subtracted to make a polynomial. They are composed of variables and constants all in multiplication.
So we know that if there is one term, then the polynomial will be called monomial.
Therefore, this expression is a monomial which have inly one term as 43πr³ .
Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.
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Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form or standard form. Express numbers as integers or
simplified fractions.
The line contains the point (-3, 6) and is parallel to 3x+3y=2.
The equation of the line is
The equation of the line is : y = -1x + 3
What is Equation of line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
Given,
3x + 3y = 2
3y = -3x + 2
y = -x + 2/3
Comparing it with
y = mx + c
we get,
m = -1
Now, let the equation of line be
y = mx + c
where, m = -1
Now we have to check for point (0,0) that it satisfies
0 = -1(0) + c
c = 0
So, the equation of line will be y = -1x
Now, let y = mx + c be the equation of line of point (-3, 6) should satisfy]
6 = -1(-3) + c
6 = 3 + c
c = 6 - 3
c = 3
So the equation of line is y = -1x + 3
Hence, The equation of the line is y = -1x + 3
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations that have the same solution?Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.
Using this given property, let's write the equation
We can subtract like terms (6.5p– 0.01p = 6.49p) to get:
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Also, we can multiply both sides of the algebraic equation by 100:
(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100
230p – 1010 = 650p – 400 – p
Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers
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A restaurant manager recorded the number of people in different age groups who attended their food festival. They created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79, and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
What percentage of the participants are ages 40 to 59? Round to the nearest whole percent.
20%
35%
60%
100%
According to the histogram, the percentage of participants aged 40 to 59, who attended the restaurant's food festival, is 35%.
What is a histogram?A histogram approximately represents a distribution of grouped data with numerical values.
A histogram uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.
Age Group (year) Number of People
0 to 19 20
20 to 39 40
40 to 59 60
60 to 79 50
Total 170
Percentage of ages 40 to 59 = 60/170 x 100 = 35.29%
Thus, using the histogram, we can assure the restaurant manager that 35% of the festival participants are between 40 and 59 years old.
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Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log4 (6(5 + 2x)). Make sure
to use parenthesis around your logarithm functions log(x + y).
[tex]log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)[/tex] is the completely expanded logarithmic expression .
What are logarithms ?Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.
The most common types of logarithms are the base 10 common logarithm, the base 2 binary logarithm, and the base e ≈ 2.71828 natural logarithm.
Calculationsthe product rule for logarithms is
[tex]log_{b}(MN) = log_{b}(M) + log_{b}(N)[/tex] for b > 0
now ,
[tex]log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)[/tex]
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Gotta answer this quick this is timed please
Answer:
Step 1:subtract 5 from both sides
step 2: divide both sides by two
final answer: c= p-5/2
Answer:
Step 1: Subtract 5 from both sides.
Step 2: Divide 2 from both sides.
Final answer: C= p-5 / 2
Step-by-step explanation:
If WX equals to XY , what is the length of WZ?
Answer:
the length of WZ is 10
Step-by-step explanation:
What is the asymptote of the exponential function graph below?
y=1
y=5
y=2
y=0
Answer: y=5 is the asymptote answer
1.25x10^-3/1.25x10^3
By solving the given fraction equation we get the answer is 1.
What is an exponent?
Exponent is the process of expressing large numbers in terms of powers. In other words, the exponent describes how many times a number has been multiplied by itself.
According to the zero exponent rule, any base with a zero exponent is equal to one. For instance, [tex]x^{0} = 1[/tex].
We have,
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\ * \\ 10^{-3}}[/tex]
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\} * 10^{3}[/tex]
Using the multiplication rule of fraction [tex]a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]= \frac{1.25 \ * \ 10^{-3} \ * \ 10^{3}}{1.25 \\}[/tex]
= [tex]= 10^{-3} * 10^{3}[/tex]
By applying the exponent rule [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] we get,
Add or subtract the numbers = 3 + 3 = 0
[tex]= 10^{0}[/tex]
By applying the rule [tex]a^{0} = 1[/tex], [tex]a \neq e^{0}[/tex]
= 1
Hence, by solving the above fraction equation we get the answer is 1.
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What is the expression 9-z when z=8
A rectangular box is 12 in. x 14 in. x 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in
terms of pi.
The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²
The surface area of sphere = 324π inches²
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the surface area of the Sphere be = S
Let the dimensions of the rectangular box be L x W x H
12 inches x 14 inches x 18 inches
Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum
From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere
So , Height of the Box = Diameter of the Sphere
And , Radius of the sphere = Height of the Box / 2
= 18 / 2
Radius of the sphere = 9 inches
Now ,
Surface Area of a Sphere = 4πr²
r = 9 inches
Substituting the values in the equation , we get
Surface Area of a Sphere S = 4 x π x ( 9 )²
= 4 x π x 81
= 324π inches²
Therefore , the value of S is 324π inches²
Hence , The surface area of sphere = 324π inches²
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Please help ASAP
See Attached!!
When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.
When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.
The answers:
a) False, degrees not added,b) False, degrees added but not multiplied.Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit is y=25+22x .
The independent variable x is the hour of work.
The dependent variable y is the total money Ethan earn per visit.
The y-intercept is 25.
The slope is 22.
Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.
How to solve linear equations?Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work.
A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 22x.
Using slope intercept equation,
y = mx + b
where
m = slopeb = y-intercepty = 25 + 22x
The independent variable x is the hour of work.
The dependent variable y is the total money Ethan earn per visit.
The y-intercept is the value of y when x = 0. Therefore, the y-intercept is 25.
The slope is the change in the dependent variable with respect to the change in the independent variable. The slope is 22.
Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.
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Help pls I need a fraction answer
7 4/10 + 2/10 =
Answer: 7 4/10 + 2/10 = 38/5 = 7 3/5 = 7.6
Answer Overall : 38/5
Step-by-step explanation: Conversion a mixed number 7 4/10 to a improper fraction: 7 4/10 = 7 4/10 = 7 · 10 + 4/10= 70 + 4/10= 74/10
To find a new numerator:
a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10
b) Add the answer from previous step 70 to the numerator 4. New numerator is 70 + 4 = 74
c) Write a previous answer (new numerator 74) over the denominator 10.
Seven and four tenths is seventy-four tenths
Add: 74/10 + 2/10 = 74 + 2/10 = 76/10 = 2 · 38/2 · 5 = 38/5
The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 38/5.
In other words - seventy-four tenths plus two tenths is thirty-eight fifths.
First convert the mixed number to a fraction by multiplying 7 by 10 and adding 4
74/10+2/10add them together but DONT add the denominators
76/10These numbers can be simplified by 2 so the final answer is:
38/5To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
a. Write an expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs.
An expression is (?) dollars.
Question 2
b. What does the coefficient of the expression in part (a) represent?
Responses
the total cost (in dollars) of adopting one dog
the total cost (in dollars) of adopting one dog
the total amount (in dollars) the veterinarian is paid when one dog is adopted
the total amount, (in dollars), the veterinarian is paid when one dog is adopted
the total cost (in dollars) of adopting x dogs
the total cost (i, n dollars), of adopting x dogs
the total amount (in dollars) the animal shelter earns when x dogs are adopted
the total amount (, in dollars) the animal shelter earns when , x, dogs are adopted
please and thank you!
Answer:$190
Step-by-step explanation:
for an expression is $80+$65+$50=190 per dog to adopt a from the animal shelter.
Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. Their investments are in the ratio
1:2:0.5, respectively.
How much has Zach invested, in dollars?
Enter your answer in the space provided.
Zach's investment is $100,000.
A ratio shows us the number of times a number contains another number.
Given that Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. And their investments are in the ratio 1:2:0.5, respectively.
Therefore, Zach, Kolby, and Peyton's investment can be written as 1x, 2x, and 0.5x, respectively.
Now, the total sum of the investment of the three can be written as,
Zach's investment + Kolby's investment + Peyton's investment = $350,000
1x + 2x + 0.5x = $350,000
3.5x = $350,000
x = $350,000 / 3.5
x = 100,000
Further, Zach's investment can be written as,
Zach's investment = 1x = 1($100,000) = $100,000
Hence, Zach's investment is $100,000.
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Lee Holmes deposited $17,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $42,000 at 9% interest compounded semiannually.
At the end of 6 years, what is the balance in Lee’s account? (Use the Table provided.)
The balance in Lee's account at the end of 6 years is $384,830.53.
What is the balance?The first step is to determine the future value of the initial amount deposited in the savings account.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate = 9% / 2 = 4.50%m = number of compoundingN = number of yearsBalance at the end of 3 years: $17,000 x (1.045)^(3 x2) = $22,138.42
The total value of the account after $42,000 is deposited is:
$42,000 + $22,138.42 = $64,138.42
The future value of $64,138.42 at the end of 6 years is:
Balance at the end of 6 years: $64,138.42 x (1.045)^(3 x2) = $384,830.53
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i need some help on these, can anybody help me?
A laundromat has a wash-and-fold service for a monthly fee of $28.00. The laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service. One customer paid $41.42 in total for the month.
Which equation can be used to determine the pounds of laundry the customer brought in to be washed and folded that month?
A. 0.61x + 28.00 = 41.42
B. 0.61x + 41.42 = 28.00
C. 28.00 - 0.61x = 41.42
D. 41.42 + 28.00 = 0.61x
The required equation can be used to determine the pounds of laundry the customer brought in is A. 0.61x + 28.00 = 41.42
What is an equation?An equation is a mathematical expression that shows the relationship between two variables.
How to find equation can be used to determine the pounds of laundry the customer brought in to be washed and folded that month?To find the given equation,
Let x be the number of pounds of clothes washed and folded at the laundromat.
Given that the laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service, the total amount paid for the number of poundsof clothes is P = rate × number of pounds = $0.61 × x = 0.61x
Also, the laundromat has a wash-and-fold service for a monthly fee of $28.00.
So, the total amount paid is T = P + $28.00 = $0.61x + $28.00
Now, since one customer paid $41.42 in total for the month, since this is the total amount paid, then T = $41.42
So, $0.61x + $28.00 = $41.42
So, the required equation is A. 0.61x + 28.00 = 41.42
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This is just a question but. if I had a power of ten that was let's say.... 10 3 would i write it like 10000 or 1000?
Answer:
10^3 = 1000
Step-by-step explanation:
10 * 10 * 10 = 1000
Answer:
1000
Step-by-step explanation:
it is ten to the third power so 10*10*10 and then you get the answer of:
1000
I hope this helped!
need help asap please
Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. Jada gets if she allows s to take on any value between 0 and 7.5.
The domain of the function that represents Jada's trip is the set of input value the function can take
The appropriate domain is all real numbers except
x = 5.5
by looking at the graph, we can see that:
The x-value starts at negative infinity, and ends near 5.5
The x-value then continues near 5.5, and ends at positive infinity
This means that the input of the graph cannot be 5.5
Hence, an appropriate domain would be: x # 5.5
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Give the answer and an explanation
A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° .
The given right-angle triangle has the following sides,
AC = Base
BC = Perpendicular
AB = Hyp.
By tan function,
Since,tanθ = Perp/Base
tan29° = 28/x
x = 50.51
Hence, "A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51".
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adult tickets
A total of 390 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times ti
number of adult tickets sold. How many adult tickets were sold?
The number of adult tickets were sold is 130 tickets.
Given,
In the question:
Total tickets were sold for the school play is 390 tickets.
The number of student tickets sold was two times number of adult tickets sold.
To find the how many adult tickets were sold?
Now, According to the question:
Based on the given conditions:
Let the number of adult tickets be x.
Formulate the condition:
x × (1 + 2) = 390
x × 3 = 390
Simplify
x = 390/3
x = 130
Hence, The number of adult tickets were sold is 130 tickets.
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A teacher runs each morning before school. Last week, he ran a total of 5 3/4 miles. This week, he ran 4/5 of the total number of miles he ran last week. What is the total number of miles that the teacher ran last week and this week?
The total number of miles that the teacher ran both last week and this week was 10.35 miles
How to find the total number of miles?Last week, the teacher ran a total of 5 3/4 miles. For easier calculation, convert this to a decimal:
= 5 + 3/4
= 5 + 3 ÷ 4
= 5 + 0.75
= 5.75 miles
This week, the teacher ran 4 / 5 of the miles he ran the previous week:
= 5. 75 x 4/5
= 4.6 miles
The total number of miles the teacher ran both last week and this week were:
= 5.75 + 4.6
= 10.35 miles
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Answer:
10 7/20 miles
Step-by-step explanation:
Mr.Marx has been in the journalism industry for 24 years. She has worked at her current job 8 of those years. What fraction of her career has she been at her current job? What is this fraction as a decimal?
Fraction of her career has she been at her current job is 1/3 or 0.333.
Given:
Mr.Marx has been in the journalism industry for 24 years.
She has worked at her current job 8 of those years.
Fraction = number of year in current job/number of years in journalism industry.
= 8 years/24 years
= 8/24
= 1/3 ≈ 0.333.
Therefore fraction of her career has she been at her current job is 1/3 or 0.333.
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please answer 25 points
The number of miles (m) between the two cities as represented in the equation given 2[(4m * 3.5) / 400] = 171.5 is 2450 miles
EquationsThe definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
In the equation given;
2[(4m * 3.5) / 400] = 171.5
Using changing the subject of formula to find the miles travelled;
2[(4m * 3.5) / 400] = 171.5
28m / 400 = 171.5
28m = 400 * 171.5
28m = 68600
m = 68600 / 28
m = 2450
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NO LINKS!! Please help me with these graphs Part 2a
Answer:
Left graph.
Domain: all real numbers.
Range: y ≤ 4
Middle graph.
Domain: all real numbers
Range: y ≥ 3
Right graph.
Domain: x ≥ -2
Range: y ≥ -3
Answer:
1. Domain: (-∞, ∞) Range: (-∞, 4]
2. Domain: (-∞, ∞) Range: [3, ∞)
3. Domain: [-2, ∞) Range: [-3, ∞)
Step-by-step explanation:
Definitions
Domain: The set of all possible input values (x-values).Range: The set of all possible output values (y-values).Open circle: The value is not included in the interval.Closed circle: The value is included in the interval.Arrow: The function continues indefinitely in that direction.Note: Assume that each square on the given graphs is 1 unit.
Question 1As there are arrows at both endpoints of the curve, the domain of the function is unrestricted.
Domain: (-∞, ∞)The curve has a maximum point at (2, 4) and continues indefinitely towards negative infinity at both endpoints.
Therefore, the range of the function is restricted.
Range: (-∞, 4]Question 2As there are arrows at both endpoints of the function, the domain is unrestricted.
Domain: (-∞, ∞)The function has a minimum point at y = 3.
When x > -2, the line continues indefinitely at y = 3.
When x < -2, the line continues indefinitely towards infinity.
Therefore, the range of the function is restricted.
Range: [3, ∞)Question 3The domain of the function is restricted since there is a closed circle at one endpoint: (-2, -3). When x > -2, the line continues indefinitely towards infinity.
Domain: [-2, ∞)The function has a minimum point at (-2, -3). As x continues towards infinity, so does y.
Therefore, the range of the function is restricted.
Range: [-3, ∞)What is 9.65+0.4, 16.058- 1.2
Answer:
Step-by-step explanation:
9.65+0.4=10.05
16.058-1.2=14.858
Find the rate if a principal of $1,100 earned $1,089 interest in 12 years.
Answer:
8.25
Step-by-step explanation:
ERROR ANALYSIS Describe and correct the error in finding m<1
Answer:
m∠1 = 26°
Step-by-step explanation:
Interior angles of a triangle sum to 180°, not 360°.
Therefore, the correct calculations to find the measure of angle 1 are:
[tex]\boxed{\begin{aligned}115^{\circ}+39^{\circ}+m \angle 1 &=180^{\circ}\\\\154^{\circ}+m \angle1 & = 180^{\circ}\\\\m \angle1 & = 26^{\circ}\end{aligned}}[/tex]