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Use the number line below, where RS = 9y +5, ST = 3y + 6, and RT = 59.
a. What is the value of y?
b. Find RS and ST.
R
a. What is the value of y?
y = (Type an integer or a decimal.)
b. Find RS and ST.
RS=
ST=
(Type an integer or a decimal.)
(Type an integer or a decimal.)
S
Answers
Answer:
RS = 41 , ST = 18
Step-by-step explanation:
from the number line
RT = RS + ST ( substitute values )
59 = 9y + 5 + 3y + 6
59 = 12y + 11 ( subtract 11 from both sides )
48 = 12y ( divide both sides by 12 )
4 = y
Then
RS = 9y + 5 = 9(4) + 5 = 36 + 5 = 41
ST = 3y + 6 = 3(4) + 6 = 12 + 6 = 18
Related Questions
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.7 years, with a standard deviation of 3.2 years. The winner in one recent year was 31 years old.
Answers
The transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.
What is mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations).
Given:
Population mean,
μ=27.7 years
Population standard deviation,
σ=3.2 years
Winner's age =31 years
According to given question we have
If "x" represents the age of the winner then the z-score for "x":
z=x−μ/σ
a) Transforming the winner's age to a z-score
z=31−27.7/3.2
=1.03
(b) Interpretation of the z-score:
The winner's age of 31 years is 1.03 standard deviation below the mean age of the winners.
Therefore, the transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.
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To find the
a) Transforming the winner's age to a z-score
(b) Interpretation of the z-score
is missing
Is the following a power function, a polynomial, both, or neither?
f(x) = -5x² + 3x +3
Answers
The variable have positive integer exponent. so f(x) = -5x² + 3x +3 is a polynomial function.
Polynomial function also describe:A polynomial function is one that uses only non-negative integer powers or positive integer exponents of something like a variable in an equation such as the quadratic equation, cubic equation, and so on. For illustration, 2x+5 is a polynomial with an exponent of one.
What constitutes a polynomial?A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, as well as division (No division operation by a variable).
According to the given equation:f(x) = -5x² + 3x +3
Make the leading coefficient positive:
= 5x² - 3x -3
identify the coefficient:
a = 5, b = -3, c = -3
substituting into the:
[tex]$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$[/tex]
[tex]$x=\frac{-(-3)+\sqrt{(-3)^2-4 \times 5 \times(-3)}}{2 \times 5}$[/tex] or [tex]$x=\frac{-(-3)-\sqrt{(-3)^2-4 \times 5 \times(-3)}}{2 \times 5}$[/tex]
[tex]$x=\frac{3+\sqrt{3^2+4 \times 5 \times 3}}{2 \times 5}$[/tex] or
[tex]$x=\frac{3+\sqrt{9+4 \times 5 \times 3}}{2 \times 5}$[/tex]
[tex]$x=\frac{3+\sqrt{69}}{10}$[/tex]
x = ± [tex]\frac{3+\sqrt{69}}{10}$[/tex]
As we can see that the general form of a power function is f(x) = axⁿ , where a is a non zero co-efficient and 'n' is a real number.
so the given function is not a power function.
So,
the variable have positive integer exponent. so f(x) = -5x² + 3x +3 is a polynomial function.
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If f(x) = 5x + 40, what is f(x) when x = –5?
–9
–8
7
15
Answers
The value of f(x) when x equals -5 is 15. Option D
What is a function?A function can be defined as an expression, law or rule that explains the relationship between two variables;
The independent variableThe dependent variableGiven the function;
f(x) = 5x + 40
To determine the value of the function when x = - 5, we have to substitute the value of x as -5 in the function.
With this, we have;
f(-5) = 5(-5) + 40
Now, expand the bracket
f(-5) = -25 + 40
Add the values, we have;
f(-5) = 15
We can see that the value of the function with the input of the variable x as -5 is 15
Thus, the value of f(x) when x equals -5 is 15. Option D
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Jana bought 15 grapefruit. They were selling 3 for $2.
How much did she spend?
Answers
Answer: 10$
Step-by-step explanation: 15 divided by 3 is 5. 5 times 2 is 10. Therefore, the answer is 10 $
A researcher wants to estimate the proportion of depressed individuals taking a new anti-depressant drug who find relief. A random sample of 200 individuals who had been taking the drug is questioned; 152 of them found relief from depression. Based upon this, compute a 95% confidence interval for the proportion of all depressed individuals taking the drug who find relief. Then find the lower limit and upper limit of the 95% confidence interval.
Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.
Lower Limit:
Upper Limit:
Answers
Using the z-distribution, the limits of the 95% confidence interval are given as follows:
Lower: 0.70.Upper: 0.82.What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the parameters are given as follows:
[tex]n = 200, \pi = \frac{152}{200} = 0.76[/tex]
Then the bounds are given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 - 1.96\sqrt{\frac{0.76(0.24)}{200}} = 0.70[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 + 1.96\sqrt{\frac{0.76(0.24)}{200}} = 0.82[/tex]Which are the lower and upper limits, respectively.
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You consider buying a phone from one of two cell phone carriers. The table shows the total costs (in dollars) of the phone and service for different numbers of months at Carrier A. The total cost $y$y (in dollars) of the phone and x$x$x months of service at Carrier B is represented by the equation y is equal to 55 x plus 300$y=55x+300$y=55x+300 . Which carrier has the lower initial fee?
Answers
Answer:
Carrier B
Step-by-step explanation:
The linear equation that represents Carrier B is y=55x+300. it's a linear equation so 55 represent the monthly fee and 300 represents the initial fee. So the initial fee of carrier B is 300. In case of Carrier A, the total cost increases by $150 as months increases by 3. So The initial fee of Carrier A is 500-150=$350 . Hence, Carrier B has lower initial fee.
Find the set (An C)'.
U=(1, 2, 3, 4, 5, 6, 7)
A=(2, 4, 6, 7)
C= {1, 2, 3, 4, 5)
Answers
The set (A∩C)' is {1, 3, 5, 6, 7}.
The universal set is denoted by "U".U = {1, 2, 3, 4, 5, 6, 7}The set A is {2, 4, 6, 7}The set C is {1, 2, 3, 4, 5}A∩C stands for the set containing the common elements from set A and set C. The symbol "∩" stands for the intersection of the sets.A∩C = {2, 4}(A∩C)' stands for the complement of the set (A∩C).(A∩C)' is equal to the universal set minus the set (A∩C).(A∩C)' = U - (A∩C)(A∩C)' = {1, 2, 3, 4, 5, 6, 7} - {2, 4}(A∩C)' is {1, 3, 5, 6, 7}.Simply said, a set in mathematics is a grouping of different items. Any group of objects, such as a collection of numbers, days of the week, different kinds of cars, etc., can be included in a set. An element of the set is any component of the set. When writing a set, curly brackets are utilized. An extremely basic set might look somewhat like this. Set A = {1,2,3,4,5}. The components of a set can be represented using a variety of notations. Typically, sets are represented by a set builder form or a roster form.
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Look at BDC and ADB in the image below.
8
D
Which of the following is the best description for this pair of angles?
O complementary
Oright
O supplementary
O acute
Answers
Answer: right
Step-by-step explanation:
What’s the correct answer asap for brainlist
Answers
Deleterious means to do harm and the sentence used it as a name for a muscle.
A. Is correct, prodigious means grand or large, describing the dessert.
C. Is correct, ominous means threatening like the storm.
Micah had $76.10 in his bank account. He earned $18 washing his uncle’s car and then deposited the money in his account. What is his new account balance?
Answers
Answer:
$94.10
Step-by-step explanation:
$76.10 + $18.00 = $94.10
what is the length of segment LN?
Answers
Answer:
(b) 8 cm
Step-by-step explanation:
You want to know the length of segment LN with midpoint M and the length of LM given as 4 cm.
Segment additionThe segment addition theorem tells you the length of a line segment is equal to the sum of the lengths of its parts.
LN = LM +MN
MarkingsThe hash marks on segments LM and MN mean those segments have the same length. Then the sum is ...
LN = (4 cm) +(4 cm) = 8 cm
The length of segment LN is 8 cm.
Suppose that Nacho takes a multiple choice test. The test has 4 questions. Each question has 4 choices.
What is the probability that Nacho will get all 4 questions wrong?
Answers
The probability that Nacho will get all 4 questions wrong will be 0.3164.
How to illustrate the information?From the information, Nacho takes a multiple choice test, the test has 4 questions and each question has 4 choices.
The probability of getting the correct option is 1 out of 4 which is 0.25 and the incorrect option is 0.75.
Therefore, the probability that Nacho will get all 4 questions wrong will be:
= (0.75)⁴
= 0.3164
Therefore, the probability that Nacho will get all 4 questions wrong will be 0.3164.
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Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:
DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600
CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260
DEBIT: Cash Dividends: 1,000
CREDITS: Fees Earned: 75,000
DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.
Total Debits = 135,260; Total Credits = 135,260
Determine the amount of Net Income Adventure Travel will report for the year ending December 31, 20XX. Specify whole number.
Answers
The net income of Adventure Travel using its Adjusted Trial Balance for Year Ended December 31, 20XX, is $14,640
What is net income?
The net income is the excess of fees earned by Adventure Travel in the year ended over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense
total expense=32,800+16,800++3960+4000+2800
total expenses=60,360
fees earned=75,000
net income =fees earned-total expenses
net income=75,000-60,360
net income=$14,640
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Maya and Praisy are planting corns on a same farm. Maya plants 4 rows and Praisy plants 6 rows. If Mayas corns are ready to be picked in 8 weeks, how many weeks will it take Praisys corn to ready?
Answers
It will take 12 weeks for Praisys corn to be ready for picking.
We have been given that,
Maya plants corns In = 4 rows
Praisy plants corns in = 6 rows
Maya corns ready to be picked in = 8 weeks
We have to find the number of weeks will it take Praisys corn to be ready for picking.
To find we will use the unitary method that is,
4 rows = 8weeks
6 rows = 8/4*6 weeks
= 12 weeks
Thus 12 weeks will it take Praisys corn to be ready for picking.
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Question 4 options: If random variable X has a binomial distribution with n =10 and P(success) = p =0.6, find the probability that X is more than 3. (That is, find P(X>3)
Answers
The probability that X is more than 3 i.e. P(x > 3) is 0.945
How to find the probability that X is more than 3?The given parameters are
Number of experiments, n = 10Number of success, x > 3Probability of success, p = 0.6The probability that X is more than 3 can be calculated using the following equation
P(x <= 3) + P(x > 3) = 1
So, we have
P(x > 3) = 1 - P(x <= 3)
This gives
P(x > 3) = 1 - P(0) - P(1) - P(2) - P(3)
The individual probabilities are calculated using
P(x) = C(n,x) * p*x * (1 -p)^(n-x)
So, we have
P(0) = C(10,0) * 0.6^0 * (1 -0.6)^(10 - 0) = 0.0001
P(1) = C(10,1) * 0.6^1 * (1 -0.6)^(10 - 1) = 0.00157
P(2) = C(10,2) * 0.6^2 * (1 -0.6)^(10 - 2) = 0.01062
P(3) = C(10,3) * 0.6^3 * (1 -0.6)^(10 - 3) = 0.04247
So, we have
P(x > 3) = 1 - 0.0001 - 0.00157 - 0.01062 - 0.04247
Evaluate
P(x > 3) = 0.945
Hence, the probability that X is more than 3 is 0.945
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Determine the domain and the range of the relation. The domain for this relation is (0, 1, 3). The range for this relation is (-2, 1, 2)
Answers
The domain for this relation is {1,3} and the range for this relation is {2}.
According to the question, the given domain and range of the relation is as follows:
The domain for this relation is : {0, 1, 3}
The range for this relation is : {-2, 1, 2}
As per definition, the domain is the set of all possible values which a function take as an input.
Therefore, the domain for this relation is : {1, 3}
And the range for this relation is: {2}
Hence, the domain for this relation is {1,3} and the range for this relation is {2}.
What is domain and range of a function?
The domain is the set of all the possible values which a function can take as an input. And the range is also the set of paired values which represent the output of a function.
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At age 20, a person deposits $395 in a savings account paying 1% interest compounded quarterly. How much money will be in the account 60 years later, when he is 80 years old? Would his savings have tripled in that time?
Answers
The amount in the account after 60 years is $719.
His saving has not tripled after 60 years.
What is compound interest?
Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
We have,
Principal = $395
Rate = 1%
Number of years = 60
The amount compounded quarterly is given by:
A = P [ 1 + (R/4)/100 [tex]]^{4n}[/tex]
P = principal
R = rate
n = number of years
A = 395 [ 1 + 1/400 [tex]]^{4 \times{60}}[/tex]
A = 395 [ 1 + 1/400 [tex]]^{240}[/tex]
A = 395 [ 1 + 0.0025 [tex]]^{240}[/tex]
A = 395 [ 1.0025 [tex]]^{240}[/tex]
A = 395 x 1.8207549953165
A = 719.19625
A = $719
Thus the amount in the account after 60 years is $719.
His saving has not tripled after 60 years.
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TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a combined total of 129 MP3 and DVD players.
Let x be the number of MP3 players TechWiz sold last week. Write an expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week.
Answers
According to the given statement
Combined total profit (in dollars) TechWiz made from MP3 and DVD players last week is (7x+2268)
What is Total Profit?Total Profit is the sum of the following amounts (before taxes): I the amount received by Grantee pursuant to Issuer's repurchase of the Option (or any portion thereof) pursuant to Section 7; (x) the amount received by Grantee pursuant to Issuer's repurchase of Option Shares pursuant to Section 7 less (y) the Grantee's purchase price for such Option Shares; and (x) the net cash amounts received by Grantee pursuant.
According to the given value;
Number of Number of MP3 = X
Number of Number of DVD,= (126-x)
so
Profit from MP3 = 35 x
Profit from DVD = 18 (126-x)
Total = 35X+18 (126-x)
= 35x +2268-18x
= (7x+2268)
Hence,Combined total profit (in dollars) TechWiz made from MP3 and DVD players last week is (7x+2268).
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Find all the integer solutions of each system of intequalities. 12a - 37 > 0, 6a ≤ 42. Any right answer is named brainliest !
Answers
Answer:
For 12a - 37 > 0 answer is a > 37/12
For 6a ≤ 42 answer is a ≤ 7
Step-by-step explanation:
one positive number is 4 more than twice another.their product is 48
Answers
4x+2x^2 = 48
2x+x^2 = 24
x^2+2x-24 = 0
(x+6)(x-4) = 0
x = -6,4
positive number: x = 4
A grocery store sells a bag of 4 oranges for $1.04. If Jace spent $2.34 on oranges, how many did he buy?
Answers
Answer: 9 oranges
Step-by-step explanation:1.04/4=0.26
1 orange =0.26
2.34/0.26=9 oranges
Answer:
$2.86
Step-by-step explanation:
1.04 divided by 4 is 0.26 per orange. So 0.26 times 11 is 2.86
Please give brainliest
ASAP!!!!!!!!!!!!!!!!!!!!! 40 points!!!Create your own division problem and show how to use the Remainder Theorem to determine whether a binomial is a factor of a polynomial function.
Answers
Because the remainder is 0, then the binomial x + 3 is a factor of the polynomial (-3)^2 + 5(-3) + 6
What is a division problem?A division problem is an expression or an equation that involves the quotients of numbers or polynomials
How to create the division problem?To create the division problem, we make use of the following expression
(x^2 + 5x + 6)/(x + 3)
Using the remainder theorem, we have
Dividend = x^2 + 5x + 6
Divisor = x + 3
Set the divisor to 0,
So, we have
x + 3 = 0
This gives
x = -3
Substitute x = -3 in the dividend to get the remainder
So, we have
Remainder = (-3)^2 + 5(-3) + 6
Evaluate
Remainder = 0
Because the remainder is 0, then the binomial x + 3 is a factor of the polynomial (-3)^2 + 5(-3) + 6
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please help
please hury
Answers
The relation that is a function is relation (b)
How to determine the relation that is a function?The ordered pairs in the option represent the given parameters
For a relation (i.e. the ordered pairs) to be a function, the following must be true:
Each y value on the ordered pair must have exactly one x value
i.e. no x value must point to the different y value
Having said that the relation that is a function is relation (b)
Hence, the the relation that is a function is relation (b)2
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Find the missing numbers 2, 1, 0, ?, ?,.....
Answers
Answer:
Step-by-step explanation:
It's just a countdown sequence
2 1 0 -1 -2 ....
-1,-2
Pls 5 star
interval notation, and domain and range
Answers
The domain and the range of the graph in interval notation are (-∝, ∝) and [-3, ∝) respectively
What is the domain and the range of a function?The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.
How to determine the domain and the range of the function?The graph represents the given parameter
Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph
On the graph, we can see that:
The x values extend indefinitely on the graph;
This means that the domain is (-∝, ∝)
While y values start from -3 and increases up
This means that the range is [-3, ∝)
Hence, the domain and the range of the function in interval notation are (-∝, ∝) and [-3, ∝) respectively
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Késhaun conducted an experiment using a toy car and ramps of various
heights. He measured the distance, in centimeters (cm), the toy car
traveled from the end of the ramp. He also recorded the height, in
centimeters (cm), of the ramp. He found that the toy car traveled 64 cm
when the ramp height was 15 cm. The toy car traveled 112 cm when the
ramp height was 26 cm.
Write the equation of the line, in standard form, where x represents the
ramp height, in cm, and y represents the distance, in cm, the toy car
travels.
Answers
Step-by-step explanation:
we have 2 points on the line :
(15, 64) and (26, 112)
the standard form I assume is the slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y-intercept (the y value when x = 0).
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
the direction does not matter, but when picking one for one coordinate difference calculation, we have to use the same direction for the other.
I prefer to go from left to right.
so, in our case here
x changes by +11 (from 15 to 26).
y changes by +48 (from 64 to 112).
the slope "a" is +48/+11 = 48/11
so, our equation looks already like this :
y = 48/11 x + b
now, we use any of our points to get b.
let's pick (15, 64) :
64 = 48/11 × 15 + b = 720/11 + b
704/11 = 720/11 + b
-16/11 = b
and our full equation is
y = 48/11 x - 16/11
or
y = 1/11 × (48x - 16/11)
or
y = 16/11 × (3x - 1)
Line J: y=2/3x + 1/2
Line k: y= 1/2x + 2/3
Line L : y= 2/3x + 3/2
Line m: y= 3/2x+ 1/2
These four lines have been graphed on the same coordinate grid. Which lines are parallel to each other?
A: j and m
B: k and L
C: k and m
D: j and L
Answers
2 lines that are parallel are (D) J and L.
What are lines?A line is an infinitely long object with no width, depth, or curvature in geometry. Lines are thus one-dimensional objects, even though they can exist in two, three, or higher dimensions. In everyday language, the term line can also refer to a line segment with two points denoting its ends. A line is a straight one-dimensional figure with no thickness that extends in both directions indefinitely.So, plot all 4 lines on the graph (refer to the graph attached below).
We can observe that line J is parallel to line L.Therefore, 2 lines that are parallel are (D) J and L.
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S Slitsnails are large mollusks that live in deep waters. They have been found in the range of elevations $e$ shown.
A photo shows elevations under water. The range of elevations extends from negative 100 feet to negative 2500 feet.
Write the compound inequality that represents this range.
Answers
The range could be written in inequality form will be:
-2500 ≤ x ≤ -100.
Living in the deep sea are slitsnails. It is assumed that they inhabit depths ranging from 100 to 2500 feet.
Let x represents the distance between the water and the surface.
The depth will decrease as we sink further into the water.
Therefore, the depth could range from 100 to 2500 feet.
The maximum depth is 2500 feet, and the lowest depth should be 100 feet.
So, the range could be expressed as follows in inequality form:
-2500 ≤ x ≤ -100.
Hence the required compound inequality is framed.
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Which Are the correct answers A B C D?
Answers
Answer:
A. You can write the number as a Ratio of two entegers
D. You know what the next number is
the length of a rectangular sign is 12ft less than twice its width. Its permiteter is 114ft. What is the length and the width
Answers
X=42
Width is 42 ft
Length is 30 ft
