Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.
We can write the linear inequality as follows:
8x + 4y ≤ 46
What is inequality?An inequality is a mathematical statement that shows the relative size of two values.
What is linear inequality?A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.
This inequality can be rewritten as follows:
x + 0.5y ≤ 5.75
This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.
Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.
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Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.
We can write the linear inequality as follows:
8x + 4y ≤ 46
What is inequality?
An inequality is a mathematical statement that shows the relative size of two values.
What is linear inequality?
A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.
This inequality can be rewritten as follows:
x + 0.5y ≤ 5.75
This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.
Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.
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help i need perimeter of these
Answer: A= 52cm B= 94mm C= 9m D= 17cm
Step-by-step explanation:
A) You first need to find the missing sides by doing
11-9= 2
and 15-9= 6
you then add it all together
6+2+9+9+15+11=52cm
B) You first need to find the missing sides by doing
25-18=7
and 22-6= 16
you then add it all together
25+22+18+16+7+6=94mm
C) You first need to find the missing sides by doing
0.5+1=1.5 then 2.5-1.5=1
and 1.2+0.8=2 then 2-0.5=1.5
you then add the numbers all together
1+1.5+0.8+1+0.5+0.5+1.2+2.5=9m
D) You first need to find the missing sides by doing
2.5+1= 3.5 then 3.5-2=1.5
and 1.5+2.5=4 then 5-4=1
you then add all the numbers together
2.5+2.5+1.5+1+5+2+1+1.5=17cm
Which of the following is the solution to the following system of inequalities?
x+2y<=4
3x-y>=2
See the picture for the graphs. Any help is appreciated!! This is honors algebra 2 on Apex learning.
Answer: B.
Step-by-step explanation:
x+2y≤4
3x-y≥2
in a hypothetical case-control study of female participants regarding exposure to emf's and breast cancer, the following data were obtained: 11 cases exposed, 108 controls exposed, 5 cases not exposed, 436 controls not exposed. what is the odds ratio for the association between exposure to emf's and breast cancer?
The odds ratio for the association between exposure to emf's and breast cancer would be (11/5) / (108/436) = 2.2.
1. Calculate the odds of exposure for cases: 11/5 = 2.2
2. Calculate the odds of exposure for controls: 108/436 = 0.25
3. Divide the odds of exposure for cases by the odds of exposure for controls: 2.2/0.25 = 8.8
4. Finally, the odds ratio for the association between exposure to EMF's and breast cancer is 2.2.
The odds ratio for the association between exposure to EMF's and breast cancer can be calculated by dividing the odds of exposure for cases by the odds of exposure for controls. To calculate this, first take the number of cases exposed (11) and divide it by the number of cases not exposed (5). This will give the odds of exposure for cases (2.2). Second, take the number of controls exposed (108) and divide it by the number of controls not exposed (436). This will give the odds of exposure for controls (0.25). Finally, divide the odds of exposure for cases (2.2) by the odds of exposure for controls (0.25). This will give the odds ratio for the association between exposure to EMF's and breast cancer (2.2).
Odds ratio = (11/5) / (108/436) = 2.2
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Need help with this equation and graphing table asap!! Look at the image
first 2;
a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32
36 - 22 = 14/2 = 7
32 - 16 = 16/2 = 8
7<8
the table has a greater rate of change
y intercept
equation; 8
table; 0
8> 0
the equation has a greater y intercept
Elevation (meters) -2 , 2 , -4 which is higher ???
Answer:
2
Step-by-step explanation:
-2 and -4 are less than 0
2 is greater than
If you write down in descending order ===> 2, -2 , -4
∠Cis a right angle and AB=14 miles, determine the length of BC and AC.
The length of BC is approximately 5.72 miles and the length of AC is approximately 12.67 miles.
Let's represent the length of the side opposite angle A "BC" and the length of the side adjacent to angle A "AC". We can then use the sine function to find BC:
sin(A) = BC / AC
Substituting the given values, we get:
sin(24°) = BC / 14
We can use a calculator or look up the value of sin(24°) to get:
sin(24°) ≈ 0.406
Solving for BC, we get:
BC = 14 * sin(24°) ≈ 5.72
To find AC, we can use the cosine function:
cos(A) = AC / AC
Substituting the given values, we get:
cos(24°) = AC / 14
We can use a calculator or look up the value of cos(24°) to get:
cos(24°) ≈ 0.913
Solving for AC, we get:
AC = 14 x cos(24°) ≈ 12.67
Thus, BC is about 5.72 miles long while AC is about 12.67 miles in length.
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Help help help help help
Net profit is a company's profit after all expenses have been deducted. What remains after deducting fixed costs from gross profit is the net profit.
Why do we calculate net profit?Subtracting the cost function from the revenue function yields the profit function. Assume that the profit is denoted by P(x), the revenue is denoted by R(x), the cost is denoted by C(x), and x is the quantity of goods sold. Consequently, the profit function is denoted by P(x) = R(x0 - C) (x).
Total Revenue - Total Expenses = Net Profit
A company that sells online has a $350,000 revenue and a $50,000 cost of products sold.The net income formula is defined as the difference between the total revenue earned and the total costs.Total revenue minus all costs equals net income.
The money a corporation makes after deducting interest, operational costs, and taxes over a specific time period is known as net profit.Profit After Tax is another name for Net Profit (PAT).
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Identify the pattern.
-4. -5.5, -7, -8.5, -10, -11.5, -13,..
Answer:
The pattern is that each number in the sequence is the previous number minus 1.5. For example, -5.5 is -4 minus 1.5, -7 is -5.5 minus 1.5, and so on.
Answer:
-1.5
Step-by-step explanation:
You take two of the variables in the pattern and subtract them with the second one being the minuend, and the first being the subtrahend.
For example we will use -4 and -5.5
(-5.5) - (-4) = -1.5
There is a negative sign present so it indicates subtraction towards the pattern.
Hence, the pattern change rate is -1.5
How to solve this problem? I need the answer quick as possible!
Consider the following three systems of linear equations. Answer the questions below.
For each, choose the transformation and then fill in the blank with the correct number.
The arrow → means the expression on the left becomes the expression on the right.
Answer:
24 Inches
Step-by-step explanation:
The length of a piece of wood that uses 8 nails as required in the task content is; 24 inches.
What is the length of a piece of wood that uses 8 nails?
It follows from the task content that the length of a piece of wood that uses 8 nails is to be determined from the task content.
Use the tax table below to answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Consider cases where the number of withholding allowances is less than 6. Which will cause the amount of federal income tax withheld to increase?
a.
Gross pay stays the same and withholding allowances increase.
b.
Gross pay increases by more than $20 and withholding allowances stay the same.
c.
Gross pay increases by more than $20 and withholding allowances increase.
d.
Gross pay decreases by more than $20 and withholding allowances stay the same.
Using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
What is the Percentage?A percentage is a relative figure that has the ability to represent 1/100th of any quantity.
Since 1% denotes one percent, 100 percent and 200 percent indicate the full amount and double the quantity, respectively.
By multiplying by 100 and inserting the "percentage sign"%, a ratio and fraction can be transformed into a percentage.
So, Luce is single and makes $763 twice weekly.
She does not request any compensation from federal withholding.
The value of this amount ranges from $760 to $780.
If we look at the table in the issue, the federal tax for this slab is $86.
Federal taxes now make up 19% of all state taxes.
Hence, the $86 in federal tax at a rate of 19% is:
Tax = 86 * 19/100
Tax = 16.34
Therefore, using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
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Correct question:
Use the tax table to help answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Luce is single and makes $763 biweekly. She claims no federal withholding allowances. If the state tax is 19% of the federal tax, how much in state tax does Luce contribute?
a. $12.92
b. $15.13
c. $15.77
d. $16.34
Fátima, Gabriel y José tienen un total de $1080 en sus carteras. Gabriel tiene 3 veces lo que José tiene. Fátima tiene $70 menos
que José. ¿Cuanto dinero tienen en sus carteras?
Fátima tiene un total de $ 160, Gabriel tiene un total de $ 690 y José tiene un total de $ 230.
¿Cómo determinar el dinero requerido en sus carteras?
En este problema tenemos a tres personas, Fátima, Gabriel y José, que reúnen un total de $ 1.080. A continuación, traducimos las variables y ecuaciones asociadas a la situación:
x - Cantidad de dinero de Fátima.
y - Cantidad de dinero de Gabriel.
z - Cantidad de dinero de José.
Ecuaciones: Fátima, Gabriel y José tienen un total de $ 1080.
x + y + z = 1080
Gabriel tiene 3 veces lo que José tiene.
y = 3 · z
Fátima tiene $ 70 menos que José.
x = z - 70
A continuación, resolvemos el sistema de ecuaciones lineales:
x + y + z = 1080
(z - 70) + 3 · z + z = 1080
5 · z - 70 = 1080
5 · z = 1150
z = 1150 / 5
z = 230
x = z - 70
x = 230 - 70
x = 160
y = 3 · z
y = 3 · 230
y = 690
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Ms. Hall is buying Ms. Ward some gifts for Christmas. She is buying one big gift that
will cost $90 as well as some small gifts that cost $7 each.
1+90 +7
What is its :
Constant:
Coefficient
Equation:
When Ms. Hall is buying Ms. Ward some gifts for Christmas as described in the problem,
the Constant: $90 and $7
the Coefficient: $7
the Equation: $90 + $7x
How to find the constantInformation form the problem shows that
one big gift that will cost $90
some small gifts that cost $7 each
the constant in this case is the price of the gifts
$90 and $7
the coefficient is $7
the equation is
$90 + $7x
where x is the number of the small gifts
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Jill made a popcorn container that is shaped like a cone. The diameter of the opening is 8 inches and the height is 9 inches. What is the volume of the popcorn container? Leave answer alone, do not round.
Domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this
The reasonable domain for the range: 68,71,74,77,80 is { 1,2,3,4,5 } .
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.
Given:
range: 68,71,74,77,80
Domain:1,2,3,4,5
Here, the situation is not given.
So, the reasonable domain is { 1,2,3,4,5 }
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Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
The rate of interest in one account whose investment is $2300 will be 3.21%.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.
Let 'x' be the interest. Then the equation is given as,
(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130
Simplify the equation, then we have
23x + 56 = 130
23x = 74
x = 3.21%
The pace of revenue in one record whose speculation is $2300 will be 3.21%.
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Is this true or false?
TRUE: The given contrapositive statement are correct,
If m ≤ 3, then, m < 5.
Explain the contrapositive statement?An inference rule called proof by contrapositive, also known as proof by contraposition, is used in proofs to infer a conditional assertion from its contrapositive. To put it another way, the assertion "if B, then not A" is proven rather than the conclusion "if A, then B."When you reverse the hypothesis as well as the conclusion in a statement and reject both of them, you have a contrapositive statement.For the stated conditional statement -
If m ≤ 3, then, m < 5.
Then, contrapositive statement for the given statement will be
(m < 5)' ⇒ (m ≤ 3)'
That is;
(m > 5) ⇒ (m > 3)
That is, if m> 5 then, m > 3, which is true.
Thus, the contrapositive statement for the given conditional statement is true.
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Grace has 2 quartera . Jen have 4 dimesss were ans 1 nickels. Keesha has 3 dimes and 3 nickels. Terry has 1 quarters , 1 dime who has the most money
Answer: grace has the most money
Step-by-step explanation:
Because
Grace has 2 quarters = 50 cents
Jen has 4 dimes and 1 nickel = 45 cents
Keesha has 3 dimes and 3 nickels = 33 cents
Terry has 1 quarter and 1 dime = 26 cents
so as you can see grace has the most money
Pleaseeee help I’m so confused
Answer:
D
Step-by-step explanation:
if you move the preimage on the image you can see that the two figures are equals
Billy pulled a number of colored marbles from a large bag. green 1 orange 4 red 1 yellow 9 white 3 Based on experimental probability, how many of the next 20 marbles selected should you expect to be yellow marbles?
The likelihood that the next 20 marbles picked will be yellow marbles is 9/20.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The probability that of the next 20 marbles selected it is expect to be yellow marbles,
=9/20
The probability that of the next 20 marbles selected it is expect to be yellow marbles will be 9/20.
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Answer:
the answer is 10
Step-by-step explanation:
ixl says its ten
Find x in the equation. 4 times x plus one half equals one half times x plus 4
After solving the equation, the value obtained for x will be equal to 1.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
4 times x plus one-half equals one-half times x plus 4.
Let's write it in mathematical form,
4x + 1/2 = 1/2x + 4
Now, solve the equation for x,
4x - 1/2x = 4 - 1/2
(8x - x)/2 = (8 - 1)/2
7x/2 = 7/2
x = (7 × 2)/(2 × 7)
x = 14/14
x = 1
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the manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456. based on this information, what are the chances that the revenue on the first show will exceed $800?
The chances that the revenue on the first show will exceed $800 when mean revenue is $336.25 and standard deviation is $38.16 is essentially zero. i.e. 0
A normal distribution is a type of continuous probability distribution in which the majority of data points cluster in the middle of the range, while the remainder taper off symmetrically toward either extreme. The mean of the distribution is also known as the middle of the range.
The normal distribution is primarily used to calculate the likelihood of an observation in a distribution falling above or below a given value.
Given,
Mean, [tex]\mu[/tex] = 336.25
variance, [tex]\sigma^2[/tex]= 1456
then,
standard deviation, [tex]\sigma = \sqrt{1456}[/tex] = 38.16
To determine the chances that the revenue on the first show will exceed 800 is1:
[tex]1-p(z=\frac{x-\mu}{\sigma})\\\\=1-p(z=\frac{800-336.25}{38.16})\\\\=1-p(z=\frac{436.75}{38.16})\\\\=1-p(z=12.15)\\\\=1-1=0[/tex]
Hence, there is no chance that the revenue will exceed $800 on the first show.
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(x-14)÷7=12 I just need help
Answer:
x = 98
Step-by-step explanation:
Solve for x:
(x - 14)/7 = 12
Multiply both sides of (x - 14)/7 = 12 by 7:
(7 (x - 14))/7 = 7×12
(7 (x - 14))/7 = 7/7×(x - 14) = x - 14:
x - 14 = 7×12
7×12 = 84:
x - 14 = 84
Add 14 to both sides:
x + (14 - 14) = 14 + 84
14 - 14 = 0:
x = 84 + 14
84 + 14 = 98:
Answer: x = 98
What is the smallest prime number that is the sum of two other distinct prime numbers?
Answer:
5
Step-by-step explanation:
2 +3 = 5
I need help please ok okokokookokook
Answer:
should be angle 7, 1, and 3
hope i could helpppp
Answer: 1 , 7 , 3
Step-by-step explanation:
The angles that habe the same measurement of angle 5 are;
1 , 7 , 3
Because the lines are parallel, these angles correspond to angle 5.
1. The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?
The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.
2. A savings account is opened with an initial deposit of $425.00. Determine the account balance after 9 years if the account earns 2.7% simple interest annually.
$3,928.28
$1,457.75
$528.28
$103.28
3. An arithmetic sequence begins with 56, 59, 62, 65, 68, …
Which option below represents the formula for the sequence?
f(n) = 56 + 3(n − 1)
f(n) = 53 + 3(n − 1)
f(n) = 56 + 3(n)
f(n) = 53 + 3(n + 1)
4. The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account. Solve for r.
r = 0.04
r = 0.14
r = 0.26
r = 0.40
Answer:
Answers below
Step-by-step explanation:
1. The value 550 represents the initial balance in the account, which means the account started with $550.
2. 528.28
425.00 x 2.7% x 9 = 103.275
Then we add 103.275 to the initial deposit of $425.00
425.00 + 103.275 = 528.275
Therefore the answer is $528.28
3. The answer for this one is f(n) = 56 + 3(n − 1)
So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex]
Therefore, its 56 + 3(n − 1)
4. For this one we solve for r and using a calculator its r = 0.04
The value of r from the given equation is 0.04. Therefore, option A is the correct answer.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
1) The given equation is 687.5=550(1+0.05t)
Here, amount=$687.5, principal (initial balance)=$550 and rate of interest =0.05×100 =5%
So, the value 550 represents the initial balance in the account, which means the account started with $550.
2) Given that, principal=$425.00, time period=9 years and rate of interest=2.7%
We know that, S.I=(P×T×R)/100
= (425×9×2.7)/100
= 103.275
Amount=103.275+425
= 528.275
≈ $528.28
3) The given arithmetic sequence is 56, 59, 62, 65, 68,.…
Here, first term (a)=56 and common difference=59-56=3
We know that, general form of arithmetic sequence is aₙ=a+(n-1)d
Now, f(n)=56+(n-1)3
4) The given equation is 816=600(1+9r)
1+9r =816/600
1+9r =1.36
9r=0.36
r=0.04
The value of r from the given equation is 0.04. Therefore, option A is the correct answer.
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it has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause illness if improperly cooked. chickens are delivered to grocery stores in crates of 24. assume the chickens are chosen for inclusion in a crate at random. what is the probability that a randomly selected crate has more than 4 contaminated chickens?
Using the binomial distribution, it is found that there is a 0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
For each chicken, there are only two possible outcomes, either they are contaminated, or they are not. The chickens are independently selected, hence, the binomial distribution is used.
What is the binomial probability distribution formula?
The formula is:
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
Cₙ,ₓ = n!/x!(n-x)!
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
About 30% of frozen chickens are contaminated, hence p=0.3.
Chickens are delivered to grocery stores in crates of 24, hence n=24
The probability that a certain crate has more than 4 contaminated chickens is:
P(X>4)=1-P(X≤4)
In which:
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
Then
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
P(X=0) = C₂₄,₀.(0.3)⁰.(0.7)²⁴ = 0.0002
P(X=1) = C₂₄,₁.(0.3)¹.(0.7)²³ = 0.0020
P(X=2) = C₂₄,₂.(0.3)².(0.7)²² = 0.0097
P(X=3) = C₂₄,₃.(0.3)³.(0.7)²¹ = 0.0305
P(X=4) = C₂₄,₄.(0.3)⁴.(0.7)²° = 0.0687
Hence
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
= 0.0002+0.0020+0.0097+0.0305+0.0687
= 0.1111
0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
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Type the correct answer in each box. Use numerals instead of words. If necessary, round to the nearest hundredth.
The relationship between the values of two different currencies is modeled by a linear function that varies depending on the current value of each currency. The table shows the relationship between an amount in U.S. dollars, x, and the equivalent amount in euros, f(x), where f(x) = x/1.06.
The inverse function is given by f⁻¹(x) = 1.06x. 2 euros is equivalent to 2.12 U.S. dollars. 4 euros is equivalent to 4.24 U.S. dollars
How to find the inverse function?Given that: the two different currencies is modeled by a linear function f(x) = x/1.06
where, x = an amount in U.S. dollars and f(x) = the equivalent amount in euros
To find the inverse function f⁻¹(x). Let y = f(x):
y = x/1.06
x = 1.06y
Since x = f⁻¹(y) = 1.06y
Thus, f⁻¹(x) = 1.06x
Note: f⁻¹(x) will help you convert from euros to dollar
2 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(2) = 1.06(2) = 2.12
Thus, 2 euros is equivalent to 2.12 U.S. dollars
4 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(4) = 1.06(4) = 4.24
Thus, 4 euros is equivalent to 4.24U.S. dollars
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a line passes through point (1, 6) and has a slope of 2. what is the y-intercept?
A line passes through point (1, 6) and has a slope is y=8x-14 We want to write the equation of the line that passes through (1, -6) and has a slope of 8 in slope-intercept form
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
As we are already given the slope (8), we can immediately plug that into the equation
So far, the equation of the line is:
y=8x+b
Now we need to find b
The line passes through the point (1, -6), which means that the point is a solution to the equation; when plugged into the equation, it'll create a true statement. This can help us find unknown variables, like b
Substitute 1 as x and -6 as y in the equation to solve for b
-6=8(1)+b
Multiply
-6=8+b
Subtract 8 from both sides
-14=b
Substitute -14 as b into the equation
y=8x-14
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Cora plans to buy some calligraphy pens priced at $5 each. Write an equation that shows how the total cost, y, depends on the number of calligraphy pens Cora buys, x. Do not include dollar signs in the equation.
Answer: y = 5x
Step-by-step explanation:
find an equation for a line perpendicular to y=2x-3, passing through the origin.
