Answer:
x < 9
Step-by-step explanation:
Our original inequality:
[tex]9(4x-8) < 4(6x+9)[/tex]
Firstly, let's expand the brackets on both sides:
[tex]36x - 72 < 24x + 36[/tex]
Now, we add the 72 over to isolate the [tex]x[/tex]:
[tex]36x < 24x + 108[/tex]
Next, we take away the [tex]24x[/tex] to isolate the [tex]x[/tex]:
[tex]12x < 108[/tex]
Finally, we divide both sides by 12 to convert the [tex]12x[/tex] to [tex]x[/tex]:
[tex]x < 9[/tex]
This means our final answer is [tex]x < 9[/tex].
Find the measure of one interior angle of a regular 21-gon.
A. 160
B. 162.9
C. 165.6
D. 165
The gravel path is 5.6 cm long
10 1/9 rounded to the whole or half
Answer:
Your answer is 68. Hope you got a big score!
Answer both 2 and 3 please
2.
1 day = 24h
1h = 60min
We have 4h 20min
[tex]4h + 20min = 4h+\dfrac{20}{60}h=4h+\dfrac{1}{3}h=4\dfrac{1}{3}h=\dfrac{13}{3}h[/tex]
[tex]\dfrac{\frac{13}{3}}{24}=\dfrac{13}{3}\cdot\dfrac{1}{24}\\\\\huge\boxed{(D)\ \dfrac{13}{72}}[/tex]
3.
6:51PM + 9min → 7:00PM
7:00PM + 27min → 7:27PM
9min + 27min = 36min
[tex]36min=\dfrac{36}{60}h=\dfrac{3}{5}h[/tex]
[tex]\huge\boxed{(C)\ \dfrac{3}{5}}[/tex]
Which of the following graphs represents the solution set
x>5?
Answer:
Graph A is correct.
Step-by-step explanation:
Graph A is the graph with the open circle and the arrow pointing to the right.
i need helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
sorry. thats a hard one. math isn't. my area best of luck
Consider the circle represented by this equation.
x² + 4x + y2 - 2y - 4 = 0
Which features are features of the circle?
Answer:
See below
Step-by-step explanation:
arrange to standard form (x-h)^2 + (y-k)^2 = r^2 h,k = center r = radius
x^2 - 4x + y^2 + 2y = 4 complete the square for 'x' and 'y'
(x-2)^2 - 4 + (y-1)^2 -1 = 4
(x-2)^2 + ( y-1)^2 = 4 + 4 + 1 = 9 '9' is equal to r^2 so r = 3
center = 2,1 radius = 3
Answer:
you're welcome!!!
Step-by-step explanation:
HELP PLEASE
which choice is equivalent to the quotient below? √15/3√3
A. √5/3
B. √5/9
C. √5/√3
D. √4
Answer:
A - [tex]\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{15} = \sqrt{5} *\sqrt{3} \\\frac{\sqrt{5} *\sqrt{3}}{3*\sqrt{3}} = \frac{\sqrt{5}}{3}[/tex]
Answer: √5/3
Step-by-step explanation:
Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)
Answer:
-63
Step-by-step explanation:
3 - 6(12 - 1) = 3 - 6(11) = 3 - 66 = -63
Laboratory tests show that the lives of
light bulbs are normally distributed with
a mean of 750 hours and a standard
deviation of 75 hours. Find the
probability that a randomly selected
light bulb will last between 750 and 825
hours.
Answer in percentage!!!
This result is approximate.
=========================================================
Explanation:
mu = 750 = mean
sigma = 75 = standard deviation
The raw scores or x values are x = 750 and x = 825
Let's compute the z score for each x value
z = (x - mu)/sigma
z = (750 - 750)/75
z = 0
and
z = (x - mu)/sigma
z = (825 - 750)/75
z = 1
Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.
Use a z score table to determine that
P(z ≤ 0) = 0.5
P(z ≤ 1) = 0.84314 approximately
So,
P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)
P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)
P(0 ≤ z ≤ 1) = 0.84314 - 0.5
P(0 ≤ z ≤ 1) = 0.34314 approximately
The value 0.34314 then converts to 34.314% which rounds to 34%
Or you could use the empirical rule as shown below. The pink section on the right is marked 34% which is approximate. This pink section is between z = 0 and z = 1.
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(-3) = -1
B.
h(13) = 18
C.
h(2) = 16
D.
h(8) = 21
The true statement is h(2)=16.
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function. The range of a function is the set of values that the function assumes.
Given:
domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25,
Also, h(8) = 19 and h(-2) = 2,
Now,
2=h(-2)< h(2)<h(8) =19
h(8)=19≠21
h(13)> h(8) =19
h(-3)< h(-2) =2 [1 ≤ h(x) ≤ 25]
Hence, h(2)=16
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Situation:
A 45 gram sample of a substance that's
used to preserve fruit and vegetables has
a k-value of 0.1109.
N-Noe-kt
No - initial mass (at time t - 0)
N = mass at time t
k - a positive constant that depends on
the substance itself and on the units
used to measure time
t-time, in days
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Enter the correct answer.
+00
DONE
A function assigns the values. The half life of the substance is 6.25 days.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function for the substance as [tex]N= N_o e^{-kt}[/tex], therefore, the half life of the substance can be written as,
[tex]N= N_o e^{-kt}\\\\\dfrac{N}{N_o}= e^{-kt}[/tex]
Since we need to find the half life, therefore, the ratio of the initial mass and the mass after half-life will be 1/2.
[tex]\dfrac12= e^{-kt}\\\\\ln (0.5) = -kt[/tex]
Given the value of k is 0.1109, therefore,
[tex]\ln (0.5) = -kt\\\\\ln (0.5) = -(0.1109)t\\\\t = 6.25[/tex]
Hence, the half life of the substance is 6.25 days.
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1) Which situations are BEST modeled by an exponential function?
es
A) The yearly depreciation of a car.
B) An investment compounded annually.
C) The cost of screws sold by the pound.
D) The amount of sugar to make a pound of fudge.
E) The annual growth rate of a city's population.
A function assigns the values. The correct options are A, B, and E.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The situations that can be best modelled by exponential functions are:
A) The yearly depreciation of a car.
B) An investment compounded annually.
E) The annual growth rate of a city's population.
Hence, the correct options are A, B, and E.
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Given the function h of x equals negative 5 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (–∞, 0).
The function is decreasing on the interval (0, ∞).
The function is increasing on the interval (0, ∞).
Answer:
The function is decreasing on the interval ( 0,∞)The function h(x) = -5√x is decreasing on the interval (–∞, 0) is true, Option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function h of x equals negative 5 times the square root of x.
h(x) = -5√x
The value of h(x) decreases as the value of x increases.
The function h(x) is a decreasing function over the interval (–∞, 0) because it is a negative function over the interval.
Hence, the function is decreasing on the interval (–∞, 0) is true.
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Nitrogen and oxygen are the most abundant gases in Earth’s atmosphere. A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.
Which statements describe writing 0.00000000003 in scientific notation?
The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.
The complete question is
Which statements describe writing 0.00000000003 in scientific notation? Check all that apply.
A.The exponent is negative.
B. The exponent is positive.
C.The coefficient is 0.3.
D.The exponent represents the number of places the decimal moves.
E.The decimal moves to the right.
What is meaning of Scientific Notation ?Scientific Notation means writing a decimal number in the form of 10ˣ .
It is given that
A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.
= 3 × 10⁻¹¹
(scientific notation)
The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.
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Which statement describes the quadratic inequality in factored form that represents the relationship greater than or equal to the quadratic equation containing the point (6, -8) on the boundary and zeros -4 and 10?
In the equation given, the quadratic inequality that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).
What is the quadratic inequality about?Note that a quadratic function exist in factored form is as:
y = a(x - a)(x - b)
The zeros of the equation is seen at x = (-4, 10)
Therefore, one need to write an expression for the quadratic inequality and so it will be:
y ≥ a(x - a)(x - b)
Also note that at At point (6, -8), we also have:
-8 = a(6 - (-4))(6 - 10)
-8 = a(6 + 4)(6 - 10)
-8 = a(10)(-4)
-8 = -a(40)
a = 0.2.
Therefore, In the equation given, the quadratic inequality that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).
See full question below
Which statement describes the quadratic inequality in factored form that represents the relationship greater than or
equal to the quadratic equation containing the point (6, -8) on the boundary and zeros-4 and 10?
Oy2-0.2(x + 4)(x - 10)
Oy≥ 0.2(x + 4)(x - 10)
O y 20.2(x-4)(x + 10)
Oy2-0.2(x-4)(x + 10)
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The most efficient first step in the process to factor the trinomial 2x^3 - 18x^2 + 40x is:
A. Factor out 2
B. Factor out -1
C. Factor out 2x
D. Factor out (x-5)
Considering the common factor, the most efficient way to factor the expression 2x³ - 18x² + 40x is given by:
C. Factor out 2x.
How to factor an expression?The most efficient way to factor the expression is factoring out the common factor.
In this problem, the expression is:
2x³ - 18x² + 40x
We have that:
The common factor of 2, -18 and 40 is 2.Of x³, x² and x, it is of x.Hence the common factor is of 2x, which means that option C is correct.
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What is the research hypothesis when using anova procedures?
When using ANOVA procedures, the research hypothesis is: there is no significance difference within the mean values of the groups.
What is a Research Hypothesis in ANOVA Procedure?ANOVA procedure compares the mean values of different groups that are administered with treatments. The research hypothesis, such as the null hypothesis would be stated as: no significance difference in the mean values within the groups.
Thus, we can conclude that the research hypothesis when using the ANOVA procedures can be stated as a null hypothesis, which states that: there is no significance difference within the mean values of the groups.
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Brainliest!
Which system is represented in the graph?
y>x²-2x-3
y > x + 3
Oy
y
Oy2x²-2x-3
y ≤ x + 3
Oy>x²-2x-3
y
Answer:
y ≥ x² -2x -3y ≤ x +3Step-by-step explanation:
When matching graph to inequality, the first things to look for are the nature of the boundary line (solid or dashed), and the direction of shading relative to the boundary line (above or below, left or right).
Boundary lineThe boundary line of the solution set of an inequality will be solid if the line is included in the solution. That is, the inequality will include the "or equal to" case. The corresponding inequality symbols are ≤ or ≥.
The boundary line of the solution set will be dashed if the line is not included in the solution. The corresponding inequality symbols are < or >.
ShadingThe shading will be above the boundary line if the solution set includes larger y-values than those on the boundary. This will be the case when the inequality is of the form y > ( ) or y ≥ ( ).
For inequalities of the form y < ( ) or y ≤ ( ), the shading will be below the boundary line.
Similarly, the shading for an inequality of the form x > ( ) will be right of the boundary line, where x-values are greater. For inequalities of the form x < ( ), the shading will be to the left of the boundary line.
ApplicationIn the given graph, both boundary lines are solid, so both inequalities will include the "or equal to" case. This eliminates choices A, B, D.
The shading is above the quadratic boundary line, and below the linear boundary line, so the inequalities can be expected to be of the forms ...
y ≥ x² +...y ≤ x +...These forms match choice C:
y ≥ x² -2x -3y ≤ x +3I need help with this
Step-by-step explanation:
please mark me as brainlest
Find the values of a and b if 5+3√3/7+4√3 = a + √3b
The values of a and b are :
[tex]a = \sqrt{3} \\ \\ •\sqrt{3} b = - 1 \\ \\ b = \frac{ - 1}{ \sqrt{3} }. [/tex]
Expand & simplify
3(t+5)+5(t−6)
Answer:
8t - 15
Explanation:
⇒ 3(t+5)+5(t−6)
distribute inside parenthesis
⇒ 3(t) + 3(5) + 5(t) + 5(-6)
multiply the variables
⇒ 3t + 15 + 5t - 30
collect like terms
⇒ 3t + 5t + 15 - 30
add/ subtract like terms
⇒ 8t - 15
Solution: 8t-15
Detailed explanation:
First the problem asks us to expand
[tex]\tt 3(t+5)=3\cdot t +3\cdot5=3t+15[/tex]
Similarly
[tex]\tt 5(t-6)=5\cdot t -5\cdot 6=5t-30[/tex]
Therefore
[tex]\tt 3t+15+5t-30[/tex]
Upon combining like terms
[tex]\tt 8t+15-30[/tex]
Upon doing this further
[tex]\tt 8t-15[/tex]
The sum of ages of Clayman and Ato is 25 years. In five years' time, the age of Ato will twice the age of Clayman now. a. How old is Clayman? b. How old is Ato?
Clayman is 10 years old and Ato is 15 years old
Word problems leading to equationsLet the age of Clayman be x
Let the age of Ato be y
If the sum of ages of Clayman and Ato is 25 years. then;
x + y = 25
x = 25 - y ...... 1
In five years time;
Age of Clayman = x + 5
Age of Ato = y + 5
If in five years' time, the age of Ato will twice the age of Clayman now, then;
y+5 = 2x ............. 2
Substitute equation 1 into 2
y +5 = 2(25-y)
y + 5 = 2(30 - y)
y + 5 = 50 - 2y
3y = 45
y = 15
Since x + y = 25
x = 25 - 15
x = 10
Therefore Clayman is 10 years old and Ato is 15 years old
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1. Michael Murphy is employed at Agilent Technologies. He has family medical coverage through the group medical plan that Agilent provides for its employees. The annual premium cost for Michael's family is $5,260. The company pays 70 percent of the cost. How much is deducted from his weekly paycheck for medical insurance? (Note: 52 weeks in a year)
$28.12
$29.74
$30.35
$32.66
None of these choices are correct.
2. Brenda Baker has a group health insurance policy from her job at a bank. Her annual premium is $3,500. The policy has a $500 deductible and pays 80% of all medical costs with a stop-loss provision of a limit of $4,000 for out-of-pocket expenses, after the deductible is paid. If Brenda had medical bills totaling $12,000, how much were her out-of-pocket medical costs, including her premiums?
$5,900
$6,300
$6,700
$6,900
None of these choices are correct.
Addition is one of the four fundamental mathematical operations. The correct option is E, None of these choices are correct.
What is Addition?Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
1. The annual premium cost for Michael's family is $5,260. The company pays 70% of the cost. Therefore, the cost he needs to may is,
30% of $5,260
= 0.30 × $5260
= $1578
Since the premium is needed to be paid in 52 week, therefore, the premium cost per week will be,
Premium cost = $1578/52 = $30.35
Hence, the correct option is C, $30.35.
2. Brenda annual premium is $3,500. Also, her medical bills is totaling to $12,000. Therefore, the total amount that is paid by the Brenda in purchasing Insurance and paying the bill is,
Amount Brenda spend = $3,500 + $12,000 = $15,500
The policy has a $500 deductible and pays 80% of all medical costs with a stop-loss provision of a limit of $4,000 for out-of-pocket expenses, after the deductible is paid. Therefore, the amount that she can get is,
Amount she can get = $500 + $4,000 = $4,500
Now, the amount that she needs to pay from her pocket is,
Amount = $15,500 - $4, 500 = $11,000
Hence, the correct option is E, None of these choices are correct.
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A fishing gear shop from boulder, co bought $23,000 worth of fishing rods from a liquidator in pasadena, ca. the shop sold the fishing rods for $49,000, making a profit of $250 per fishing rod. there were __?__ fishing rods involved.
Subtraction is a mathematical operation that reflects the removal of things from a collection. The boulder.co bought 104 fishing rods.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given the cost price of all the fishing rods is $23,000, also the selling price of all the fishing rod is $49,000. Therefore, the total profit from this transaction is,
Profit = $49,000 - $23,000 = $26,000
Since the profit on a single fishing rod is $250, while the total profit is $26,000. Therefore, the number of fishing rods can be written as,
Number of Fishing rod = Total profit/ Profit per rod
= $26,000 / $250
= 104
Hence, the boulder.co bought 104 fishing rods.
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How much of a radioactive kind of francium will be left after 44 minutes if you start with 2,616 grams and the half-life is 22 minutes?
Step-by-step explanation:
sorry but I dont know
Answer: 654 grams
Step-by-step explanation:
that's the answer it gave it when I got it wrong.
Kevin earns $240,000 a year as a surgeon. He contributes $20,500 to
his pre-tax 401(k) retirement account and pays the government 28% of his
remaining salary per year. How much is his net pay?
Using proportions, it is found that his net pay is of $158,040.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
His first discount is for the retirement account, hence the taxable amount is:
T = 240000 - 20500 = $219,500.
He pays 28% of that in taxes, hence his net pay is of 100 - 28 = 72% of $219,500, hence:
N = 0.72 x 219500 = $158,040.
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The vertex of this angle is:
R
T
S
The vertex of this angle is point S.
which one is it? I will give you twenty points, if you will answer
Answer:
A fraction equivalent to [tex]\frac{1}{2}[/tex] on the number line is [tex]\frac{3}{6}[/tex].
Drag the dot to [tex]\frac{3}{6}[/tex] on the number line.
Step-by-step explanation:
3 is half of 6. To check if this is correct multiply [tex]\frac{1}{2}[/tex] and 3.
[tex]\frac{1}{2}*3=\frac{3}{6}[/tex]
Hope this helps!
If not, I am sorry.
4
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6?
4
O y=-6x+²/
O y=x-6
Oy=x+6
Oy=6x+
k
Answer:
y = 5x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 5 and c = - 6 , then
y = 5x - 6 ← equation of line
The equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
The equation of a linear function is typically written in the form "y = mx + b," where "m" represents the slope and "b" represents the y-intercept.
Given that the slope is 5 and the y-intercept is -6, the equation becomes:
y = 5x - 6
Here's the calculation:
The slope (m) is 5, and the y-intercept (b) is -6. Therefore, the equation becomes:
y = 5x - 6
This equation represents a linear function with a slope of 5 and a y-intercept of -6.
Hence the equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
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