Ratio of red apples to all apples in the basket is 9:14 and ratio of red apples to green apples 9:5
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
The number of apples are in basket =14
The number of green apples in basket = 5
The number of red apples are 14-5=9
As we know that 5 in 14 apples are green and remaining apples red.
So the red apples = 14-5=9
the ratio of red apples to all apples in the basket is 9:14
the ratio of red apples to green apples 9:5
Hence ratio of red apples to all apples in the basket is 9:14 and ratio of red apples to green apples 9:5
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Solve for x: −2x − 4 > 8 (1 point)
x < −6
x > −6
x < −2
x > −2
Option A : x < -6 is the correct choice.
We have a inequality -
−2x − 4 > 8
We have solve and find the solutions to this inequality.
What is an Inequality in mathematics ?An inequality compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
−2x − 4 > 8
Add 4 on both sides -
-2x - 4 + 4 > 8 + 4
-2x > 12
Multiply both sides by -1, we get -
2x < - 12
Divide by 2 on both sides -
x < -6
Hence, x < -6 represents the solution of the inequality.
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what is 0.0018 in scientific notation
Scientific notation makes it easier to work with very small numbers, like 0.0018.
To express the number 0.0018 in scientific notation, we need to rewrite it as a product of a number between 1 and 10, and a power of 10. Here are the steps:
Identify the Initial Decimal Point Position: The number 0.0018 initially has the decimal point immediately after the zero whole part, before any significant figures.
Move the Decimal Point to the Right: Move the decimal point to the right until there is exactly one non-zero digit to the left of the decimal point. For 0.0018, moving the decimal point three places to the right converts it to 1.8.
Count the Moves: In this case, we moved the decimal three places to the right. Each move to the right represents a negative exponent in scientific notation.
Write in Scientific Notation: The scientific notation form of 0.0018 is written as:
[tex]1.8 \times 10^{-3}[/tex]
The [tex]10^{-3}[/tex] indicates that the decimal point was moved three places to the right.
Fred the clown can create 17 animal balloons every 15 minutes.how many animal balloons he could create in 30 minutes and in 60 minutes.
Answer:
34 balloons in 30 minutes.
68 balloons in 60 minutes.
Step-by-step explanation:
We have been given that Fred the clown can create 17 animal balloons every 15 minutes. We are asked to find the number of balloons created by Fred in 30 minutes and 60 minutes.
To find number of balloons created by Fred in 30 minutes, we will multiply 17 by 2 as 30 is 2 times 15.
[tex]\text{Balloons created in 30 minutes}=2\times 17[/tex]
[tex]\text{Balloons created in 30 minutes}=34[/tex]
Therefore, Fred can create 34 balloons in 30 minutes.
To find number of balloons created by Fred in 60 minutes, we will multiply 17 by 4 as 60 is 4 times 15. This means Fred will create 4 times more balloons in 60 minutes than 15 minutes.
[tex]\text{Balloons created in 60 minutes}=4\times 17[/tex]
[tex]\text{Balloons created in 60 minutes}=68[/tex]
Therefore, Fred can create 68 balloons in 60 minutes.
If angle A and angle B are complementary then the measure of angle A is 45, find a counterexample
The measure of a angle B is 45°.
Given that, angle A and angle B are complementary and ∠A=45°.
What are complementary angles?In geometry, complementary angles are defined as two angles whose sum is 90 degrees.
Now, ∠A + ∠B = 90°
⇒ 45° + ∠B = 90°
⇒ ∠B = 45°
Counter example: If angle A is 90°, then the angle A and angle B are not complementary angles.
Therefore, the measure of a angle B is 45°.
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Which quadratic equation is equivalent to (x + 2)2 + 5(x + 2) – 6 = 0?
(u + 2)2 + 5(u + 2) – 6 = 0 where u = (x – 2) u2 + 4 + 5u – 6 = 0 where u = (x – 2) u2 + 5u – 6 = 0 where u = (x + 2) u2 + u – 6 = 0 where u = (x + 2)
we have
[tex](x+2)^{2} +5(x+2)-6=0[/tex]
Let
[tex]u=(x+2)[/tex]
Substitute in the expression
[tex](u)^{2} +5(u)-6=0[/tex]
therefore
the answer is
[tex](u)^{2} +5(u)-6=0[/tex] is equivalent to [tex](x+2)^{2} +5(x+2)-6=0[/tex]
Answer: C
Step-by-step explanation:
Took the test
Best answer ????...........
-6 - -2 = -4
-5 - - 1 = -4
so y would = x -4
-6 = -2-4
-5 = -1-4
Answer is C
A water tank is in the shape of a cone.Its diameter is 50 meter and slant edge is also 50 meter.How much water it can store In it ? it releases water to a gated apartment building at the rate of 400 liters per second. In how many minutes tank will be empty?
The picture below shows a pole and its shadow: What is the height of the pole? A.196 B.244 C.388 D.364
Answer: 364
Step-by-step explanation: a^2+b^2=c^2
27^2+b^2=365^2
729+b=133,225
-
729 cancel that out then
133,225
-
729
————
132,496 squared~ 364
An item costs $410 before tax, and the sales tax is $20.50 . find the sales tax rate. write your answer as a percentage.
The percentage of sales tax is 5%.
Given that, an item costs $410 before tax, and the sales tax is $20.50.
What is the sales tax?Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.
Let x% be the sales tax.
Now, x% of 410 = 20.50
0.01x ×410 = 20.50
⇒ 4.1x=20.50
⇒ x=20.50/4.1
⇒ x=5
Therefore, the percentage of sales tax is 5%.
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Which of the following is a fundamental quantity?
A) Volume
B) Density
C) Area
D) Mass
E) Acceleration
Find the value of x that makes m ∥ n, m ∥ n.
The value of x that will make m parallel to n is: 40.
Recall:According to the Converse of Corresponding Angles Theorem, the two lines cut across by a transversal line are parallel to each other if the two corresponding angles formed are congruent.
Therefore, let's find the value of x that will make m parallel to n.
Thus,[tex]3x^{\circ} = 120^{\circ}[/tex] (corresponding angles)
Solve for x. Divide both sides by 3[tex]x = 40[/tex]
Therefore, the value of x that will make lines m and n to be parallel to each other is 40.
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what is an equation of the line in slope intercept form m=3 and the y-intercept is (0 4)
And object is traveling at a steady speed of 8 2/3 mph how long will it take to object to travel 5 1/5 miles
Jose drives a truck for a soft drink company. His truck is filled with
15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the truck is carrying, and let b be the number of 70-ounce bottles.Suppose the truck can carry at most 6000 pounds (96,000 ounces).
Using the values and variables given, write an inequality describing this.
PLEASE HELP! I'm struggling so much
Answer : 15c+70b<96,000
Step-by-step explanation:
Ms. Rao buys a computer, a printer, and a scanner for $2,543. The computer costs $1,502 more than the printer. The printer costs $123 more than the scanner. How much does Ms. Rao pay for the computer?
How did you get the answer? I got the answer of $1808. Please explain...
Write an expression of the verbal phrase: the quotient of twelve and the product of three times x
The expression of the verbal phrase 'the quotient of twelve and the product of three times x' is 12 / (3x).
Explanation:The verbal phrase 'the quotient of twelve and the product of three times x' can be expressed as:
12 / (3x)
In this expression, '12' represents the dividend or numerator, '3' represents the factor or multiplier, and 'x' represents the variable or unknown. The quotient symbol '/' represents division, and the multiplication symbol 'x' represents the product of three times x.
A car travel at an average speed of 48 miles per hour. how many miles does it travel in 4 hours and 15 minutes
Bettina’s age is three times Melvina’s age. If 20 is added to Melvina’s age and 20 is subtracted from Bettina’s age, their ages will be equal. How old is each now?
Need help on answer I’m not so sure what to do
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is:
A)5
B)3
C) 2.5
D) 0.2
The slope represents:
A)The total cost of the taxi ride
B)The total number of miles driven
C)The cost per mile traveled
D) the initial cost of the ride
the slope is 2.5
i know this because:
(0,2) (6,18)
18-2 = 16/6 = 2.5
6 - 0 =16/6 = 2.5
Find the derivative of y = sin2 (4x) cos (3x) with respect to x.
A. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)
B. 8 sin (4x) cos (3x) - 3 sin2 (4x) sin (3x)
C. 8 sin (4x) cos (4x) cos (3x) - 3 sin2 (4x) sin (3x) cos (3x)
D. 8 cos (4x) cos (3x) - 3 sin2 (4x) sin (3x)
The function g(x) is a continuous quadratic function defined for all real numbers, with some of its values given by the table below.The quadratic function ƒ(x) is represented by the parabola below. x g(x) -3 0 -2 5 0 9 2 5 3 0 Select all the statements that are true. The function ƒ(x) has a maximum value at x = 4.5. The function g(x) has a minimum value of 0. The maximum value of g(x) is twice the maximum value of ƒ(x). Neither function has a minimum value.
The function g(x) has a minimum value of 0, but we cannot determine the maximum value of g(x) or compare it to the maximum value of f(x). The statements about the maximum value of ƒ(x) and the lack of minimum value for both functions are not supported by the given information.
Explanation:The function g(x) is a continuous quadratic function that can be represented by a parabola. From the given table, we can observe that the minimum value of g(x) is 0 and it occurs when x = -3 or x = 3. Therefore, the statement 'The function g(x) has a minimum value of 0' is true.
To determine the maximum value of g(x), we need to find the vertex of the parabola representing g(x). Since the function is continuous and quadratic, the vertex occurs at the axis of symmetry. The axis of symmetry is given by x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, the equation representing g(x) is not given, so we cannot determine the exact maximum value of g(x) or compare it to the maximum value of f(x).
Based on the given information, we cannot determine whether the function f(x) has a maximum value at x = 4.5 or if the maximum value of g(x) is twice the maximum value of f(x). Therefore, the statements 'The function ƒ(x) has a maximum value at x = 4.5' and 'The maximum value of g(x) is twice the maximum value of ƒ(x)' are false.
Regarding the statement 'Neither function has a minimum value,' it is not accurate based on the given information. We already established that g(x) has a minimum value of 0.
What is the slope of the line passing through the points (2,7) and (-1,3)?
Slope of line passing through 2 points, The slope of line passing through points (2,7) and (-1,3) is 4/3.
What is formula for slope of line passing through 2 points?Slope=(y2-y1)/(x2-x1)
The line is passing through two points (2,7) and (-1,3).
The formula for slope is (y2-y1)/(x2-x1).
x1=2,x2=-1,y1=7,y2=3
Slope=3-7/-1-2
=-4/-3
=4/3
Therefore slope of line is 4/3 if line passing through the points (2,7) and (-1,3).
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a bag contains 42 cups of dog food. your dog eats 2 1 3 cups of dog food each day how many days does the bag of dog food last
divide 42 by 2 1/3
2 1/3 = 7/3
42 / 7/3 =
42 * 3/7 =
126/7 = 18
it will last 18 days
The number of days it will take the dog to consume the 42 cup of food will be 18 days.
Total cups of dog food = 42 cups Amount of cups consumed per day = [tex] 2 \frac{1}{3} \: cups [/tex]To obtain the number of days it will take to consume the entire food :
Divide the total amount of food by the amount consumed per dayHence,
(42 ÷ (7/3))
Take the reciprocal of 7/3 and change the operation sign to multiplication
42 × 3/7 = (42 × 3) / 7 = 126 / 7 = 18 days
Therefore, it will take the dog 18 days to finish up the 42 cups of food.
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Given the quadratic function 3x^(2) =8x-5 what are the values of x?
Answer:
The values of x are [tex]\frac{5}{3}[/tex] and 1.
Step-by-step explanation:
Given quadratic function[tex]3x^2=8x-5[/tex]
We have to solve for x.
Consider the given quadratic function [tex]3x^2=8x-5[/tex]
This can be written as [tex]3x^2-8x+5=0[/tex]
We can solve the above quadratic equation using middle term split method,
-8x can be written as -3x - 5x
Thus, the equation becomes,
[tex]3x^2-8x+5=0[/tex]
[tex]\Rightarrow 3x^2-3x-5x+5=0[/tex]
Taking 3x common from first two term and -5 common from last two terms, we get,
[tex]\Rightarrow 3x(x-1)-5(x-1)=0[/tex]
[tex]\Rightarrow (3x-5)(x-1)=0[/tex]
Now using zero product property [tex]a.b=0 \Rightarrow a=0\ or\ b=0[/tex] , we have,
[tex]\Rightarrow (3x-5)=0[/tex] or [tex]\Rightarrow (x-1)=0[/tex]
[tex]\Rightarrow x=\frac{5}{3}[/tex] or [tex]\Rightarrow x=1[/tex]
Thus, The values of x are [tex]\frac{5}{3}[/tex] and 1.
When fractions share the same number on the bottom what is it called?
Step-by-step explanation: When fractions have the same bottom number, they're called like fractions. When adding and subtracting fractions, our goal is to get like fractions or fractions that have the same denominator.
Also, it's easy to compare like fractions because you just have to look at the numerators of each of the fractions you are givemn.
in the diagram below eg=100, ef=4x-20, and fg=2x+30
The lengths of segments x=15, EF=40, FG=60.
To solve for x, we can use the fact that the total length of segment EG is equal to the sum of the lengths of segments EF and FG.
EG = EF + FG
Substituting the given values, we get:
100 = 4x - 20 + 2x + 30
Combining like terms, we get:
100 = 6x + 10
Subtracting 10 from both sides, we get:
90 = 6x
Dividing both sides by 6, we get:
15 = x
Therefore, the value of x is 15.
We can now solve for the lengths of segments EF and FG.
EF = 4x - 20
Substituting the value of x, we get:
EF = 4(15) - 20
EF = 60 - 20
EF = 40
FG = 2x + 30
Substituting the value of x, we get:
FG = 2(15) + 30
FG = 30 + 30
FG = 60
Therefore, the lengths of segments EF and FG are 40 and 60, respectively.
Answer:
x = 15
EF = 40
FG = 60
Which is greater 300 kelvins or 34 degrees Celsius ? Show your work
To answer this item, we are to convert one of the unit to the other. The approach to answering is to convert the 34 degrees Celsius to kelvin by the equation,
T = C + 273.15
Substituting the known value,
T = (34) + 273.15 = 307.15 K
Since 307.15K is greater than 300K then, the greater value is 34 degrees C.
ANSWER: 34 degrees C
Using the segment addition postulate, which is true?
AB + BC = AD
AB + BC = CD
BC + CD = AD
BC + CD = BD
Answer: The answer is (d) BC + CD = BD.
Step-by-step explanation: We are given the number line and four points A, B, C and D on the line with co-ordinate -6, -1, 2 and 8 respectively.
We are to select the correct statement out of the given four.
(a) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = AD = 14 ≠ 8.
So, this option is incorrect.
(b) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = CD = 6 ≠ 8.
So, this option is incorrect.
(c) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = AD = 14 ≠ 9.
So, this option is incorrect.
(d) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = BD = 9.
So, this option is correct.
Thus, the correct option is (d).
What does it mean for event b to be independent of event​ a?