Answer:
[tex]\dfrac{27}{20}[/tex]
Step-by-step explanation:
First, convert both numbers into fractions:
[tex]\dfrac{15}{1} \div \left(\dfrac{10}{3}\right)^2[/tex]
Then, apply the exponent of the second fraction in parentheses to its numerator and denominator.
[tex]\dfrac{15}{1} \div \left(\dfrac{10^2}{3^2}\right)[/tex]
[tex]\dfrac{15}{1} \div \dfrac{100}{9}[/tex]
Finally, multiply the first fraction by the reciprocal of the second fraction.
(Skip, Flip, Multiply)
[tex]\dfrac{15}{1} \times \dfrac{9}{100}[/tex]
[tex]\dfrac{135}{100}[/tex]
And simplify.
[tex]\dfrac{135 \div 5}{100 \div 5}[/tex]
[tex]\dfrac{27}{20}[/tex]
-8-x=x-4x for solving linear equations: variable on both sides. Please hurry I need the answer quickly.
Answer: -4
Step-by-step explanation:
1. Add x on both sides
-8-x=x-4x → -8=2x-4x
2. Combine like terms
-8=2x-4x → -8=-2x
3. Divide negative 2 from both sides
-8=2x → -4=x
19. MODELING In Example 6, 44% of the voters say they plan to reelect the mayor. The poll has a margin of error of ±3% percentage points. Use a model to write and solve an absolute value inequality to find the least and greatest percents of voters who plan to reelect the mayor.
The absolute value inequality to find the percentages is given as follows:
|P - 44| ≤ 3.
Then the percentages are given as follows:
Least: 41%.Greatest: 47%.What is the absolute value inequality?The estimate of the percentage is of:
44%.
The margin of error is of:
±3%.
Both the estimate and the margin of error are taken from the problem.
This means that the absolute difference between the percentage P and the estimate of 44% is of at most the margin of error of 3%, hence the inequality is given as follows:
|P - 44| ≤ 3.
The absolute difference means that the difference can be either positive or negative.
Then the lowest percentage is obtained when:
P - 44 = -3
P = -3 + 44
P = 41.
The highest percentage is obtained when:
P - 44 = 3
P = 3 + 44
P = 47.
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There are 22 girls and 28 boys on the dukes team. Write the ratio of boys to total students on the dukes team
Answer:
28:50
Step-by-step explanation:
22+28=50, and that is the total amount of students. The number of boys go first in the ratio, then total students.
need help assap look at attachment
Answer: See the attachment
Step-by-step explanation: You would use the formula y=mx+b and since b is the y-intercept you would plug that into the equation and then plug in 3/4 as m resulting in
y=3/4x -1 then you just graph it!
Place a point on -1 in the y axis, (0,-1) then go up three units up and four units right, (4,2)
The amount of carbon 14 present in a paint after t years is given by A(t)=Ae-0.000121. The paint contains 25% of its
carbon 14. Estimate the age of the paint.
The age of the paint is 14,290.0 years old
What is the rule of half-life?For any particular drug, understanding the concept of half-life is helpful in calculating steady-state concentrations and excretion rates. Although different drugs have different half-lives, they all adhere to the same principle: 50% of the initial drug dose is eliminated from the body after one half-life.
What is the half-life of carbon 14?Since radiocarbon (14C) has a half-life of 5700 30 years, it is especially helpful for dating in archaeology. However, the so-called Gamow-Teller ß-decay, an exceptional hindrance to the beta decay from 14C to 14N, is what causes this half-life to be so long.
According to the given question :-
0.18 = e^(-0.00012t)
ln(0.18) = -0.00012t
t = - ln(0.18) / 0.00012 ≈ 14289.98690076605833 ≈ 14,290.0 years old
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Identify the slope and y-intercept of the line below.
Answer:
Negative slope of 3 so -3x and -9y
Step-by-step explanation:
-3x=-9y
Answer:
slope = -3 ; y- intercept = (0,-9)
Step-by-step explanation:
A (-3,0)
B(0,-9)
slope = (-9-0)/(0-(-3)
-9/3
-3
30 PTS, SHOW YOUR WORK How much carbon dioxide will you prevent from entering the atmosphere in one year, if you replace a 100-watt light bulb with a CFL bulb that uses 30 watts in a fixture that you have on 8 hours per day? (round to the hundredths place)
(1.37 pounds of CO2 per kWh)
The amount of carbon dioxide will you prevent from entering the atmosphere in one year is 280028 lb
How much carbon dioxide will you prevent from entering the atmosphere in one year?We are given 1.37 pounds of carbon dioxide per kWh
Using a 100-watt light bulb daily for 8 hours, for a year, the amount of carbon dioxide produced will be:
100 × 1.37 × 8 ×365 = 400040 lb
Using a 30-watt CFL bulb for 8hrs/ day for a year, the amount of carbon dioxide produced will be:
30× 1.37 × 8 × 365 = 120012 lb
Therefore, carbon dioxide prevented:
= 400040-120012
= 280028 lb
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In Exercises 1 and 2, classify the triangle by its sides and by measuring its angles.
Figure 1 is representing a right-angle triangle and figure 2 is representing the isosceles triangle.
What is a triangle?
The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given diagram in the question,
For figure 1.
It is a right-angle triangle because it contains an angle of 90°.
For figure 2.
It is an isosceles triangle because according to the figure its two sides are the same which indicates that it is an isosceles triangle.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answer:
[tex]18x-9=18x-9\\\\3(6x-3)=18x-9\\\\x=4.5[/tex]
Step-by-step explanation:
Each equation is =72. So for the first 4 options, just find equivalent expressions for the left side:
[tex]\frac{3}{5}(30x-15)=18x-9\\\\18x-15\neq 18x-9\\\\50x-25\neq 18x-9\\\\18x-9=18x-9\\\\3(6x-3)=18x-9[/tex]
For x=4.5, must solve original equation:
18x-9 = 72
18x = 81
x = 4.5
You are visiting Mexico and need to convert your U.S. dollar to the Mexican Peso. How many Mexican Peso will you have from $350?
Conversion Ratio:
$1 = Mex$20.16
Answer:
Mex$7,056
Step-by-step explanation:
$1 = Mex$20.16
$350 = x
cross multiply
$350 * Mex$20.60 = Mex$7,056
Answer: Mex$7056
Step-by-step explanation:
Make the proportion:
$1 - Mex$20.16
$350 - x
[tex]\displaystyle\\x=\frac{ 350(20.16)}{1} \\\\x=350(20.16)\\\\[/tex]
x=Mex$7056
Suppose Briana spends an average of 0.5 hours on each assignment from her classes
and 2 hours per day at basketball practice.
a) How much total time would be required for 4 assignments and 2 days of practice?
Answer:
6 hours I think
100 Points
What is the value of the logarithmic or exponential expression?
Select True or False for each statement
Answer:
True, False, False-------------------------------------------
Let's simplify left sides of each statement and compare with right sides:
[tex]3^{5log_32}=3^{log_32^5}=3^{log_332}=32 \implies True[/tex][tex]2 ln\ e^{1/4}=2*1/4*ln\ e^{}=2*1/4*1=1/2\implies False[/tex][tex]e^{2ln e-1}=e^{2*1-1}=e^{2-1}=e^1=e \implies False[/tex]"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The rocket reaches its maximum height at 2.25 second(s) after launch
The maximum height reached by the object is 88 feet.
What is the maximum height the rocket reached?Given function:
h(t) = -16t² + 72t + 7
By differentiating the function, we have
h'(t) = -32t + 72
Set the function to 0
-32t + 72 = 0
32t = 72
Divide both sides by 32
t = 2.25
Hence, the time is 2.25 seconds
To find the maximum height reached by the rocket,
Substitute t = 2.25 into
h(t) = -16t² + 72t + 7
h(2.25) = -16(2.25)² + 72(2.25) + 7
= -16(5.0625) + 162 + 7
= -81 + 162 + 7
h(2.25) = 88
In conclusion, the maximum height the rocket reached is 88 feet
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A new employee charged $7220 on his credit card to relocate for his first job. After noticing that the interest rate for his balance was 27% compounded monthly, he stopped charging on that account. He wishes to pay off his balance in years using automatic payments sent at the end of each month.
a. What monthly payment must he make to pay off the account at the end of 4 years?
b. How much total interest will he have paid?
a. The monthly payment must be $193.53 in order to pay off the account at the end of 4 years.
b. The total interest paid will be $4372.02.
i’ve been struggling with this and it’s due soon! pictures are below of the question.
a) If the sum of the square of the larger side is smaller than the squares of the shorter sides, then the triangle is an acute triangle.
b) To determine if a triangle is a right triangle.
c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.
What is converse of the Pythagorean Theorem?If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Given,Pictures
According to the converse of the Pythagorean Theorem.
a) If the sum of the square of the larger side is smaller than the squares of the shorter sides, then the triangle is an acute triangle.
b) To determine if a triangle is a right triangle.
c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.
Therefore,
a) If the sum of the square of the larger side is smaller than the squares of the shorter sides, then the triangle is an acute triangle.
b) To determine if a triangle is a right triangle.
c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.
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Arianna invests $5700 in a new savings account which earns 5.2 % annual interest, compounded monthly. What will be the value of her
investment after 3 years? Round to the nearest cent.
The amount will be $6660 after 3 years. It can be solved by the cocept of the compound interest.
What is compound interest?
In compound interest, the interest is added in the principal amount after the end of each term. The value after addition the interest is considered as the principal amount for the next term.
The annual interest is 5.2% hence, monthaly interest will be 5.2\12%
Apply the formula of conpound interest.
[tex]A=P(1+\frac{r}{100})^t[/tex]
Here, A is the total amount after the end of time period t, P is the initial amount, and r is the rate of intrest at which the amount is compounded.
Substitute $5700 for P, 5.2/12% for r and 36 for t. Here t is 36 becasue the amount compounded monthly and there are 36 months in a year.
[tex]A=\$ 5700(1+\frac{5.2/12}{100})^{36}\\= \$ 6660[/tex]
Hence, the amount will be $6660 after 3 years. It can be solved by the cocept of the compound interest.
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What is a zero of the function f(x)=5x-20?
Answer:
x = 4
Step-by-step explanation:
to find the zero equate f(x) to zero , that is
5x - 20 = 0 ( add 20 to both sides )
5x = 20 ( divide both sides by 5 )
x = 4
then the zero is x = 4
Can't do this write this number in standard forms 3,000 + 1,600 + 8/10 + 3 ones what how would you solve this problem
we get the desired result after solving as 4603.8 .
What is the rule of BODMAS?In mathematics, the BODMAS rule is a rule or order that is used to condense arithmetic expressions with several operators. When an equation has multiple operators, we must first determine the correct order in which to solve the expression. The BODMAS rule is always used to resolve the issue of using algebraic symbols.
For this type of problem,
We generally use BODMAS
Here,
B= Bracket
O= Off
D= Divide
M= Multiply
A= Addition
S= Subtraction
Given expression,
3,000 + 1,600 + 8/10 + 3
By following above steps we get,
First we going to divide,
3,000 + 1,600 + 0.8 + 3
Then we move to addition,
4603.8
Hence we get the desired result as 4603.8
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pls help me on this question
Answer:
[tex]B. \;\dfrac{24}{40}[/tex]
[tex]C. \;\dfrac{3}{5}[/tex]
Step-by-step explanation:
What is the solution of this inequality?
r−6>−11
Drag and drop the choices to correctly complete the inequality.
Plss help me
The solution to the inequality r - 6 > −11 will be r > -5.
How to solve inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Based on the information, the solution to the inequality r - 6 > −11 will be solved thus:
r - 6 > −11
Collect the like terms
r > - 11 + 6
r > -5
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the sign at the garbage sale said 12 paper back books could be purchased for 8$ how much 3 paper backbooks cost
[tex]\begin{array}{ccll} books&\$\\ \cline{1-2} 12 & 8\\ 3& x \end{array} \implies \cfrac{12}{3}~~=~~\cfrac{8}{x} \\\\\\ 4 ~~=~~ \cfrac{ 8 }{ x }\implies 4x=8\implies x=\cfrac{8}{4}\implies x=2[/tex]
Answer:
2$
Step-by-step explanation:
If 12 paperback books could be purchased for 8$,
We need to divide by 4 on each side to find the answer.
Therefore, 3 paperback books costs 2$.
I would appreciate it if you mark my answer as brainliest.
A population of lizards in a large region doubles every year. The number of lizards can be
modeled by the equation y = 500 * 2 ^ x where
× is the number of vears after a researcher
measures the population size . When x = - 3
-3what does the value of y represent ?
The value of y when x = -3 represents that the population of the lizard three years before the researcher measures the population size is 63
How to interpret the function at x = -3?From the question, we have the following parameters that can be used in our computation:
y = 500 * 2 ^ x
The above equation is an exponential function
Such that
x is the number of years after a researcher measures the population size
When x = -3, we have the equation to be
y = 500 * 2^-3
Evaluate the product
y = 62.5
Approximate
y = 63
This means that the value of y at x = -3 is 63
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A town has a population of 17000 and grows at 3% every year. What will be the
population after 10 years, to the nearest whole number?
If the population grows 3% every year, then each year's population is 103% of the previous year's population. This gives us the exponential function:
[tex]f(x) = 17000 (1.03)^x[/tex]
17000 for the current population, 1.03 growth factor for the 103%, raised to the x power because we'll need 103% of 103% of 103% and so on until we multiply by 103% for the correct number of years.
[tex]f(10) = 17000(1.03)^{10} \approx 22846.578448850072648[/tex]
Following standard math rounding this would round to 22,847 people.
If you argue that last 0.57844 of a person really round up, you could argue that this is really 22,846 people.
Question
Evaluate the expression when b=9 .
24/b+8 =
The evaluated expression of 24 / b + 8 when b = 9 is [tex]10\frac{2}{3}[/tex]
How to evaluate an expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) .
In other words, an expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
Therefore, let's evaluate 24 / b + 8 when b = 9
Hence,
[tex]\frac{24}{9}+8 = \frac{24+ 72}{9}=\frac{96}{9} = 10\frac{6}{9}=10\frac{2}{3}[/tex]
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What is one over 2 X -5 equal 10 -3 over 4X
The value of x is 15 if the expression is 1/2x−5=10−3/4x after applying the arithmetic operation.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The expression is:
1/2x−5=10−3/4x
After solving:
5x/4 = 15
5x = 60
x = 60/5
x = 12
Thus, the value of x is 15 if the expression is 1/2x−5=10−3/4x after applying the arithmetic operation.
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HELPPPPPPPP! please!
Select all the statements that are true for any value of x.
A. 7x + (2x + 7) = 9x + 7
B. 7x + (2x - 1) = 9x + 1
C. 1/2x + (3 - 1/2x) = 3
D. 5x – (8 - 6x) = -x - 8
E. 0.4x - (0.2x + 8) = 0.2x - 8
F. 6x - (2x - 4) = 4x + 4
The statements that are true for any value of x are
A. 7x + (2x + 7) = 9x + 7C. 1/2x + (3 - 1/2x) = 3E. 0.4x - (0.2x + 8) = 0.2x - 8F. 6x - (2x - 4) = 4x + 4How to determine the true statements?The equations are given as
A. 7x + (2x + 7) = 9x + 7
B. 7x + (2x - 1) = 9x + 1
C. 1/2x + (3 - 1/2x) = 3
D. 5x – (8 - 6x) = -x - 8
E. 0.4x - (0.2x + 8) = 0.2x - 8
F. 6x - (2x - 4) = 4x + 4
Next, we solve one side of the equations and then compare them with the other side
So, we have the following representations
A. 7x + (2x + 7) = 9x + 7
Evaluate
9x + 7 = 9x + 7 --- true
B. 7x + (2x - 1) = 9x + 1
Evaluate
9x - 1 = 9x + 1 --- false
C. 1/2x + (3 - 1/2x) = 3
Evaluate
3 = 3 --- true
D. 5x – (8 - 6x) = -x - 8
Evaluate
11x - 8 = -x - 8 --- false
E. 0.4x - (0.2x + 8) = 0.2x - 8
Evaluate
0.2x - 8 = 0.2x - 8 --- true
F. 6x - (2x - 4) = 4x + 4
Evaluate
4x + 4 = 4x + 4 -- true
Hence, the true statements are (a), (c), (e) and (f)
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what is 3d-4 if d=1.2
Answer:
= -0.4
Step-by-step explanation:
3d-4 when d=1.2
3(1.2) - 4
3.6 - 4
= -0.4
Answer: 0.4
Step-by-step explanation:
Equation: 3d - 4
1. Substitute the variable with the given number (d = 1.2)
3(1.2) - 4
2. Solve 3 × 1.2
3.6 - 4
3. Solve
3.6 - 4 = -0.4
the number of devices a particular manufacturing company can produce is a function of the number of hours spent making the devices. On average, 4 devices are produced each hour. Assume that devices are produced at a constant rate. Write an equation in two variable that describes the number y, as a function of time the company sends making the devices x
Answer: y = 4x
Step-by-step explanation: The number of devices a company can produce is a function of the number of hours spent making the devices. On average, 4 devices are produced each hour. If we let x represent the number of hours spent making the devices and y represent the number of devices produced, we can write an equation to describe this relationship as follows:
y = 4x
This equation states that the number of devices produced is equal to 4 times the number of hours spent making the devices. For example, if the company spends 10 hours making the devices, the number of devices produced will be 4 * 10 = 40.
Therefore, the equation y = 4x describes the number of devices produced by the company as a function of the number of hours spent making the devices.
5 / 7/10 answer in fraction form
When we divide fractions, we multiply the first fraction by the second fraction's reciprocal.
Solving the Question[tex]5\div \dfrac{7}{10}[/tex]
⇒ Multiply by the reciprocal of 7/10:
[tex]= 5\times \dfrac{10}{7}[/tex]
[tex]= \dfrac{50}{7}[/tex]
⇒ If you would like, you can change this into a mixed number fraction. The whole number value from 50/7 is 7. 7 times 7 is 49, which is 1 less than 50. 1 is the numerator and 7 is the whole number:
[tex]= 7\dfrac{1}{7}[/tex]
Answer[tex]\dfrac{50}{7}[/tex] or [tex]7\dfrac{1}{7}[/tex]
A jewelry designer plans to make a triangular pendant out of gold wire. The wire costs $31.65 per centimeter. What is the possible range of costs for the wire?
The wire can cost more than $____ and less than $____
The wire used for the triangular pendant can have a cost more than 664.65 USD and less than 791.25 USD.
How to determine the possible lengths of the missing side
In this problem we find the case of a triangle, in which the length of two sides are known and we need to determine the range of costs associated to the set of all possible triangles. This can be derived by the geometric system described in the image attached below. The minimum and the maximum costs of the pendant:
θ = 0°
l = 10.5 cm - 2.5 cm
l = 8 cm
s = 10.5 cm + 8 cm + 2.5 cm
s = 21 cm
C = (31.65 USD / cm) · (21 cm)
C = 664.65 USD
θ = 180°
l = 10.5 cm + 2.5 cm
l = 13 cm
s = 10.5 cm + 2.5 cm + 12.5 cm
s = 25 cm
C = (31.65 USD / cm) · (25 cm)
C = 791.25 USD
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