The constraints of the equation will be x > 13 y and 340 x + 670 y < 5650.
Let the number of new bicycles be x
Let the number of new treadmills be y.
Cost of 1 new bicycle = $ 340
Cost of 1 new treadmill = $ 670
Also, he must spend less than $ 56,50
Now, the constraints for this will be:
x > 13 y
x greater than 13 y
340 x + 670 y < 5650
340 x plus 670 y less than or equal to 5650
Therefore, the constraints of the equation will be x > 13 y and 340 x + 670 y < 5650 .
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Which function represents this sequence -10,-2,6,14
Answer:
8n-18
Step-by-step explanation:
You can use this formula: 1st term+(n-1)(difference)
First term of sequence: 10
Difference between each term: 8
-10+(n-1)(8)
= -10+8n-8
= 8n-18
Identify each function or situation as an example of exponential growth or decay. What is the y -intercept?
c. You put $ 2000 into a college savings account for four years. The account pays 6% interest annually.
The function is exponential growth function and the y- intercept is (0,$2000).
Given that the we put $ 2000 into a college savings account for four years and the account pays 6% interest annually.
Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.
If a is positive and b is greater than 1 then it is exponential growth.
If a is positive and b is less than 1 but greater than 0 then it exponential decay.
When we put $2000 in our college savings account and we receive 6% annual interest then this situation can be modeled by using equation f(x)=a(1+r)ˣ in which we put a=$2000, r=6%, x=4
Thus we will receive the amount after 4 years:
f(4)=2000(1+(6/100))⁴
Since equation is an exponential growth function so it is also an exponential growth function.
Now, to find the y-intercept we will put x=0.
So, y-intercept is (0,$2000).
Hence, By putting $2000 into a college savings account for four years and the account pays 6% interest annually the function is exponential growth function and the y-intercept is (0,2000).
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It cost Chloe $17.70 to send 177 text messages. How much would it cost to send 98 text messages?
Answer:
Step-by-step explanation:
17.7 -> 177
19.1 -? ?
17.7177=19.1x
cross multiply
17.7x=19.1(177)
can you solve from there?
The cost to send 98 text messages will be $9.8.
What is mean by proportion?
A proportion is a fraction of a total amount, in which two ratios are set equal to each other.
Given that;
The cost of 177 text messages = $17.70
Now,
Since, The cost of 177 text messages = $17.70
So, The cost to send 98 text messages will be;
= $17.70 x 98 / 177
= $9.8
Thus, The cost to send 98 text messages will be $9.8.
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Alissa has two pieces of carpet runner one is 2 1/3 yards long and the other is 3 1/3 yard long she needs 10 yards of carpet runner altogether how much more does she need to buy
Find the inverse of each function.
y=log (x+1)
The inverse of the function y = log(x₊1) is f ⁻¹(x) = 10ˣ ₋ 1.
Given the function is :
y = log(x₊1)
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now interchange the positions of x and y in the function.
x = log₁₀ (y ₊ 1)
the next step is to isolate the dependent variables.
f ⁻¹(x) = ₋1 ₊ 10ˣ
f ⁻¹(x) = 10ˣ ₋ 1
hence, we get the inverse of the given function as f ⁻¹(x) = 10ˣ ₋ 1.
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Find values of X and Y
Answer:
Step-by-step explanation:
plllllllsssss hhhhheeeellllpppp
Answer:
Step-by-step explanation:
Two years ago a father was four times as old as his son. Three years from now the father will be only
three times as old as the son. How old is each now?
If x represents the son's age two years ago, which expression represents his father's age three years
hom now?
3x+15
3x+3
x+3
An expression which represent his father's age three (3) years from now is: A. 3x + 15.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to write and solve this word problem, we would assign variables to the son's and father's age and then evaluate the resulting algebraic expression.
Let x represent the son's age two years ago.Let y represent the father's age three years ago.Translating the word problem into an equation, we have;
y = 4x
y + 2 + 3 = 3(x + 2 + 3)
y + 5 = 3(x + 5)
y + 5 = 3x + 15
Therefore, an expression which represent his father's age three years from now is 3x + 15.
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12+15 in distributive property
Answer:
3(4 + 5)
Step-by-step explanation:
Create a real life context that can be represented by the linear equation y=-2.65x+ 25.
Answer:
If you have 2 dollars and 65 cents per day, and you get 25 dollar commission.
Step-by-step explanation:
Look at the picture please
The minimum value is 20
The maximum value is 9
The range is 11.
The mean is 16.8
The median is 18.
The mode is 18.
The landmark that best describes the dot plot is the mean because it incorporates all the data in the dotplot.
What are the measures of the data in the dotplot ?A dot plot is a graph that displays the information of a dataset. A dot plot consists of a number line and dots above the numbers on the number line. The dots in the dot plot is indicate the frequency of the data in the dataset.
The minimum value is the smallest number in the dataset. The smallest number that is represented in the dot plot is 9. The maximum value is the largest number in the dataset. The largest number that is represented in the dot plot is 20.
The range is the difference between the maximum value and the minimum value.
Range = maximum value - minimum value
20 - 9 = 11
The mean is the average of he numbers in the dataset.
Mean = [(9 x 1) + (12 x 1) + (14 x 1) + (15 x 5) + (16 x 2) + (17 x 3) + (18 x 6) + (19 x 3) + (20 x 4)] / 26
438 /26 = 16.8
The mode is the number that occurs most in the dataset. The number that occurs most frequently is 18 with a dot of 6.
The median is the number at the center of the dataset. The median is 18.
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A light bulb consumes 16200 watt-hours in 4 days and 12 hours. How many watt-hours does it consume per day?
watt-hours per day
Answer:
3600
Step-by-step explanation:
16500/4.5 to find watt-hours per day.
Simplify each number. 32 . 256¹/₂
32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 32 = 2 x 2 x 2 x 2 x 2 = [tex]2^{5}[/tex]
Prime factorization of 256= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = [tex]2^{8}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m})^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} . a^{n } =a^{m+n}[/tex]
According to the given condition,
∴[tex]32 = 2^{5}[/tex]
[tex]256^{\frac{1}{2}} = (2^{8})^{\frac{1}{2} }[/tex]
∴ 32. [tex]256^{\frac{1}{2} }[/tex] = [tex]2^{5}[/tex] × [tex](2^{8})^{\frac{1}{2} }[/tex]
Applying the laws of indices mentioned above,
32. [tex]256^{\frac{1}{2} }[/tex] = [tex]2^{5}[/tex] × [tex](2^{8 X }^{\frac{1}{2} })[/tex]
= [tex]2^{5}[/tex] × [tex]2^{4}[/tex]
= [tex]2^{5 + 4}[/tex] = [tex]2^{9}[/tex]
= 512.
Thus, 32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.
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PLEASE I NEED THE ANSWER TO THIS solve for x
I need help bc we only learned this literally once pls help
Answer:Gotta Be G tbh
Step-by-step explanation: Calculator on brainly
simplify 25p^6q^9 / 45p^8q^4. write answer using a positive exponent
/ is division
^ elevated to
The simplification of 25p^6q^9 / 45p^8q^4 using a positive exponent;
Division is 5p^6 q^9 / 9p^8 q^4Elevated form is 5/9 p^-2 q^5What are algebraic expressions?Algebraic expressions are expressions made up of factors, variables, terms, coefficients and constants.
They are also comprised of arithmetic operations such as addition, subtraction, multiplication, division, etc
We also know that index forms are also know as standard forms.
They are mathematical expressions showing the power of exponent of a variable in terms of another variable.
Given the index algebraic forms;
25p^6q^9 / 45p^8q^4
Using the rule of indices, we take the negative exponent of the divisor and multiply through.
We have;
5p^6 q^9 × 9p^-8 q^-4
Add exponential values
5/9 p^6-8 q^9 -4
5/9 p^-2 q^5
Thus, the expression is simplified to 5/9 p^-2 q^5
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What’s the algebraic expression of:
Six times the sum of a and b squared minus four times the product of a and b squared
The algebraic expression is 6(a+ b)² + 4(ab)².
What is algebraic expression?The concept of representing numerical values with letters or alphabets without providing their precise values The fundamentals of algebra taught us how to represent an unknown value using letters like x, y, and z. Here, these letters are referred to as variables. A mathematical expression may have both variables and constants. A coefficient is any value that is introduced before and increased by a variable.
Given that,
So, six times the sum of (a+ b)
Then, four times the product of (ab)
Therefore, the algebraic expression is 6 (a+ b)² + 4(ab)².
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Simplify each radical expression. Use absolute value symbols when needed. √81 x²
The simplified value of radical expression √81 x² is 9x.
By considering the given expression
√81 x²
=(9²)^1/2 ( x²)^1/2
=9x
An expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
The 'V'-shaped portion of the radical symbol will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8.
The radical symbol, which resembles a check mark, the index, a small number written outside the radical symbol, and the radicand, a quantity written beneath the horizontal bar of the radical symbol, are the three main components of the radical expression ab.
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What is the domain of the exponential function shown in the graph?
-8
-6
9
-4
-2
y
8+
6+
4-
2+
2+
9
-6-
-8
ස
No
2
4
to
too!
8
44
X
Answer:
Hey there, your domain is all real numbers!! the graph is staying above the x-axis, but it's crossed from the negative x-values to the positive x-values. that means choice D is incorrect, because some of the function does cross through negative values.
if the domain was either of the inequality choices, the function wouldn't extend all over the graph--it would be ONLY between 0 and 5, or 5 and -5. this graph would be all real numbers because it isn't restricted like that.
Hope this helps!!!
A supervisor at an American company earns $40,764 per year. Find the amount of her earnings in any 3 month period
plsss help
Point L is on line segment
K
M
‾
KM
. Given
K
L
=
15
KL=15 and
L
M
=
3
,
LM=3, determine the length
K
M
‾
.
KM
.
Answer:
KM = 18
Step-by-step explanation:
KL and LM make up KM so if added together, we'd get the value of KM.
3 + 15 = 18
Need answer to question 1 and 2, Please show work, I need a good explanations giving brainly
The expressions are:
1. 6h² - 4h - 2
2. 6c² + c - h +9
What are algebraic expressions?
Algebraic expressions are expressions made up of constants, terms, coefficients and variables.
Given the expressions;
h² + 4h - 4
5h² - 8h + 2
Let's take the sum
h² + 4h - 4 + 5h² - 8h + 2
collect like terms
h² + 5h² + 4h - 8h - 4 + 2
6h² - 4h - 2
Let's subtract 3c - 5 from 6c² + 3c + 9
6c² + 3c + 9 - 2c - h
collect like terms
6c² + 3c - 2c - h +9
6c² + c - h +9
Hence, the expressions are 6h² - 4h - 2 and 6c² + c - h +9
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The populations of cities A and B are 3.6*10 to the 5 and 2,060,000, respectively. The population of City C is twice the population of City B. The population of City C is how many times the population of City A?
The population of City C is 11.4 times the population of City A.
How to calculate the value?From the information, the populations of cities A and B are 3.6*10 to the 5 and 2,060,000, respectively
It was stated that the population of City C is twice the population of City B. That means the population of C will be:
= 2060000 × 2
= 4120000
Therefore, the population of City C is how many times the population of City A will be:
=4120000 / 360000
= 11.4
Therefore, the population of City C is 11.4 times the population of City A.
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please help, I put down the drop down menu this time
Answer:
0.2 billion visits per year
Step-by-step explanation:
-
Hope that helps.
An earthquake of magnitude 9.1 occurred in 2004 in the Indian Ocean near Indonesia. It was about 74,900 times as strong as the greatest earthquake ever to hit Texas. Find the magnitude of the Texas earthquake. (Remember that an increase of 1.0 on the Richter scale means an earthquake is 30 times stronger.)
a. Can you write an exponential or logarithmic equation?
The Magnitude of earthquake that hit Texas is 5.8; The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex].
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given:
Magnitude of earthquake that hit Indian Ocean = 9.1 [tex]I_1[/tex] = Intensity of weaker earthquake[tex]I_2[/tex] = Intensity of greater earthquake.To find: Magnitude of earthquake that hit Texas.
Finding:
From the given, [tex]\frac{I_2}{I_1}[/tex] gives the ratio of the greater earthquake's intensity to the weaker earthquake's intensity.This ratio, when written as an exponential equation, equals [tex]30^M[/tex] where M is the increase in magnitude difference:=> [tex]\frac{I_2}{I_1}[/tex] = [tex]30^M[/tex]
For [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:
=> 74900 = [tex]30^M[/tex]
Taking logarithm on both sides, with base 10 gives:
=> log (74900) = log ([tex]30^M[/tex])
As [tex]log_b(a)^m = m(log_b(a))[/tex],
=> log (74900) = M ( log (30))
=> [tex]\frac{log(74900)}{log (30)}[/tex] = M
=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.
Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.
The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex]
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Shop A sells a dress for $79.50 with a 20% discount while Shop B sells the same dress for $69.50 with a 10% discount. Write down a calculation you could do mentally to help you decide which shop to buy the dress from.
Shop A sells a dress for $79.50 with a 20% discount while Shop B sells the same dress for $69.50 with a 10% discount is $ 318 and $ 625.5.
The proportion of value in relation to the original value is measured using the percentage discount concept. In business, percentages are frequently employed to calculate a company's profit or loss percentage.
Let x be the actual cost of the dress in the store. A
20/100 ×x = 79.50 x = 79.50 ×100/20 xx = 7950/20
x = $ 397.5
The actual cost of clothing A is $397.5.
Discount of outfit A therefore equals 20%
$397.5-79.5$= $ 318
Let x represent the true cost of dress B.
(10/100)× x = 69.50$
x = $695
The actual cost of dress B is $695.
So, the dress B's discount is 10%.
$ 695 - 69.50 = $ 625.5
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An insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is $5,000. After introducing several plans to prevent loss, it randomly samples 200 policyholders and finds the mean amount per claim was $4,800 with a standard deviation of $1,300. Does it appear the prevention plans were effective in reducing the mean amount of a claim? use the 0. 05 significance level. A. What is the decision rule? (negative amount should be indicated by a minus sign. Round your answer to 3 decimal places. )
In this case, the population consists of an insurance company's policyholders. The sample consists of his 200 policyholders under study. The sample size is 200.
H0: µ ≥ $5,000
Ha: µ < $5,000 (claimed)
As we can see that the sample size is 200, which is way greater than 30, so a z-test is appropriate here.
z(test) = (4800 - 5000) / (1300 / √200) = -2.1757
p (z = -2.1757) = 0.0148
The critical z-value for the left-sided test at α = 0.05 is -1.645
The tested value of z is less than the critical value, so we reject the null hypothesis. The hypothesis drawn here ( null hypothesis) will be rejected as an alternate decision because the p-value is less than the significance level (0.05).
At the 0.05 significance level, the prevention plan effectively reduced the average amount of harm. Insurers should continue these plans and try to improve them where possible.
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HELP ASAP ONLY IF YOU KNOW THE ANSWER
Decide if the following biconditional statement is true or false:
Two angles are congruent if and only if they are vertical angles
True or false?
Answer: TRUE
Step-by-step explanation:
i got it right.
Solve each equation. Check your answers. ln x-ln 3=4
The value of ln x-ln 3=4 is 163.7
What is logarithm function?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to create a specific number x, is represented by the logarithm of that number.
given, our equation is -
ln x-ln 3=4
It can be expressed in the form of
⇒ loge (x/3) = 4
⇒ e⁴ = x/3
⇒ x = 3e⁴
⇒ 163.7
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Function or Not a Function?