Carol, the band director, tracked how many minutes each saxophone player practiced last week. She found that Sven practiced for 30 minutes, Li Mihn practiced for 45 minutes, Wendy practiced for 90 minutes, Thomas practiced for 75 minutes, and Gabriel practiced for 60 minutes. Find the mean length of practice time.
The mean length of practice time will be equal to 60 minutes.
What is a mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Given data:-
She found that Sven practised for 30 minutes, Li Mihn practised for 45 minutes, Wendy practised for 90 minutes, Thomas practised for 75 minutes, and Gabriel practised for 60 minutes
The mean will be calculated as:-
M = ( 30+45+90+75+60) / 5
M = 60 minutes
Therefore mean length of practice time will be equal to 60 minutes.
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The graph below shows a system of equations:
The x-coordinate of the solution to the system of equations is _____
Answer:
the x-coordinate is 1 in the graph
Which property is illustrated in this equation?
32 • 15 = (3210) + (325)
A. Associative Property
B. Commutative Property
C. Distributive Property
D. Identity Property
Answer:
c)
Step-by-step explanation:
c). Distributive Property
32*15 = 32*(10+5) = 32*10 + 32*5
=320 + 160 = 480
Half of a number q is 14 written as a equation
Answer:
q/2=14
Step-by-step explanation:
Half of q is q/2
We know that it is 14
So, q/2=14
The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
This is solving quadratic word problems.
Answer:
The integers are
5 and 7
Step-by-step explanation:
Let
x ---> the first consecutive odd integer
x+2 ---> the second consecutive odd integer
we know that
The algebraic expression that represent this situation is
[tex]x(x+2)=x+30[/tex]
solve for x
[tex]x^2+2x=x+30\\x^2+2x-x-30=0\\x^2+x-30=0[/tex]
Solve the quadratic equation
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +x-30=0[/tex]
so
[tex]a=1\\b=1\\c=-30[/tex]
substitute in the formula
[tex]x=\frac{-1\pm\sqrt{1^{2}-4(1)(-30)}} {2(1)}[/tex]
[tex]x=\frac{-1\pm\sqrt{121}} {2}[/tex]
[tex]x=\frac{-1\pm11} {2}[/tex]
[tex]x=\frac{-1+11} {2}=5[/tex]
[tex]x=\frac{-1-11} {2}=-6[/tex] ---> is not a odd integer
For x=5
The numbers are
[tex]x=5\\x+2=7[/tex]
so
5 and 7
DIUILUUUUUUUUULIC POLL
8
Stephanie is paid $1898 per fortnight and Tahlia $3821 per month. Calculate each person's
equivalent annual income. Who earns more per week and by how much?
1
.
1
L
ol
Final answer:
Stephanie's annual income is $49,348, while Tahlia's is $45,852, making Stephanie's weekly earnings $67.61 higher than Tahlia's. Stephanie earns $949.38 per week, and Tahlia earns $881.77 per week.
Explanation:
To calculate each person's equivalent annual income, we must standardize their earnings to a common time frame. We consider a year to have 26 fortnights and 12 months.
Stephanie's Annual Income
Stephanie is paid every fortnight, so we multiply her fortnightly income by the number of fortnights in a year:
$1898 per fortnight x 26 fortnights per year = $49,348 per year.
Tahlia's Annual Income
Tahlia is paid monthly, so we multiply her monthly income by the number of months in a year:
$3821 per month x 12 months per year = $45,852 per year.
To determine who earns more per week, we divide the annual income by the number of weeks in a year (52). Stephanie earns $949.38 per week ($49,348 / 52), while Tahlia earns $881.77 per week ($45,852 / 52). Stephanie earns more per week by:
$949.38 - $881.77 = $67.61.
Therefore, Stephanie earns $67.61 more than Tahlia per week.
Four more than five times a number is two less than the number
make it into an algebraic expression
Answer:
4+5x<x
Step-by-step explanation:
four more than is saying addition so youd add the 4 and the 5x together. the less than is referring to the less than sign. and the number is referring to x.(;
What are the x-intercepts of the graph of the function below?
y= x2 + 2x-15
O A. (5,0) and (3,0)
O B. (-5,0) and (-3,0)
O C. (-50) and (3,0)
OD. (5,0) and (-3,0)
Answer:
C. (-5,0) and (3,0)
Step-by-step explanation:
y= x² + 2x-15
y = 0
x² + 2x-15 = 0
(x - 3) (x + 5) = 0
x = 3 or x = -5
The x-intercepts of the graph of the function are (-5,0) and (3,0).
Option C is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the x-intercepts of the graph of the function,
We need to set y = 0 and solve for x.
So we have:
x² + 2x - 15 = 0
Factoring this quadratic equation.
(x + 5) (x - 3) = 0
Setting each factor equal to zero.
x + 5 = 0 or x - 3 = 0
Solving for x.
x = -5 or x = 3
Therefore,
The x-intercepts of the graph of the function are (-5,0) and (3,0).
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Marcus has 824 marbles and wants to put marbles into 5 bags to give as gifts. Marcus knows he cannot divide the marbles evenly, but he wants to use as many of the marbles as possible, while making sure there is the same amount in each bag. How many marbles will be in each bag Please Explain.
Answer:
there will be 164 marbles in each bag
Step-by-step explanation:
The question is simply asking you to divide the total number of marbles by five; for each bag. 824/5= 164.8 and 164.8 rounded down; (underline means important), is 164 marbles.
Answer:
164
Step-by-step explanation:
carol invests 6250 at a rate of 2 per year compound interest calculate the total amount carol has after 3 years
Answer:
$6,632.55
Step-by-step explanation:
What a coincidence I was doing the same question. Ok so you should know about the Compound Interest formula which is A=P (1+r/100) n. (n) is btw in the exponent.
A= ?
P=6250
r=2
n=3
Anyways we will input everything we are given so it will be:
A=6250(1+2/100)3
Since A is final amount - it will be our answer which is $6,632.55
Final answer:
Carol invested $6,250 at a rate of 2% per year compound interest. After 3 years using the compound interest formula A = P(1 + r/n)^(nt), her investment will grow to $6,632.55.
Explanation:
Carol invested $6,250 at a rate of 2% per year compound interest. To calculate the total amount Carol has after 3 years, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (decimal). n is the number of times that interest is compounded per year. t is the time the money is invested for in years.
Since the interest is compounded yearly, n will be 1. Assuming the 2% interest rate is already in decimal form (0.02), and the time is 3 years, we substitute these values into the formula:
A = 6250(1 + 0.02/1)^(1*3)
A = 6250(1 + 0.02)^3
A = 6250(1.02)^3
A = 6250 * 1.061208
A = $6632.55
Therefore, after 3 years, Carol's investment will have grown to $6632.55.
In triangle ABC, angle C is a right angle. Find the value of the trig function indicated. Find tan A if c = 17 and a = 8
Answer:
Step-by-step explanation:
Final answer:
To find tan A in a right-angled triangle where the sides are given, first use Pythagoras' theorem to find the missing side, then apply the definition of tangent as the ratio of the opposite to the adjacent side, resulting in tan A = 1.875.
Explanation:
In triangle ABC, where angle C is a right angle, and we are given that c = 17 (hypotenuse) and a = 8 (adjacent to angle A), the task is to find tan A. Since we are dealing with a right-angled triangle, we can use Pythagoras' theorem to find the length of side b (opposite to angle A). The theorem states a² + b² = c². Given a = 8 and c = 17, we can find b:
b² = 17² - 8² = 289 - 64 = 225, thus b = 15.
The tangent of an angle in a right-angled triangle is given by the opposite side divided by the adjacent side. Therefore, tan A = b/a = 15/8. Hence, tan A for this triangle equals 1.875.
The weight, in pounds, of each wrestler on the high school wrestling team at the beginning of the season is listed below.
178 142 112 150 206 130
B. What is the mean weight of the wrestlers?
Answer:
(178+142+112+150+206+130) /6
HELPPPPPP asap
Which of these expressions can be used to calculate the monthly payment for
a 30-year loan for $195,000 at 6.6% interest, compounded monthly?
Answer:
$195P00*0.0055(1+0.0055)^360
____________________________
(1+0.0055)^360-1
Step-by-step explanation:
F(x)=12x+1
Find f(4)
f(4) is 49
Explanation:
Given:
f(x) = 12x + 1
f(4) = ?
we have to substitute the value of x = 4 in the given equation.
f(4) = 12 X 4 + 1
f(4) = 49
Whenever there is such type of question then we have to just put the value of x in the equation. In case of f '(4) then we have to differentiate the given equation with respect to x first and then substitute the value of x in the differentiated equation.
Therefore, f(4) is 49
How many values are in the range 35 to 95?
62
61
60
59
Answer:
Option B, 61
Step-by-step explanation:
Step 1: Find the range
To find the range, subtract the lowest number from the highest number.
Example: 1, 50
What is the highest number: 50
What is the lowest number: 1
50 - 1 = 49
Problem: 96, 35
What is the highest number: 96
What is the lowest number: 35
96 - 35
61
Answer: Option B, 61
Answer:
Only one value is in the range,
61
Step-by-step explanation:
Calculate range by subtracting the smaller value from the larger value
96 - 35 = 61
Only one of the given options corresponds with the solution of the range, which is 61, or the second option.
Hope this helps :)
Can you please show me what 56%/43% is?
Answer: 1.3
Step-by-step explanation:
Step 1: convert to decimal
56% = 56/100 = 0.56
43% = 43/100 = 0.43
Step 2; divide the values
0.56/0.43= 1.3
I hope this helps.
Tell whether the expression is positive or negative without evaluating.
1/12÷(−1/4)
Answer:
negative
Step-by-step explanation:
the answer will be negative because one fraction is negative and the other is positive. there is nothing to cancel out the negative sign
Which of the following best explains the value of sinä on the u
sual holnw?
Which is the largest: 27/30, 28/32, 38/40, 36/39, 75/85
What is -x^2 if x=-2
Answer:
-4
Step-by-step explanation:
plug in -2
-(-2)^2 = -4
4. You substitute the x with -2, which means the problem is -(-2^2).
At a store 30 pieces of candy cost a total of $2.40 each piece of candy cost the same amount what is the total cost of 4 pieces of candy
Answer:
0.32
Step-by-step explanation:
First you divide 2.40 by 30 and then it gives you the cost of each individual piece of candy.then you multiply 4 by that amount.
Example 1
The school district designed a district-wide end-of-course exam for math. Last year, 330 students took the exam. A random sample of exam scores, shown below, were chosen to represent the entire group.
85, 92, 65, 85, 65, 85, 77, 92, 92, 66, 77, 92, 77, 77, 65, 85
What is the median?
What is the mean?
What is the mode?
What is the range?
Answer:
Step-by-step explanation:
Mode=77&92&85 (mode is most common number)
Mean= 85+92+65+85+65+85+77+92+92+66+77+92+77+77+65+85=1277
1277/16=79.8 = 80 (Mean is add all numbers and divide how many there is.)
Range=92-65=27 (Range is highest number take away lowest number)
Median: 65,65,65,66,77,77,77,77,85,85,85,85,92,92,92,92
so median is 81 (put numbers in order and find the middle number. if order is even add two numbers in middle and divide by two. If order is odd, find ONE number.)
Final answer:
The median of the sample exam scores is 81, the mean (or average) is 75.75, the mode is bimodal with values 85 and 92, and the range is 27.
Explanation:
Measures of Central Tendency and Variability
To determine the median of the provided exam scores, we must first arrange the scores in ascending order and then find the middle value. With 16 scores, the median will be the average of the 8th and 9th values in this ordered list. For the mean, we add all the scores together and then divide by the total number of scores. The mode is the score that occurs most frequently. The range is calculated by subtracting the smallest score from the highest score.
Calculating the Median
Arranged Scores: 65, 65, 65, 66, 77, 77, 77, 77, 85, 85, 85, 85, 92, 92, 92, 92 Median: (77 + 85)/2 = 81Calculating the Mean
Sum of Scores = 85 + 92 + 65 + 85 + 65 + 85 + 77 + 92 + 92 + 66 + 77 + 92 + 77 + 77 + 65 + 85 = 1277 Mean: 1277 / 16 = 79.81Determining the Mode
The Mode: 77, 85 and 92Finding the Range
Range: 92 - 65 = 27What value does the 1 represent in the number 4,105.8
Answer:
100/Hundreds
Step-by-step explanation:
4 is the thousands -> 4000
1 is the hundreds -> 100
0 is the tens -> 0
5 is the ones -> 6
8 is the tenths -> 0.8
Answer: 100
Answer:
hundreds place
Step-by-step explanation:
When a number is 3 places to the left of the decimal, then it is in the hundreds place. Same thing if it is 3 places to the right of the decimal, only it'll be in the hundredths.
Josh decided to rent an SUV for a family trip he was planning. On the way
back from his trip, Josh rear-ended another vehicle. Unless he purchased
Josh will have to pay for damages to both vehicles out of his own
pocket.
A. uninsured motorist coverage
B. no-fault accident insurance
c. a collision damage waiver
D. relital-equipment insurance
a collision damage waiver
Josh have to use Collison Damage waiver.
What is Insurance?Managing your risk is possible with insurance. You purchase protection against unforeseen financial losses when you purchase insurance. If something unpleasant happens to you, the insurance company pays you or someone else of your choosing.
Collision damage waiver (CDW), often known as car rental insurance, releases a car renter from responsibility for all or some accident-related damage to a rental car.
If you are struck by a driver without auto insurance, you are protected by uninsured motorist coverage.
No fault insurance can assist in paying your medical costs and lost wages in the event of a covered accident, regardless of who was at fault.
So, Josh have to use Collison Damage waiver.
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Is area a function of the radius ? Is radius a function of area?
Answer: The area (A) of a circle is a function of its radius (r) and is given by the function A = f(r) = πr2.
Step-by-step explanation: google help
The area is a function of the radius and the radius is a function of the area.
Is the area a function of the radius?
For a circle of radius R, we can write the area as:
A = pi*R^2
So we can write the area in terms of the radius, meaning that yes, the area is a function of the radius of a circle.
Is the radius a function of the area?If we take the above equation and we isolate R, we get:
R = √(A/pi)
So you can also write the radius in terms of the area, meaning that the radius is also a function of the area.
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If f(x) =4x^2 + 1 and g(x) =x2 -5, find (f+g)(x)
The value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]
Explanation:
Given that the functions [tex]f(x)=4 x^{2}+1[/tex] and [tex]g(x)=x^{2}-5[/tex]
We need to determine the value of [tex](f+g)(x)[/tex]
The value of [tex](f+g)(x)[/tex] can be determined by substituting the value of [tex]f(x)[/tex] and [tex]g(x)[/tex] and simplifying the terms.
Thus, let us assign [tex]f(x)=4 x^{2}+1[/tex] in the function [tex](f+g)(x)[/tex], we have,
[tex]4 x^{2}+1+g(x)[/tex]
Now, let us assign [tex]g(x)=x^{2}-5[/tex] in the function [tex](f+g)(x)[/tex], we get,
[tex]4 x^{2}+1+x^{2}-5[/tex]
Grouping the like terms, we have,
[tex]4 x^{2}+x^{2}+1-5[/tex]
Adding the like terms, we get,
[tex]5 x^{2}-4[/tex]
Hence, the value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]
A weatherman collected data on snow accumulation. A line of best fit was computed. The equation for the line is: y = 1.5x + 0.125. Which BEST interprets the slope of the linear model?
A) The snow is accumulating at 1.5 inches every hour.
B) The snow is accumulating at 1 inch every 1.5 hours.
C) The snow is accumulating at 1 inch every 0.125 hours.
D) The snow is accumulating at 1.5 inches every 0.125 hours.
Answer:
Option A) The snow is accumulating at 1.5 inches every hour.
Step-by-step explanation:
The general form of the equation of the line is y = mx + c
where m is the slope or rate of change
For the given equation y = 1.5x + 0.125
Where y is The snow is accumulation and x is number of hours
So, comparing the given equation to the general form
∴ m = 1.5 which represents the The snow accumulation per hour
Which mean every one hour the snow accumulation is 1.5 inches.
According to the previous the answer is option A
A) The snow is accumulating at 1.5 inches every hour.
Answer:
The correct answer is A. The snow is accumulating at 1.5 inches every hour.
Step-by-step explanation:
Let's evaluate the given linear equation, this way:
y = 1.5x + 0.125, where:
y represents the total inches of snow accumulated after x hoursx represents the number of hours the weatherman collected data0.125 that represents the constant value, no matter how many hours the weatherman collects data, this value will not change at all1.5 that represents the ratio of change or slope in inches of snow accumulated every hourTherefore, options B, C, and D are not true. The correct answer is A. The snow is accumulating at 1.5 inches every hour.
A flower garden is shaped like a circle. Its diameter is 36 yd. A ring-shaped path goes around the garden. The width of the path is 5 yd.
The gardener is going to cover the path with sand. If one bag of sand can cover 4 yd", how many bags of sand does the gardener need? Note that sand comes
only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for n.)
Answer:
3
Step-by-step explanation:
subtract six hundred fifty three thousand from two million.
Answer:
2,000,000- 653,000= 1,347,000
Step-by-step explanation:
first write this in a equation with numbers
2,000,000- 653,000
million = 1,000,000
hundred thousand= 100,000
now solve the equation
2,000,000- 653,000= 1347000
Which equation represents a function?
OA) x = -2y2
OB) x = y2 - 9
OC) x2 + y2 = 1
OD) y= 3x2 + 2
The correct equation which represents a function is,
⇒ y= 3x² + 2.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
To find the correct equation which represents a function.
Now, We know that;
The equation that represents a function is option D,
⇒ y= 3x² + 2.
This is because for every value of x, there is a unique value of y.
In other words, each x value has only one corresponding y value.
And, The other options either have multiple outputs for the same input or do not qualify as a function for other reasons.
Thus, The correct equation which represents a function is,
⇒ y= 3x² + 2.
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