Answer:
(i) 16 cm.
(ii) 37 pieces in total.
Step-by-step explanation:
Through determining each lengths factors, it can be determined that every ribbon can be equally divided into 16 cm. long ribbons, so we already have our first answer. A 160 cm. long ribbon divided into 16 cm. long pieces will create 10 ribbons from that one piece; the 192 cm. long ribbon cut into the same 16 cm. lengths will equal 12 pieces of equal length; and the 240 cm. long ribbon will divide its 16 cm. lengths into 15 pieces of equal length. So the 10 pieces, plus the 12 pieces, plus the 15 pieces, will equal 37 total pieces, each 16 cm. in length.
Final answer:
This answer explains how to find the largest length of pieces and total number of pieces cut from different ribbon lengths. Therefore, the largest piece length is 16 cm. and Total number of pieces of ribbons cut is 37.
Explanation:
(i) Largest possible length of each piece of ribbons: To find the largest piece length, we need to determine the greatest common divisor (GCD) of the ribbon lengths. The GCD of 160, 192, and 240 is 16. Therefore, the largest piece length is 16 cm.
(ii) Total number of pieces of ribbons cut: To find the total number of pieces, divide each ribbon length by the largest piece length. For 160 cm, it gives 10 pieces. For 192 cm, it gives 12 pieces, and for 240 cm, it gives 15 pieces. Adding these, the total number of pieces is 37.
Larry is taking orders for lunch. A roast beef sandwich costs $5 and a taco salad costs $7.50. He collects $127.50 from the 19 people who ordered. Assuming everyone who ordered just ordered 1 item, How many people ordered taco salads? (3 points. 1 point for setting up a correct system of equation, 1 point for the work, 1 point for the correct solution.)
Answer:
System of equations:
5r +7.50t = 127.50
r +t = 19
Answer:
t = 13 . . . number of people who ordered taco salads
Step-by-step explanation:
One equation expresses the total bill: the number of each item ordered multiplied by its price, all item subtotals added to make the order total.
The other equation expresses the total number of orders: the sum of the orders of roast beef sandwich and the orders of taco salads.
__
The solution can be found easily by substitution.
r = 19 -t
5(19 -t) +7.50t = 127.50
95 +2.50t = 127.50 . . . . . . simplify
2.50t = 32.50 . . . . . . . . . . subtract 95
t = 13 . . . . . . . . . . . . . . . . . . divide by 2.50
The number who ordered taco salads is 13.
Which of the following is a true
A. -9<-4
B. |-10| >| 2 |
C. | -3 | < | 2 |
D.6< - 12
Answer:
A and B
Step-by-step explanation:
A. -9<-4 ....TRUE
B. |-10| >| 2 | => 10 > 2 ...TRUE
C. | -3 | < | 2 | => 3 > 2 ....FALSE
D. 6< - 12 ....FALSE
Answer A and B
The measure of an angle is 94°. What is the measure of its supplementary angle?
Answer:
86°
Step-by-step explanation:
Supplementary angles add up to 180°. So the supplementary angle of 94° is:
x + 94° = 180°
x = 86°
You survey your 22 classmates on there favorite color. There are 396 students at your school. How many students in the school do you predict would choose green as there favorite color
By determining the proportion of classmates who prefer green and applying it to the entire school population, we predict that approximately 72 students at the school would choose green as their favorite color.
To predict the number of students who favor green as their favorite color, we will assume the sample of classmates is representative of the entire school.
First, we need to find out how many students in the class chose green as their favorite color. Say, for example, 4 of the 22 classmates picked green. To find the predicted number for the school, we calculate:
Number of green-favoring classmates / Total classmates = Proportion of green-favoring classmates
4 / 22 = 0.1818 (rounded to four decimal places).
Now, apply this proportion to the entire school population:
0.1818 × 396 = Predicted number of students who favor green at the school.
71.55 - Since we can't have a fraction of a student, we round to the nearest whole number, predicting that about 72 students in the school would choose green as their favorite color.
Based on the data provided, I predict that approximately 72 students in the school would choose green as their favorite color.
1. Since you surveyed 22 classmates, the percentage of classmates who prefer green can be calculated. Let's assume that [tex]\( x \)[/tex] represents the number of classmates who prefer green. Therefore, [tex]\( \frac{x}{22} \)[/tex] is the proportion of classmates who prefer green.
2. Now, we can use this proportion to estimate the total number of students in the school who prefer green. Since there are 396 students in total, the estimated number of students who prefer green would be[tex]\( \frac{x}{22} \times 396 \).[/tex]
Now, let's find [tex]\( x \):[/tex]
- Let's assume [tex]\( y \)[/tex] is the number of classmates who prefer green. Since you surveyed 22 classmates, the percentage of classmates who prefer green can be calculated as [tex]\( \frac{y}{22} \).[/tex]
- Assuming that the number of classmates who prefer green is proportional to the total number of students who prefer green in the school, we can set up a proportion: [tex]\( \frac{y}{22} = \frac{x}{396} \).[/tex]
- Cross-multiplying, we get [tex]\( 396y = 22x \).[/tex]
- Solving for [tex]\( x \),[/tex] we find [tex]\( x = \frac{396y}{22} \).[/tex]
- Since we don't know the exact number of classmates who prefer green, let's assume a hypothetical scenario where 4 of your classmates prefer green. So, [tex]\( y = 4 \).[/tex]
- Substituting [tex]\( y = 4 \)[/tex] into the equation, we get [tex]\( x = \frac{396 \times 4}{22} = \frac{1584}{22} = 72 \).[/tex]
By surveying your classmates, you get a sample proportion of those who prefer green. Extrapolating this proportion to the entire school population, you can estimate the total number of students who prefer green. However, this estimation assumes that your classmates' preferences are representative of the entire school's preferences. So, based on this calculation, approximately 72 students in the school are predicted to choose green as their favorite color.
Complete question:
You survey your 22 classmates on there favorite color. There are 396 students at your school. How many students in the school do you predict would choose green as there favorite color?
In circle Z what is measure of <2
Answer:
oof
Step-by-step explanation:
Which of the following does not name the same line?
MN
KM
KN
KL
Answer:
KL does not name the same line.
Step-by-step explanation:
You'll recognize that if you go from KM, it stays on the same. You go from MN it stays on the same line. KN also stays on the same line. By K and L are two completely different lines. L can only be with N or J
Answer:
NL
Step-by-step explanation:
Consider the following function:y=1/(x+5)+2
How does the graph of this function compare with the graph of the parent function, y=1/x
It is shifted right 5 units and up 2 units from the parent function.
It is shifted left 5 units and up 2 units from the parent function.
It is shifted right 5 units and down 2 units from the parent function.
It is shifted left 2 units and down 5 units from the parent function.
It is shifted right 2 units and up 5 units from the parent function.
It is shifted left 2 units and up 5 units from the parent function.
Answer:
Step-by-step explanation:
Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT. That +2 shifts this result UP by 2 units.
Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.
We have given that function
y=1/(x+5)+2
We have to determine,
The graph of this function compares with the graph of the parent function, y=1/x.
Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.
That +2 shifts this result UP by 2 units.
Therefore the graph of the y=1/x is given below.
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Choose the single logarithm expression that is equivalent to the one shown!!! Help needed !!
A. Log 64
B. Log 12
C. Log 20
D. Log 10
Answer:
log 64
Step-by-step explanation:
Using the rules of logarithms
• log [tex]x^{n}[/tex] ⇔ nlogx
• logx + logy ⇔ log xy
Given
2 log 4 + log 2 + log 2
= log 4² + log (2 × 2)
= log 16 + log 4
= log (16 × 4) = log 64
Answer:
A, log 64
Step-by-step explanation:
your answer A, log 64 is correct. i will explain why below:
2 log 4, log 2 and log 2 have the same bases (10), meaning they are able to be added easier. but before we add, we use the Power Rule of Logarithms on 2 log 4
the Power Rule says that we can move an exponent in a logarithm to the front then solve. this also applies to the reverse, as we can move 2 back as an exponent of 4 and solve
2 log 4 ---> log 4² < simplify the exponent and we get log 16
we can now use the Product Rule of Logarithms where log x + log y = log(xy)
we can use that on the first two terms of the addition
log 16 + log 2 ----> log (16 × 2) = log 32
now we can apply the other log 2 to the rule but instead with log 32
log 32 + log 2 ---> log (32 × 2) = log 64
our answer is log 64
A used-car dealer has a vehicle on the lot with a sticker price of $5999. If the
dealer markup on used vehicles is 20%, how much did the dealer pay for the
car?
Answer:
$4999
Step-by-step explanation:
Let the cost of the car be x
Then considering 20% markup, the sticker price is:
x + 20% = 5999Since 20% of x is 20/100x = 0.2x,
x+ 0.2x = 59991.2x = 5999x = 5999/1.2x ≈ $4999So dealer paid $4999 for the car
According to the stem and leaf plot how many trees are more than 640 inches tall? CANT MISS ANYMORE PLEASE GIVE THE FOR SURE ANSWER!!
Answer:
9
Step-by-step explanation:
Because every number next to 64 is over
can anyone solve this math question
Answer:
12.6 units²
Step-by-step explanation:
Since PX is a tangent to the circle then OP and PX are at right angles.
A ΔOPX = 12, thus
OP × PX = 12, that is
6OP = 12 ( divide both sides by 6)
OP = 2 ← radius of circle
Area of circle = πr² = π × 2² = 4π ≈ 12.6 units²
Which is the first step in simplifying the expression 2(x + 3) + 5? 2x + 2(3) + 5 2x + 3 + 5 2 + x + 3 + 5 2(5) + x + 3
Answer:
2x + 2(3) + 5
Step-by-step explanation:
Given expression
2(x + 3) + 5
In order to solve the expressions or to simplify the expressions, basic mathematical rules are considered.
Basic mathematical rules include the BODMAS. The order is Brackets, of powers, division, multiplication, addition and then subtraction is solved at last.
For the given expression, the 2 outside the bracket (x+3) will be multiplied inside first.
=> 2(x+3) + 5
Step 1:
=> 2x + 2(3) + 5
Step 2:
=> 2x + 6 + 5
Step 3
=> 2x+11
So the first step is 2x + 2(3) + 5 ..
Answer:
2x + 2(3) + 5
Step-by-step explanation:
18 lemons are required to make 15 cups of lemonade. how many lemons are being used for each cup
We find out the number of lemons needed per cup by dividing the total number of lemons by the total number of cups. In this case, 18 lemons divided by 15 cups gives us the number of lemons used per cup of lemonade.
Explanation:This question is asking how many lemons are required for each cup of lemonade if 18 lemons are used to make 15 cups of lemonade. This is a simple proportional math problem. To solve this, we divide the total number of lemons by the total number of cups.
Step 1: Identify the total number of lemons and cups, which are 18 and 15 respectively.
Step 2: Divide the total number of lemons by the total number of cups (18 lemons / 15 cups).
Step 3: The solution will show the number of lemons used per cup of lemonade.
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You are trying out for the school play. The probability that you are chosen to be in the play is 0.4. The probability that you get the lead role is 0.1. What is the probability that you get a lead role, given that you are chosen to be in the play?
I think the answer is 3/10
The probability that we will get a lead role, given that we are chosen to be in the play is 0.5.
What is probability?Probability is the ratio that shows the likelihood of an event occurring from a given set of possible events.
We can find the required probability below:The probability that we will be chosen for the play is 0.4.
The probability that we will get the lead role is 0.1.
We have to find the probability that we get a lead role, given that we are already chosen to be in the play.
In this situation, the probability can be found by adding the probability of being chosen and the probability that we will get the lead role.
This can be done as shown below:
The probability that we get a lead role, given that we are already chosen to be in the play = The probability that we will be chosen for the play + The probability that we will get the lead role
= 0.4 + 0.1
= 0.5
The probability of us getting a lead role given that we have already been chosen for the play is found to be 0.5. The correct answer is option D.
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Evaluate -3x3 - 4x for x = -1. 1 7 -1
Final answer:
When evaluating the expression -3x³ - 4x for x = -1, by plugging in the value and simplifying the expression, we obtain the result of 7.
Explanation:
The question at hand requires us to evaluate the expression -3x³ - 4x when x = -1. To do this, we substitute -1 for x into the expression and simplify. Here's the step-by-step calculation:
First, calculate the term with the cube: -3(-1)³ = -3(-1) = 3.Then, calculate the linear term: -4(-1) = 4.Add both terms together: 3 + 4 = 7.Therefore, when we evaluate the expression -3x³ - 4x for x = -1, the result is 7.
What is the solution to the inequality
Answer:
p > 5 and p <-8
Step-by-step explanation:
To solve this, you first need to isolate p.
First add 6 on both sides of the equation:
[tex]-6 + |2p+3| >7\\\\(+6) -6 + |2p+3| >7 +6\\\\2p + 3 > 13[/tex]
Then subtract 3 from both sides of the equation.
[tex]2p+3-3>13-3\\\\2p > 10\\[/tex]
The divide both sides by 2.
[tex]\dfrac{2p}{2}>\dfrac{10}{2}\\\\p>5[/tex]
Another solution is possible because of the absolute value.
If [tex]|2p+3|>13[/tex]
Then [tex]|2p+3|<-13[/tex]
Thus we can solve the second solution:
[tex]|2p+3|<-13[/tex]
[tex]2p+3<-13[/tex]
Isolate P again by subtracting both sides by 3
[tex]2p+3-3<-13-3[/tex]
[tex]2p<-16[/tex]
Then divide both sides by 2:
[tex]\dfrac{2p}{2}<-\dfrac{16}{2}[/tex]
[tex]p<-8[/tex]
Answer:
p > 5, p < -8
Step-by-step explanation:
We are given the following inequality and we are to find its solution:
[tex]-6+|2p+3|>7[/tex]
Adding 6 to both sides to get:
[tex]-6+6+|2p+3|>7+6[/tex]
[tex]|2p+3|>13[/tex]
We know the absolute rule that [tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex].
So [tex]2p+3>13[/tex] or [tex]2p+3<-13[/tex]
[tex] 2 p > 1 3 - 3 [/tex], [tex] 2 p < - 1 3 - 3 [/tex]
[tex] 2 p > 1 0 [/tex], [tex] 2 p < - 1 6 [/tex]
[tex]p>\frac{10}{2}[/tex], [tex]p<\frac{-16}{2}[/tex]
p > 5, p < -8
What is the equation of the line that passes through point (4, 12) and has a y-intercept of —2?
Answer:
y = 3.5x - 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + bm - slope
b - y-intercept
We have y-intercept b = -2. Substitute:
y = mx - 2We have the point (4, 12) → x = 4, y = 12. Put them in the equation:
12 = 4m - 2 add 2 to both sides
14 = 4m divide both sides by 4
14/4 = m → m = 3.5
Answer:
y = 3.5x - 2
Step-by-step explanation:
We know that the y-intercept of our equation is -2, so our current equation is: y = mx - 2. Now we have to find m, which is the slope. Now, we plug in the points into the equation y = mx - 2, and we get 12 = 4m - 2. Thus, m is 3.5. Our final equation is y = 3.5x - 2.
what is the solution to the system of equations y = -4x - 19 and y = 2x - 1 in (a, b) form
For this system of equation I used substitution:
Step 1: Every time you see a y in the equation y = 2x - 1 replace it with -4x - 19
-4x - 19 = 2x - 1
Step 2: Isolate x
(-4x + 4x) - 19 = (2x + 4x) - 1
-19 = 6x - 1
-19 + 1 = 6x + (- 1 + 1)
-18 = 6x
x = -3
Step 3: To solve for y replace x in the equation y = 2x - 1 with -3
y = 2(-3) - 1
y = -6 - 1
y = -7
(-3, -7)
Check:
-7 = -4(-3) - 19
-7 = 12 - 19
-7 = -7 --------------------------------> Correct!
-7 = 2(-3) - 1
-7 = -6 - 1
-7 = -7 --------------------------------> Correct!
Hope this helped!
Can someone help with this question?
Answer:
w = 4 m
Step-by-step explanation:
The volume (V) of a cuboid is
V = lwh ( l is length, w is width and h is height )
Given V = 144 m³, then
lwh = 144 ( substitute l = 3 and h = 12 )
3 × w × 12 = 144
36w = 144 ( divide both sides by 36 )
w = 4
The volume of a rectangular prism is given by the product of its dimension: let w, h, l be the width, height and length of the prism, we have
[tex]V = whl[/tex]
In your case, everything is given except the width:
[tex]144 = w\cdot 3 \cdot 12 \iff 144 = 36w \iff w = \dfrac{144}{36} = 4[/tex]
How much interest does a $482 investment earn at 5% over 3 years?
Hi there! The answer you're looking for is $72.30. Simply multiply $482 by 0.05 (5%) and multiply that answer by three (three years) to get $72.30! Let me know if this helps! <3
Answer: $72.30
Step-by-step explanation: To solve this problem, first begin with the interest formula.
Formula: Interest = principal × rate × time
In this problem, we are solving for the interest.
The principal is the amount invested which in this case is $482. The rate is 5% which we can write as .05 and the time is 3 years.
Interest = (482)(.05)(3)
Interest = 72.3
This means that the interest earned is $72.30.
A 3-gallon jug of water costs $19.68. What is the price per cup?
Answer:
0.41 per cup
Step-by-step explanation:
in 3 gallons of liquid is 48 cups so 19.68 and divide by 48 so 19.68/48=0.41
Answer:
$0.41 per cup
Step-by-step explanation:
there are 16 cups in a gallon
after that multiply 16 times 3 which would be 48
Now divide $19.68 divided by 48
check---
0.41 times 48 = 19.68
tony bought 288 1 inch nails and 5 boxes of 2 inches. each box of 2 inch nails had equal amount of nails in them. he bought a total of 548 nails. find the number of nails in each box of 2 inch nails
Answer:
each box has 52 in it
Step-by-step explanation:
first you subtract 288 from 548 =260
this is the total number of nails minus the total 1 inch nails
then you divide 260 by 5 because he has five boxes of 2 inch names which means that you have to account for the even number of nails in each box
Answer:
There were 52 2-inch nails in each box.
Step-by-step explanation:
Let the number of nails in each 2 inch box be = x
As Tony bought 288 other nails and 5 boxes of 2 inch nails with a total purchase of 548 nails, we get the following equation;
[tex]288+5x=548[/tex]
[tex]=> 5x=548-288[/tex]
[tex]=> 5x=260[/tex]
x = 52
Hence, there were 52 2-inch nails in each box.
If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?
For this case we have that if "y" varies directly with "x", we can propose:
[tex]y = kx[/tex]
Where "k" represents the constant of proportionality.
According to the data:
[tex]180 = kn\\n = k5[/tex]
We substitute the second equation in the first:
[tex]180 = k * k5\\180 = 5k ^ 2\\k ^ 2 = \frac {180} {5}\\k ^ 2 = 36[/tex]
We apply root:
[tex]k = \pm \sqrt {36}\\k = \pm6[/tex]
If k = 6, then[tex]n = 6 * 5 = 30[/tex]
Answer:
[tex]n = 30[/tex]
Answer:
EDGE 2020
Step-by-step explanation:
C) 30
trust me
A scatter plot containing the point (5, 29) has the regression equation yˆ=5x+2 .
What is the residual e when x = 5?
Enter your answer in the box.
e =
Answer:
ε₀= 0.035
Step-by-step explanation:
The question is on residual/ error which is the vertical distance between the actual value of y and the estimated value of y.
General formulae is;
ε₀= y₀ - y₁
From the graph attached, the point on the line y=5x+2 is (5.407,29.035)
ε₀= 29.035- 29.000
ε₀= 0.035
What is the least common multiple of the two denominators
6/8 4/32
Answer:
32
Step-by-step explanation:
To find the lcm of 8 and 32 by listing
multiples of 8 are : 8, 16, 24, 32, 40, ....
multiples of 32 : 32, 64, 96, ....
The least common multiple of 8 and 32 is 32
Emily, Jean, and Amanda live in apartments on the 5th, 6th and 7th floors. One girl likes basketball, one likes football, and the other likes soccer.
The girl on the 6th floor is the football fan
The girl on the fifth floor thinks soccer is boring
Jean is a baseball fan
Which floor does Jean live on?
Answer:
Assuming you mean baseball in stead of basketball, if must be the 5th floor.
Step-by-step explanation:
"The girl on the fifth floor thinks soccer is boring" implies that on the 5th floor lives the football or baseball fan. However, it cannot be the football fan since it is already known that she lives on 6th.
So the baseball fan, which is Jean, lives on 5th.
Here's a question that I'm having trouble with. Please help, thanks!
Answer:
a . is the right answer
trust me
Circle A has radius 4 feet .Circle B has
radius 9 feet .What is the ratio of the area of arcle A to the
area of circle B?
a . 1/2
b . 4/9
c . 8/27
d . 16/81
Answer:
d. 16/81Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
The ratio of the areas of the difference circles:
[tex]\dfrac{A_1}{A_2}=\dfrac{\pi r_1^2}{\pi r_2^2}=\dfrac{r_1^2}{r_2^2}=\left(\dfrac{r_1}{r_2}\right)^2[/tex]
We have
Circle A: r₁ = 4ft
Circle B: r₂ = 9 ft
Substitute:
[tex]\dfrac{A_A}{A_B}=\left(\dfrac{4}{9}\right)^2=\dfrac{16}{81}[/tex]
the ratio of the area of Circle A to the area of Circle B is 16/81, which corresponds to answer choice (d).
To find the ratio of the area of Circle A to the area of Circle B, we use the formula for the area of a circle, which is A = (pi)r^2. For Circle A, with a radius of 4 feet, the area is (pi)(4 ft)^2. For Circle B, with a radius of 9 feet, the area is (pi)(9 ft)^2.
Calculating these areas:
Area of Circle A = (pi)(4 ft)^2 = 16(pi) ft^2
Area of Circle B = (pi)(9 ft)^2 = 81(pi) ft^2
Now, we take the ratio of the two areas:
Ratio = (Area of Circle A) / (Area of Circle B) = (16(pi) ft^2) / (81(pi) ft^2) = 16/81
Therefore, the ratio of the area of Circle A to the area of Circle B is 16/81, which corresponds to answer choice (d).
1) SHOW WORK: Evaluate f(-2):
f(x) = 3x -4
2) SHOW WORK: Evaluate f(8):
f(x)=x^2 -4
Answer:
- 10 and 60
Step-by-step explanation:
1
To evaluate f(- 2) substitute x = - 2 into f(x)
f(- 2) = (3 × - 2) - 4 = - 6 - 4 = - 10
2
To evaluate f(8) substitute x = 8 into f(x)
f(8) = 8² - 4 = 64 - 4 = 60
Answer:
1) f(-2) = -102) f(8) = 60Step-by-step explanation:
[tex]1)\\f(x)=3x-4\\\\f(-2)\to\text{put x = -2 to the equation of the function}\ f(x):\\\\f(-2)=3(-2)-4=-6-4=-10\\2)\\f(x)=x^2-4\\\\f(8)\to\text{put x = 8 to the equation of the function}\ f(x):\\\\f(8)=8^2-4=64-4=60[/tex]
Need help with the question at the top
Thanks
First we must find area of a single square.
Meaning we divide total area of 80 centimetres squared by 5 since we have 5 squares in the shape.
[tex]A_{square}=\frac{A_{shape}}{5}=\underline{16}[/tex]
Now from the picture we can see that the perimeter of shape is combined by 4 times 3 times the length of side of 1 square.
So we need to find side of 1 square.
[tex]a=\sqrt{A_{square}}=\sqrt{16}=\underline{4}[/tex]
As we stated before the formula for perimeter of this shape is:
[tex]P=4(3\cdot a)=4(3\cdot4)=4\cdot12=\boxed{48}[/tex]
The perimeter of shape is 48 centimetres.
Hope this helps.
r3t40