Answer:
9.00
Step-by-step explanation:
Use proportion:-
20% is equivalent to 1.80
1% is equivalent to 1.80 / 20
100% is equivalent to (1.80 / 20 ) * 100
= 180 / 20
= 9
= 9.00
If a matrix does NOT have an inverse, what do you know about the determinant?
A) The determinant does not exist.
B) The determinant is 0.
C) The determinant is 1.
D) The determinant is -1.
A class of 25 students took a math test. Ten students had an average of 88. The other students had an average of 76. What is the average of the whole class?
A) 78.2
B) 80.8
C) 81.7
D) 82.5
The answer is B. 80.8
Answer:
The average of the whole class is 80.8.
The correct answer is B)
Step-by-step explanation:
To solve this problem, it is very important to understand the phrase: "Ten students had an average of 88". Let's see an example.
Imagine that three students in the class took a test and their scores were: 80, 89 and 95. To calculate the average of they three we must divide the sum of the scores by the total number of scores.
[tex]average=\frac{80+89+95}{3}=\frac{264}{3}=88[/tex]
The previous value is the average of the three students. Now, if we say that each student got 88, the average would be 88.
[tex]average=\frac{88+88+88}{3}=\frac{264}{3}=88[/tex]
The previous expression could be simplified as:
[tex]average=\frac{88\times 3}{3}[/tex]
Where, the number 3 means the number of students.
With that in mind, the phrase "Ten students had an average of 88" could be written as:
[tex]average_{10\, \, students}=\frac{88+88+88+88+88+88+88+88+88+88}{10}[/tex]
[tex]average_{10\, \, students}=\frac{88\times 10}{10}=88[/tex]
On the other hand, the phrase "The other students had an average of 76" means that from the 25 students, 15 students got 76 (25 - 10 = 15), and could be written as:
[tex]average_{15\, \, students}=\frac{76+76+76+76+76+76+76+76+76+76+76+76+76+76+76}{15}[/tex]
[tex]average_{15\, \, students}=\frac{76\times 15}{15}=76[/tex]
Finally, to calculate the total average of the 25 students we must divide the sum of the scores of all students by the total number of scores. The sum would be: 88+88+88+88+88+88+88+88+88+88+76+76+76+76+76+76+76+76+76+76+76+76+76+76+76, which equals [tex]88\times 10+76\times 15[/tex]. The total number of scores would be: 25.
[tex]average_{total}=\frac{88\times 10 + 76\times 15}{25}[/tex]
[tex]average_{total}=\frac{880 + 1140}{25}[/tex]
[tex]average_{total}=\frac{880 + 1140}{25}[/tex]
[tex]average_{total}=\frac{2020}{25}[/tex]
[tex]average_{total}=80.8[/tex]
Thus, the average of the whole class is 80.8. The correct answer is B)
The sum of two numbers is 96. The difference of the same two numbers is 8. What is the larger number?
Answer:
The larger number is 52.
Step-by-step explanation:
To find this number, we have to create a statement for both of the equations that are given.
x + y = 96
x - y = 8
Now we can add them together to solve for x (which is the larger number).
x + y = 96
x - y = 8
-------------
2x = 104
x = 52
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The perimeter of a rectangle is 30 cm. The width of the rectangle is 7 cm.
What is the area of the rectangle?
options:
56 cm²
49 cm²
8 cm²
14 cm²
Answer:
Hey,
your answer is 56cm^2
Maya is camping at the top of mount armstrong at an elevation of 7832 meters. Juan is scuba diving 160 meters below sea level. The two decide to meet at the midpoint. At what elevtation will Maya & Juan meet?
Answer: 3996 meters
Step-by-step explanation:
Given: Maya is camping at the top of mount armstrong at an elevation of 7832 meters.
Consider the pont of sea level be 0.
Then the height of the point where Mary is = +7832 meters (by using integers)
Juan is scuba diving 160 meters below sea level.
⇒The height of the point where Juan is =-160 meters
The distance between them =[tex]7832-(-160)=7832+160=7992\ meters[/tex]
The mid point of the distance= [tex]\frac{1}{2}\times7992=3996\ meters[/tex]
Hence, Maya & Juan meet will meet at an elevation of 3996 meters .
Final answer:
Maya and Juan will meet at an elevation of 3836 meters.
Explanation:
To find the elevation at which Maya and Juan will meet, we need to calculate the average of their elevations. Maya is at an elevation of 7832 meters and Juan is at an elevation 160 meters below sea level. The average of these two elevations is:
Average = (7832 + (-160)) / 2 = 3836 meters.
Therefore, Maya and Juan will meet at an elevation of 3836 meters.
PLEASE HELP!!
I can pay $4.50 for a 2-mile taxi ride or $8 for 7 miles ride. At this rate, how much would an 11-mile ride cost?
Slope intercept
Answer:
The answer is $10.80
Step-by-step explanation:
It goes up $0.70 every mile and the flat fee is $3.10.
The equation 3.1 + 0.7(x) when x is the number of miles traveled.
Substitute 11 for x and get 3.1 + 0.7(11).
The answer is $10.80
Translate the graph according to the rule (x, y) → (x + 2, y).
The first graph goes with the question.
(x, y) → (x, y + n) - translate the graph n units up
(x, y) → (x, y - n) - translate the graph n units down
(x, y) → (x - n, y) - translate the graph n units left
(x, y) → (x + n, y) - translate the graph n units right
---------------------------------------------------------------------------
(x, y) → (x + 2, y)
translate the graph 2 units right.
The state of Colorado is shaped like a rectangle with an approximate width of 280 mi and length of 380 mi. What is the population density of Colorado in people per square mile if the population is 5,116,800?
Answer:
Step-by-step explanation:
160miles • 330miles= 52,800square miles
Now it wants the population density in people per square miles, so you need to divide the population by the number of square miles.
4779736/52800=90.5 which is about 91people per square mile.
The population density of Colorado is 48.09 people per mile²
Population densityPopulation density is the concentration of individuals within a specific area. It is given by:
Population density = number of people / land area
Land area = length * width = 280 * 380 = 106400 mile²
Population density = 5,116,800 / 106400 = 48.09 people per mile²
The population density of Colorado is 48.09 people per mile²
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In a recent survey, 8 college graduates were each asked for the number of hours they work each week. Here is a list of the responses. 50, 52, 36, 46, 41, 36, 56, 65 Find the range of the data set.
Answer: 29
-------------------------
To get this answer, you subtract the largest and smallest values, which are also known as the max and min respectively
Range = Largest Value - Smallest Value
Range = Max - Min
Range = 65 - 36
Range = 29
If it helps, sort the data in order from smallest to largest to get this list of values: {36, 36, 41, 46, 50, 52, 56, 65} so you can see the min and max easier. The range is basically the spread of the data (more or less). The larger the range, the more spread out the data values are.
The range of the data set (36, 36, 41, 46, 50, 52, 56, 65) will be 29.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
The range of data gathering in statistics is the difference between the highest and smallest values, calculated by subtracting their sample maximum and minimum.
In a recent survey, 8 college graduates were each asked for the number of hours they work each week. Here is a list of the responses.
50, 52, 36, 46, 41, 36, 56, 65
Arrange the data in ascending order. Then we have
36, 36, 41, 46, 50, 52, 56, 65
Then the range of the data is given as,
Range = 65 - 36
Range = 29
The range of the data set 36, 36, 41, 46, 50, 52, 56, 65 will be 29.
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Which of the following are not polynomials ?
A, B, C, and E are not polynomials.
A polynomial is an expression involving exponents, constants, and variables, so long as:
You are not dividing by a variable.
You are not raising a variable to a power of a negative number.
You are not raising a variable to a power of a fraction.
You are not taking the root of a variable.
Only one of these satisfies the criteria for a polynomial, and that is D. However, the 2nd term, 0x^2 is an unnecessary term, and would only be included if dividing this polynomial by another polynomial.
A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by elimination to find the number of nickels and dimes that are in the jar.
Answer: 31 nickels and 29 dimes
Step-by-step explanation:
Nickels (.05): x
Dimes (.10): y
Value: .05x + .10y = 4.45 → -20(.05x + .10y = 4.45) → -x - 2y = -89
Quantity: x + y = 60 → 1(x + y = 60) → x + y = 60
-y = -29
y = 29
Next, substitute "29" for "y" into either equation and solve for "x":
x + y = 60
x + 29 = 60
x = 31
The number of nickels and dimes that are in the jar is 31 and 29 respectively.
Given that,
A jar containing only nickels and dimes contains a total of 60 coins.The value of all the coins in the jar is $4.45.1 nickle be 5 cents and 1 dime is 10 cents. Also we assume nickels be x and dimes be y.Based on the above information, the calculation is as follows:
x + y = 60 ........(1)
5x + 10y = 445.......(2)
Here we multiply by 5 in equation 1
5x + 5y = 300
5x + 10y = 445
-5y = 145
y = 29
So, x = 60 - 29
= 31
Therefore we can conclude that the number of nickels and dimes that are in the jar is 31 and 29 respectively.
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Ron walked 8/10 miles from his grandmother's house to the store then he walked 9/10 mile to his house use benchmarks to estimate about how far he walked altogether
Could someone help me with number 3?
Answer:X=40
Step-by-step explanation:
3inx+2in(4)=in(128)
Step 1: Add -8in to both sides.
3inx+8in+−8in=128in+−8in
3inx=120in
Step 2: Divide both sides by 3
then you will get your answer
solve for x by simplifying both side of the equation the isolating the variable.
x = 8/3 + 128/3in
Write the equation of the parabola in standard form that passes through the points (0, 3), (1, -4), and (-1, 4).
Answer
[tex]y = -3x^2-4x+3[/tex]
Explanation
The standard form of a parabola is
[tex]y = ax^2 + bx + c,[/tex]
where [tex]a \ne 0[/tex], and [tex]a,b,c[/tex] are real numbers.
If it passes through (0,3) then when x = 0, y = 3 so this means that
[tex]3 = a(0)^2 + b(0) + c \implies c = 3[/tex]
so [tex]y = ax^2 + bx + 3[/tex].
If it passes through (1,-4), then when x = 1, y = -4 so
[tex]\begin{aligned}-4 &= a(1)^2 + b(1) + 3 \\a+b+3 &= -4 \\a+b &= -7 && \text{(I).}\end{aligned}[/tex]
If it passes through (-1,4) then when x = -1, y = 4 so
[tex]\begin{aligned}4 &= a(-1)^2 + b(-1) + 3 \\a-b+3 &= 4 \\a-b &= 1 && \text{(II).}\end{aligned}[/tex]
Because both (I) and (II) need to be satisfied, we have the system of equations,
[tex]\begin{cases}a+b &= -7\qquad\text{(I)}\\a-b &= 1\qquad\text{(II)}\end{cases}[/tex]
which we can easily solve by adding the two equations up to get
[tex]\begin{aligned}(a+a) + (b-b) &= -7 + 1 \\ 2a&= -6 \\a &= -3.\end{aligned}[/tex]
Then we take any of the previous equations to solve for b:
[tex]\begin{aligned}a+b &= -7\\-3 + b &= -7 \\ b &= -4\end{aligned}[/tex]
Thus the parabola in standard form is
[tex]y = -3x^2-4x+3.[/tex]
So with the three points that are given to us, we will plug them into the standard form formula that I had mentioned earlier. Firstly, plug (0,3) into the equation since the 0 will cancel out the a and b variable:
[tex]3=a*0^2+b*0+c\\3=c[/tex]
Now we know that the value of c is 3.
Next, plug (1,-4) into the standard form formula and simplify (Remember to plug 3 into the c variable):
[tex]-4=a*1^2+1*b+3\\-4=a+b+3\\-7=a+b[/tex]
Next, plug (-1,4) into the standard form formula and simplify:
[tex]4=a*(-1)^2+b*(-1)+3\\4=a-b+3\\1=a-b[/tex]
With the last two simplified equations, we will create a system of equations:
[tex]-7=a+b\\1=a-b[/tex]
With this, I will be using the elimination method. Add the two equations together, and the following equation is the result:
[tex]-6=2a[/tex]
From here we can solve for a. For this, just divide both sides by 2:
[tex]-3=a[/tex]
Now that we have the value of a, plug it into either equation to solve for b:
[tex]-7=-3+b\\-4=b\\\\1=-3-b\\4=-b\\-4=b[/tex]
AnswerNow, plug the obtained values in our standard form equation and your final answer will be:
[tex]y=-3x^2-4x+3[/tex]
Two students use different methods to solve this multiplication problem: 1/2 • -4 4/5
Read each of their methods below and then enter numbers to correctly complete their work.
Solution:
[tex]\frac{1}{2}\times-4 \frac{4}{5}[/tex]
As one of the fraction is a proper fraction and another one is Mixed fraction.
There are two methods of solving it.
1. [tex]\frac{1}{2}\times-4 \frac{4}{5}=\frac{1}{2} \times \frac{-24}{5}=\frac{-12}{5}=-2\frac{2}{5}[/tex]
2. [tex]\frac{1}{2}\times-4 \frac{4}{5}=\frac{1}{2}[-4-\frac{4}{5}]=\frac{1}{2}\times (-4)+\frac{1}{2}\times\frac{-4}{5}=-2+\frac{-2}{5}=\frac{-10-2}{5}=\frac{-12}{5}=-2\frac{2}{5}[/tex]→→Here i have used Distributive property with respect to addition and Subtraction i.e a×(b+c)= a ×b + a×c or a×(b-c)=a×b-a×c
Now, you can fill the blanks by yourself.
Answer:Barbara writes each number as a fraction and then multiplies.
-24/5 -12/5
Answer:Christopher writes the mixed number as a sum and uses the distributive property.
-4 -4/5 -2 -2/5
Answer:Barbara's and Christopher’s answers will be equal. Write the answer as a mixed number in simplest form.
-2 2/5
Step-by-step explanation:
An avocado tree has a sale price of $27.95 dollars; this is 65% off the original price. What percent of the original price was the discount and how much was deducted from the original price?
Answer:
35% off, deducts $15.05
Step-by-step explanation:
The sale price was $27.95 and is 65% of the original price. This means the sale was 100%-65%= 35% off the original price.
We can create a proportion to find the original price to see how much was deducted. A proportion is an equation where two ratios are set equal to each other. We create two fractions using the prices and percents.
[tex]\frac{27.95}{x} =\frac{65}{100}[/tex]
We begin solving by cross multiplying numerator to denominator of each fraction.
[tex]27.95(100)=65(x)\\2795=65x\\\frac{2795}{65}=\frac{65x}{65} \\43=x[/tex]
So the original price was $43. The sale price deducts 43-27.95= 15.05
Solve the inequality below to determine and state the smallest possible value for x in he solution set 3(x+3)<5x-3
Find the value of y if the image below is a kite
10
7
12
5
Answer:
y=7
Step-by-step explanation:
We know the tops 2 parts of the kite have to be equal
x+3 = 15
Subtract 3 from each side
x+3-3 =15-3
x=12
We also know the bottoms have to be equal
3y-1 =2x-4
Substitute the value for x
3y-1 =2(12) -4
3y-1 =24-4
3y-1 =20
Add 1 to each side
3y-1+1 =20+1
3y = 21
Divide each side by 3
3y/3 = 21/3
y = 7
Curtis earns $13 per hour. He receives a pay raise of 7%. Which expression will calculate the amount Curtis earns per hour after his raise?
Answer:
He will earn 13.91 after his raise.
Step-by-step explanation:
13 x .07 = .91
13.00 + .91 = 13.91
The amount Curtis earns per hour after his raise is 13 * (1 + 7%)
How to calculate the amount Curtis earns per hour after his raise?From the question, we have the following parameters that can be used in our computation:
Initial = $13
Raise =7%
using the above as a guide, we have the following:
New = Initial * (1 + raise)
So, we have
New = 13 * (1 + 7%)
Hence, the expression is 13 * (1 + 7%)
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Charlie has been given a list of 4 bands and asked to place a vote. His vote must have the names of his favorite and second favorite bands from the list. How many different votes are possible?
Answer:
4
Step-by-step explanation:
theres only 4 to pick from
I drove 380 miles using 14 gallons of gas. At this rate, how many gallons of gas would I need to drive 418 miles?
Answer:
15.4 gallons .
Step-by-step explanation:
The rate of gas used = 380/14 = 27.14 gallons per gallon.
So for each gallon used you drive 27.14 miles.
So number of gallons used when travelling 418 miles = 418/27.14
= 15.4 gallons .
At the rate your car consumes gas, you will need 15.4 gallons to drive 418 miles.
The first thing to do here is to find out how many miles you can go with a single gallon of gas.
= Gas used / Number of miles traveled
= 14 / 380
= 0.0368 gallons per mile
Now that you have to drive 418 miles, the amount of gas you will need is:
= Number of miles to travel gas per mile
= 418 x 0.0368
= 15.4 gallons
In conclusion, you will need 15.4 gallons.
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based on the polynomial remainder theorem, what is the value of the function when x=5? f(x)=x^4-2x^3+5x^2-7x+4
Answer:
f(5)=469
Step-by-step explanation:
To find the value of the polynomial at x=5, we substitute the value 5 in for x into the polynomial. We then simplify using PEMDAS or order of operations.
[tex]x^4-2x^3+5x^2-7x+4\\(5)^4-2(5)^3+5(5)^2-7(5)+4\\625-250+125-35+4\\375+125-35+4\\500-35+4\\465+4\\469\\f(5)=469[/tex]
Answer:
469
Step-by-step explanation:
30 POINTS! WILL MARK BRAINLIEST! PLEASE HELP!
The location of four amusement park rides on a coordinate grid are as follows:
Ride 1 at (−3,− 4)
Ride 2 at (−3,2)
Ride 3 at (5,2)
Ride 4 at (5,−4)
Jesse begins at Ride 1 and then walks to Ride 2, then Ride 3, and then Ride 4. Then she walks back to Ride 3. The path between each ride is a straight line. One unit on the coordinate grid equals 50 yards.
What is the total distance Jesse walked?
Enter your answer in the box.
Answer:
from ride one to two its 300 then from two to three its 400 then from three to four its 300 then from four to three its 300.
so add it all up
300 + 300 + 300 + 400 = 1,300 yards and that is you answer
hope i helped and have a good day!
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
Simplify.
Answer: B
Step-by-step explanation:
3x³ - 7x² + 0x + 12 → 3x³ - 7x² + 0x + 12
- (3x³ + 6x² + 10x + 0) → + (-3x³ - 6x² - 10x - 0)
-13x² - 10x + 12
Tyler's height is 57 inches. What could be his height in centimeters? Explain your resoning. Nost: 1 inch=2.54 centimeters
Answer:
Tyler's height in centimeters is, 144.78 centimeters.
Step-by-step explanation:
Given the statement: Tyler's height is 57 inches.
To find his height in centimeters.
Using the conversion:
[tex]1 {\tex}inch = 2.54 {\tex}centimeters[/tex]
Proportion states that the two ratios or fraction are equal.
Using proportion method:
[tex]\frac{1}{57} = \frac{2.54}{x}[/tex]
By cross multiply, we get
[tex]x = 57 \times 2.54 = 144.78[/tex] centimeters.
therefore, his height in centimeter is, 144.78 inches.
To convert Tyler's height from inches to centimeters, we multiply his height in inches (57) by the unit conversion factor (2.54 cm/inch), giving us 144.78 cm. Thus, Tyler's height in centimeters is 144.78 cm.
Explanation:The question asks: Tyler's height is 57 inches. What could be his height in centimeters?
To answer this, we need to convert inches into centimeters. We do this using a unit conversion factor, which in this case is given as 1 inch = 2.54 centimeters. Therefore, Tyler's height in centimeters would be 57 inches multiplied by 2.54 (the unit conversion factor), giving us 144.78 cm.
Here's the step-by-step calculation:
Start with Tyler's height in inches: 57 inchesMultiply by the unit conversion factor: 57 inches * 2.54 cm/inch This gives us: 144.78 cmSo, Tyler's height in centimeters is 144.78 cm.
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Judy worked 8 hours and Ben worked 10 hours. Their combined pay was $80. When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65. Find the hourly rate of pay for each person
Answer:
The hourly rate of pay for:
Jude =$5 an hour
Ben = $4 an hour
Step-by-step explanation:
Let x represents Judy and y represents Ben.
As per the statement:Judy worked 8 hours and Ben worked 10 hours. Their combined pay was $80.
⇒[tex]8x + 10y =80[/tex] ......[1]
Also, it is given that When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65.
⇒[tex]9x+5y=65[/tex] .....[2]
Multiply equation [2] by 2 both sides we get;
[tex]2(9x+5y)=2 \cdot65[/tex]
18x + 10y = 130 .....[3]
Subtract [2] from [3] to eliminate y and solve for x;
18x + 10y -8x -10y = 130 -80
Simplify:
10x = 50
Divide both sides by 10 we get;
x = 5
⇒ Judy gets paid $5 an hour
Substitute value of x in [1] we get;
8(5) + 10y = 80
40 + 10y = 80
Subtract 40 from both sides we get;
40 + 10y - 40 = 80 -40
Simplify:
10 y = 40
Divide both sides by 10 we get;
y = 4
⇒Ben gets paid $4 an hour
Which pair of angles are Consecutive Interior Angles?
<6 and <5
<6 and <4
<1 and <5
<1 and <3
Answer:
<1 and <3
Step-by-step explanation:
The pairs of angles on one side of the line but in between the other two lines are called consecutive interior angles.
<1 and <3
<2 and <6
Solve the following equation for y
x= y – 20
Answer:
y = x + 20
Step-by-step explanation:
Isolate the variable you are solving for, y. Note the equal sign, what you do to one side, you do to the other. Add 20 to both sides
x (+20) = y - 20 (+20)
y = x + 20
y = x + 20 is your answer
Answer: Y= x+20
Step-by-step explanation: x = y-20, you must first add 20 to both sides to get Y on its own. So x+20 = y - 20 + 20, the twenties cancel each other out giving us x+20 = y or y=x+20
Lacy runs 5 1/4 km on Thursday. She runs 1 1/2 times as far on Saturday. How far does Lacy run on Saturday? Express your answer as a mixed number in the simplest form. Enter your answer in the box.
Answer: 5 1/4 x 1 1/5 = 7 1/2 + 3/8 -> 7 7/8
The answer is 7 and 7/8
A barrel filled with oil is a cylinder with a diameter of 22 inches and a height of 33.5 inches. There are 231 cubic inches in a liquid gallon. To the nearest gallon, how many gallons of oil does the barrel hold?
Answer:
55 gallons
Step-by-step explanation:
Given that the diameter of the cylindrical barrel is 22 inches, so the radius of the barrel is [tex]\frac{22}{2}=11 \text{ inches}[/tex]
And height of the cylindrical barrel is 33.5 inches.
So the volume of oil in the cylindrical barrel is
[tex]=\pi r^2 h\\=\pi (11)^2(33.5)\\\\\approx 12734.45 \text{ cubic inches}[/tex]
Also given that there are 231 cubic inches in a liquid gallon, so to find the number of gallons of oil in barrel, we use unitary method.
231 cubic inches goes in = 1 gallon
1 cubic inches will go in [tex]=\frac{1}{231} \text{ gallon}[/tex]
[tex]\text{12734.45 cubic inches oil will go in}=\frac{1}{231}\times 12734.45\approx 55.12 \text{ gallons}\\\\\text{hence there are approximately 55 gallons of oil in the barrel}[/tex]
Answer:
55
Step-by-step explanation: