Answer:
The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form
Step-by-step explanation:
The ratio indicates how many times one number contains another
The ratio can be written as:
A fraction [tex]\frac{a}{b}[/tex] a : ba to bThe two terms of the ratio must have the same units
∵ Sarah uses 9 mm of colored fabric to make her curtains
∵ She also uses 2 cm of of white fabric
- To express the amount of white fabric to colored fabric as a ratio
you must change the centimeter to millimeter because the
terms of ratio must have the same unit
∵ 1 centimeter = 10 millimeters
∴ 2 centimeters = 2 × 10 = 20 millimeters
∴ She uses 20 millimeters of the white fabric
Now write the ratio between the white fabric and the colored fabric
→ White : colored
→ 20 : 9
∵ 20 and 9 do not have a common factor
∴ The simplest form of the ratio is 20 : 9
The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form
Sarah uses 2 cm of white fabric for every 9 mm of coloured fabric. After converting to the same unit (centimeters), the simplest form of the ratio of white fabric to coloured fabric is approximately 2.22:1.
Explanation:To determine the ratio of the amount of white fabric to coloured fabric Sarah needs for her curtains in its simplest form, we first need to ensure that both fabrics are expressed in the same units. The question states Sarah uses 9 mm of coloured fabric and 2 cm of white fabric. Since there are 10 mm in a cm, 9 mm of coloured fabric can be converted to 0.9 cm.
Now, with both fabric measurements in centimeters, we can write the ratio of white fabric to coloured fabric: 2 cm of white fabric to 0.9 cm of coloured fabric. To find the simplest form of this ratio, we divide both sides by 0.9:
2 cm ÷ 0.9 cm = 2.2222...0.9 cm ÷ 0.9 cm = 1The simplest form of the ratio is therefore 2.2222...:1, which can be rounded and written as approximately 2.22:1, white to coloured fabric.
you’re score on a game show decreases by 5 points for each question you answer incorrectly. You answer 4 questions incorrectly, what integer represents the change in your score?
Answer:
-20
Step-by-step explanation:
If we get -5 points for each question you answer incorrectly, and we answer 4 questions incorrectly, than we can simply multiply -5 by 4 to get -20.
Answer:
(-20) is an integer represents the change in score.
Step-by-step explanation:
Penalty for answering a question incorrectly = -5
Number of questions answered incorrectly = 4
If we had answered 4 question incorrectly then the penalty of marks will be:
[tex]-5\times 4=-20[/tex]
(-20) is an integer represents the change in score.
Find f(x) and g(x) so that the function can be described as y=f(g(x))
y=(9/x^2)+2
there are many combinations for it, but we can settle for say
[tex]\bf \begin{cases} f(x)=x+2\\[1em] g(x)=\cfrac{9}{x^2}\\[-0.5em] \hrulefill\\ (f\circ g)(x)\implies f(~~g(x)~~) \end{cases}\qquad \qquad f(~~g(x)~~)=[g(x)]+2 \\\\\\ f(~~g(x)~~)=\left[ \cfrac{9}{x^2} \right]+2\implies f(~~g(x)~~)=\cfrac{9}{x^2}+2[/tex]
i need help w this geometry problem
Answer:
D
Step-by-step explanation:
As the angle Known to us is (2y-3)°
Now
∠B = (2y-3)° (when two parralel lines are cut by another line then angles opposite are equal)
∠D=180-(2y-3)° (Because angle to the line is same as B and as on one line total angle is 180° one part equals to B so other equals to 180-∠B)
Similarly
∠Q=∠D = 180-(2y-3)°
Because interior angles of a line cutting by a same line will be equal
Which is the approximate solution for the system of equations 3x+4y=2 and 4x+y=-4
A(-1.4,1.5)
B(1.4,1.5)
C(0.9,-0.2)
D(-0.9-0.2)
[tex]3x+4y=2\qquad\text{subtract 3x from both sides}\\\\4y=-3x+2\qquad\text{divide both sides by 4}\\\\y=-\dfrac{3}{4}x+\dfrac{2}{4}\to y=-\dfrac{3}{4}x+\dfrac{1}{2}\\\\for\ x=0\to y=-\dfrac{3}{4}(0)+\dfrac{1}{2}=0+\dfrac{1}{2}=\dfrac{1}{2}\to\left(0,\ \dfrac{1}{2}\right)\\\\for\ x=2\to y=-\dfrac{3}{4}(2)+\dfrac{1}{2}=-\dfrac{3}{2}+\dfrac{1}{2}=-\dfrac{2}{2}=-1\to(2,\ -1)\\--------------------------------\\[/tex]
[tex]4x+y=-4\qquad\text{subtract 4x from both sides}\\\\y=-4x-4\\\\for\ x=0\to y=-4(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=-1\to y=-4(-1)-4=4-4=0\to(-1,\ 0)\\\\Answer:\ \boxed{A.\ (-1.4,\ 1.5)}[/tex]
The approximate solution for the system of equations 3x + 4y = 2 and 4x + y = –4 will be (–1.4, 1.5). Then the correct option is A.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
3x + 4y = 2 …1
4x + y = -4 …2
From equation 2, we have
y = –4 – 4x
Put in equation 1, we have
3x + 4(–4 – 4x) = 2
3x – 16x – 16 = 2
–13x = 18
x = –18/13
x = –1.38
x ≈ –1.4
Then the value of y will be
y = –4 – 4(–1.38)
y = 1.52
y ≈ 1.5
Then the correct option is A.
More about the solution of the equation link is given below.
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A guy wire that is 21m long is attached to a cell phone tower 13 m high. Determine the angle formed by the guy wire and the ground
Answer:
[tex] 38^\circ [/tex]
Step-by-step explanation:
We assume that the ground is horizontal and the tower is vertical. The guy wire, the ground, and the tower form a right triangle. The guy wire is the hypotenuse. I'll call the angle formed by the guy wire and the ground angle A. For angle A, the tower is the opposite leg. Since we know the opposite leg and the hypotenuse, we use the sine ratio.
[tex] \sin A = \dfrac{opp}{hyp} [/tex]
[tex] \sin A = \dfrac{13~m}{21~m} [/tex]
To find the measure of angle A, we use the inverse sine function.
[tex] A = \sin^{-1} \dfrac{13}{21} [/tex]
[tex] A = \sin^{-1} 0.6190476 [/tex]
[tex] A = 38^\circ [/tex]
Which list shows the numbers in order from least to greatest?
2.43, 2.045, 259
2.045, 2.43, 259
2.43, 2.045, 259
259 , 2.045, 2.43
2.045, 259 , 2.43
Answer: second one (B) - 2.045, 2.43, 259
Step-by-step explanation: 2.045 is the lowest value due to the 0 in the hundredths place. 2.43 has a lower value than 259, it being a decimal.
write an equation of a line that is parallel to y=-x+3
write an equation of a line that is parallel to y= 3/4x-1
Problem 1
One possible answer is y = -x+5
This equation has a slope of -1 as does the first equation y = -x+3. Parallel lines have equal slopes but different y intercepts.
You can change the "+5" to any number you want.
=====================================
Problem 2
One possible answer is y = (3/4)x - 2. Like before, parallel lines have the same slope, just a different y intercept. The "-2" can be any number (negative or positive) you want as long as the slope remains 3/4.
Help plz.....
64 divide 2 x 8 + 12
Answer:
268
Step-by-step explanation:
64 divide 2 times 8 plus 12
32 times 8 plus 12
32 times 8
256 plus 12
268
Use elimination to solve the system
6x-4y=6
-6+3y=0
A. (5,6)
B.(-3,-6)
C.(1,0)
D.(4,-8)
Answer:
B. (-3, -6)
Step-by-step explanation:
(1) 6x - 4y = 6
(2) -6x + 3y = 0 Add (1) and (2)
-y = 6 Multiply each side by -1
y = -6 Substitute in (2)
-6x +3(-6) = 0 Remove parentheses
-6x – 18 = 0 Add 18 to each side
-6x = 18 Divide each side by -6
x = -3
The solution is (-3, -6).
Marie placed two orders at the same restaurant last month. In one order, she received 5 trays of lasagna and 3 trays of garlic bread for $163. In the other order, she received 4 trays of lasagna and 4 trays of garlic bread for $150.80. What is the price for one tray of lasagna, l, and one tray of garlic bread, g? l = $24.95 g = $12.75 l = $12.75 g = $24.95 l = $24.75 g = $12.95 l = $12.95 g = $24.75
Answer:
L=$24.95 , G=$12.75
Step-by-step explanation:
This problem is a classic system of equations problem. There are several methods of solving these problems, because of the circumstances and values given I think it's best to use the elimination method. The elimination method attempts to cancel out a variable by subtracting one equation from another.
The first statement Marie received an order of 5 trays of lasagna and 3 trays of garlic bread for a total of $163. I'm going to use "L" for lasagna and "G" for garlic bread. Therefore, the equation for the scenario above is:
[tex]5L+3G=163[/tex]
In the second statement Marie received an order of 4 trays of lasagna and 4 trays of garlic bread and so:
[tex]4L+4G=150.80[/tex]
Now we cannot use the elimination method directly because equation 1 and equation 2 do not have any coefficients in common. However, we can eliminate "G" by first multiplying the top equation by 4 and the bottom equation by 3. We are doing this because those are the coefficients of the other equation, and thus will return a common value as such:
Equation 1:
[tex]4(5L+3G=163)\\20L+12G=652[/tex]
Equation 2:
[tex]3(4L+4G=150.80)\\12L+12G=452.40[/tex]
Now we can subtract equation 2 from equation 1 and eliminate the "G" variable as such:
[tex]20L+12G=652\\-(12L+12G=452.40)\\\\8L+0G=199.60\\\\8L=199.60\\\\[/tex]
By solving for L we obtain:
[tex]8L=199.60\\\\\frac{8L}{8}=\frac{199.60}{8}\\\\L=24.95[/tex]
Therefore, one tray of lasagna is $24.95. Now that we know the value of "L" we can use any of our original equations to figure out what "G" is. I'll use the first equation and so:
[tex]5L+3G=163\\\\5(24.95)+3G=163\\\\124.75+3G=163\\\\124.75-124.75+3G=163-124.75\\\\3G=38.25\\\\\frac{3G}{3}=\frac{38.25}{3}\\\\G=12.75[/tex]
And so the price of a tray of garlic bread is $12.75. So the answer is the price of lasagna = $24.95 and garlic bread = $12.75
~~~Brainliest Appriciated~~~
Answer:
lasagna = $24.95 and garlic bread = $12.75
:)
Solve for x.
.
Simplify your answer as much as possible.
2x = 15 - 3x -- add 3x to both sides
5x = 15 -- divide both sides by 5
x = 3 -- simplest form
For this case, we must find the value of "x" of the following equation:
[tex]2x = 15-3x[/tex]
We add 3x to both sides of the equation:
[tex]2x + 3x = 15-3x + 3x\\5x = 15[/tex]
We divide between 5 on both sides of the equation:
[tex]\frac {5x} {5} = \frac {15} {5}\\x = 3[/tex]
Thus, the value of x is 3.
Answer:
[tex]x = 3[/tex]
A baker can make 30 gingerbread cookies in one half hour. How many can he make in 4 hours
Answer:
So 30:1/2
So you can times both sides by 2
60:1
Now you can multiply 60 by 4 (The total times the time you need)
Your answer is 240
The baker can make 240 gingerbread cookies in 4 hours
Hope that helps feel free to ask more questions
Brainliest??
you sold two different types of wrapping paper for your band fund-raiser. One type sold for $6 a roll and the other for $8 a roll. You collected a total of $92 for the 14 rolls you sold. How many of each type of wrapping paper did you sell?
Answer:
10 and 4
Step-by-step explanation:
So let's set up equations. So x+y=14. And 6x+8y=92. So 2y=8 or y=4. So x=10.
what is 152% of 72 plz give me answer
Answer:
152% of 72 = 109.44
Step-by-step explanation:
Trapezoid ABCD has vertices A(2, 4) , B(5, 4) , C(7, 1) , and D(0, 1) . Is this trapezoid an isosceles trapezoid?
Answer:
Yes
Step-by-step explanation:
Segments AB and CD are parallel and 3 units apart.
Point D is 2 units left of point A, and point C is 2 units right of point B. The trapezoid is symmetrical about the line x = 3.5, so is isosceles.
Answer:
Isosceles trapezoid
Step-by-step explanation:
1)By definition, an isosceles trapezoid has two congruent sides and four vertices. According to the given coordinate points, what we have is an isosceles trapezoid. Graphically, we can say that:
[tex]\overline{AD} \cong \overline BC[/tex]
2) Proving with Analytical Geometry that
[tex]\overline{AD} \cong \overline BC[/tex]
[tex]D_{BC}=\sqrt{(1-4)^{2}+(7-5)^{2}}\Rightarrow D_{BC}=\sqrt{9+4}\Rightarrow D_{BC}=\sqrt{13}\cong3.61\\D_{AD}=\sqrt{(1-4)^{2}+(0-2)^{2}}\Rightarrow D_{AD}=\sqrt{9+4}\Rightarrow D_{AD}=\sqrt{13}\cong3.61[/tex]
which property is used to simplify the expression 1+(6+0)=1+6
additive inverse property
additive identity property
associative property of addition
commutative property of addition
Answer:
commutative property of addition
Step-by-step explanation:
commutative property of addition means that both sides on the equal sign have the same numbers but just has is in a deferent order. It might be confusing for this one because there is a 0, but 0 is nothing so it still applies.
Hope this helps, have a great day!
Sarah buys a video game for $44.00 plus 4% sales tax. Her brother, Jack, buys a video game for $36.00 plus 6% tax. Show your work. (3 points)
a.) What is the total cost of Sarah’s video game? Show all work.
b.) What is the total cost of Jack’s video game? Show all work.
c.) Who spent more on tax?
Answer:
Sarah spent 45.76
Jack spent 38.16
Jack spent more on tax
Step-by-step explanation:
Sarahs game costs:
tax = 44 *.04 = 1.76
Total cost = game + tax
= 44 + 1.76
=45.76
Jacks game costs:
tax = 36 *.06 = 2.16
Total cost = game + tax
= 36 + 2.16
=38.16
Jack spent more on tax
how to divide numbers by decimals
Multiply the denominators. Way 2: Move decimal points, divide, and place a decimal point in the quotient. Step 1 Write a decimal point and a zero in the dividend. Step 2 Multiply the divisor by a power of 10 to get a whole number.
A bag contains 2 red marbles, 3 green marbles, and 2 black marbles what is the probability of NOT drawing out a black marble
Answer:
P (not black ) = 5/7
Step-by-step explanation:
We need to know the total number of marbles
2 red + 3 green + 2 black = 7 marbles
P (not black ) = Not black/ total
= ((2 red+ 3 green)/ total
= 5/7
what is the distance between points (2,-3) and (0,8) to the nearest tenth
The distance between the points (2,-3) and (0,8) can be calculated using the distance formula which derives from the Pythagorean theorem. After plugging in the coordinates into the formula, we get the distance approximately equal to 11.2.
Explanation:To calculate the distance between the points (2,-3) and (0,8), we can make use of the distance formula derived from the Pythagorean theorem. The distance formula is: d = √[(x2-x1)² + (y2-y1)²].
Here, (x1, y1) = (2, -3) and (x2, y2) = (0, 8).
Now, plug the coordinates into the formula:
d = √[(0 - 2)² + (8 - -3)²]
d = √[(-2)² + (11)²]
d = √[4 + 121]
d = √125
So, the distance to the nearest tenth between (2,-3) and (0,8) is approximately 11.2.
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Bryant Peters bought 75 shares of Elkston stock for $24.13 per share. The company paid annual dividends of $0.29 per share. What is the total annual dividend? Show work.
A) 32.10
B) 21.99
C) 21.75
D) 22.00
Answer:
The right option is C) 21.75
Step-by-step explanation:
we have given,
Number of shares = 75
Cost of each share = $24.13
Total cost of shares = 75×24.13 = $1809.75
since the company paid annual dividends of $0.29 per share.
Total annual dividends company paid = 75×0.29 = $21.75
Hence the right option is C) 21.75
What type of transformation takes the graph of f(x) = |x| to the graph of g(x) = |4+x|
A. Vertical translation of 4 units down
B. Horizontal translation of 4 units left
C. Vertical translation of 4 units up
D. Horizontal translation of 4 units right
Adding a number to the variable moves the graph horizontally to the left.
The answer is B.
Nick purchased a box of 425 thumbtacks. The box contained green thumbstacks and yellow thumbstacks. The number of green thumbstacks to the number of yellow thumbstacks was in the ratio of 7:10. How many yellow thumbstacks were in this box?
Answer:
250 yellow thumbtacks
Step-by-step explanation:
7:10 ratio (17 thumbtacks)
425 / 17 = 25
7 x 25 = 175 green
10 x 25 = 250 yellow
plz help Pru, Piper, and Phoebe share spices in the ratio 5:3:4. If Pru has 24 more spices than Piper, how many spices does Phoebe have?
Answer:
48 spices
Step-by-step explanation:
The number of spices each has is a multiple of 5, 3, and 4.
The number of spices each has is 5x, 3x, and 4x.
Pru has 5x spices.
Piper has 3x spices.
Pru has 24 more spices than Piper, so
5x = 3x + 24
2x = 24
x = 12
Phoebe has 4x spices, so Phoebe has
4(12) = 48
So remember that ratios are part to part, not part to whole like fractions are. In this case:
5 + 3 + 4 = 12
There are 12 parts total. This means that Pru has 5/12 of the spices, Piper has 3/12 (or 1/4) of the spices and Phoebe has 4/12 (or 1/3) of the spices. Now, we also know that Pru has 24 more spices than piper. With this info, we can set up our equation as (x = total amount of spices):
[tex]\frac{5}{12}x=\frac{3}{12}x+24[/tex]
From here we can solve for the total amount of spices. Firstly, subtract both sides by 3/12x:
[tex]\frac{2}{12}x=24[/tex]
Next, multiply both sides by 12/2 (or 6):
[tex]x=144[/tex]
There are a total of 144 spices. Now, to get Phoebe's amount of spices multiply 1/3 by 144:
[tex]\frac{144}{1}*\frac{1}{3}=\frac{144}{3}=48[/tex]
Answer:In short, Phoebe has 48 spices.
of the 25 sheep in the flock 34% are white.what is the total number of white sheep in the flock
A and B are independent events. P(A) = 0.40 P(B) = 0.20 What is P(A/B)
Final answer:
For two independent events A and B, the conditional probability P(A|B) is equal to the probability of A. Since P(A) is given as 0.40 and the events are independent, P(A|B) is also 0.40.
Explanation:
The question pertains to the concept of conditional probability for independent events in probability theory. When we have two independent events A and B, the conditional probability P(A|B), which is the probability of event A given that event B has occurred, is simply the probability of A, because the occurrence of B does not affect the probability of A when events are independent. This is expressed as P(A|B) = P(A).
Given P(A) = 0.40 and P(B) = 0.20, and knowing that A and B are independent, we can state that:
P(A\B) = P(A)
The probability that event A occurs given that event B has also occurred is 0.40, which is the original probability of A.
there are 230 books in a library and 60% of them are fiction. how many fictional bools are there
To find the number of fictional books in the library, multiply the total number of books by 0.60 which is 138.
Explanation:To find the number of fictional books in the library, we need to calculate 60% of the total number of books. Thus the concept of percentage calculation will be followed.
Calculating 60% of 230 -
= 60/100 x 230
= 13800/100
= 138
Therefore, there are 138 fictional books in the library.
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Jose travels 130 miles in 150 minutes. How many miles does Jose travel in 1 hour?
Answer:
52 miles
Step-by-step explanation:
We can use a ratio to solve this problem. Let put miles over time. We know that 1 hour = 60 minutes. We need to have the units the same.
130 miles x miles
-------------- = ---------------
150 minutes 60 minutes
Using cross products
130 * 60 = 150 x
Divide each side by 150
130/150 * 60 = 150x/150
52 =x
If a batch of cookies uses 1 1/3 cups of chocolate chips to make 24 cookies, how many cookies will 3 cups of chocolate chips make?
If you can explain your answer, that would be helpful, but not necessary.
Thanks for any help :)
Answer:
x = 54 cookies
Step-by-step explanation:
We can use ratios to solve this problem
1 1/3 cups chocolate chips 3 cups chocolate chips
------------------------------------ = --------------------------------------
24 cookies x cookies
Using cross products
1 1/3 * x = 3 * 24
Let change 1 1/3 to an improper fraction
1 1/3 = (3*1+1)/3 = 4/3
4/3 x = 72
Multiply each side by 3/4 to isolate x
3/4 * 4/3x = 72*3/4
x = 54 cookies
A trail mix that costs $2.45 per pound is mixed with a trail mix that costs $2.30 per pound. How much of each type of trail mix must be used to have 30 pounds of trail mix that costs $2.35 per pound?
Answer:
10 pounds of trial mix that costs $2.45 and 20 pounds of trial mix that costs $2.30
Step-by-step explanation:
[tex]\\\text{Let x pounds of the trial mix that costs \$2.45 per pound, and y pounds of the trial mix}\\\text{that costs \$2.30 per pound are added to get a 30 pounds of trial mix }\\\text{that costs \$2.35 per pound. since the total mixture is 30 pounds, so we get}\\\\x+y=30\ \ \ \ \ \ \ \ \ \ \ \ \ ...... (i)\\\\\text{and the total cost equation is given by}\\\\\$2.45 x + \$2.30 y=\$2.35 (30)\\\\2.45 x + 2.30 y=70.5 \ \ \ \ \ \ \ \ \ \ \ \ \ ...... (ii)\\[/tex]
[tex]\text{now to solve the equation (i) and (ii), we'll substitute }y=30-x \text{ from (i) into (ii)}\\\text{so we get}\\\\2.45x+2.30(30-x)=70.5\\\\2.45x+69-2.30x=70.5\\\\\Rightarrow 2.45x-2.30x=70.5-69\\\\\Rightarrow 0.15x=1.5\\\\\Rightarrow x=\frac{1.5}{0.15}\\\\\Rightarrow x=10\\\\\text{plug this value of x in (i), we get}\\\\y=30-x=30-10=20\\\\\text{so we must add 10 Pounds of trial mix that costs \$ 2.45 and 20 pounds of}\\\text{the trial mix that costs \$2.30}[/tex]
Final answer:
To create a 30-pound trail mix costing $2.35 per pound, mix 20 pounds of $2.45 trail mix with 10 pounds of $2.30 trail mix.
Explanation:
Trail mix costing: $2.45 per pound and $2.30 per pound must be mixed to get a 30-pound mix costing $2.35 per pound.
To calculate:
Let x = pounds of $2.45 mix and y = pounds of $2.30 mix.
Set up the system of equations: x + y = 30 and (2.45x + 2.30y)/30 = 2.35.
Solve the system to find x = 20 pounds of $2.45 mix and y = 10 pounds of $2.30 mix.